Scipedia: Documents published in 2020

Relación entre el Trastorno por Déficit de Atención e Hiperactividad y síntomas afectivos en estudiantes universitarios de un programa de Medicina de Manizales Caldas

Sandra Cañón — Sun, 10 May 2020 21:14:02 +0200

Introduction: Previous studies have reported high comorbidity between ADHD and anxiety and depressive spectrum disorders, however, few studies have been carried out on the subject in young university students. The present study evaluated the relationship between ADHD and the presence of depressive and anxious symptoms in university students from a medicine program in Manizales.

Materials and methods: Observational, analytical, cross-sectional research. Sample: 362 university students from a medical program. Instruments used: CAGE questionnaire, Beck's depression and anxiety scale, DSM-5 checklist for ADHD.

Results: Average age of 20.32 years. Of the total population 3.3% of a history of ADHD, of which 1.9% of treatment received. 56.36% symptoms current inattentive symptoms, 4.4% impulsive and hyperactive symptoms and 4.4% combined subtype. The absence of depressive symptoms according to the Beck scale is associated with symptoms of absence of inactive symptoms (Pvalor = 0.000), impulsive and hyperactive symptoms (Pvalor = 0.000) and mixed symptoms according to DMS-5 (Pvalor = 0.000). As the severity of depressive symptoms increases, inattentive symptoms, impulsive and hyperactive symptoms, and DSM-5 mixed symptoms increase (Pvalor = 0.000). A significant association was found between the presence of anxious symptoms and inattentive, impulsive, hyperactive and mixed symptoms according to the DSM-5 (Pvalor = 0.000).

Conclusions: ADHD symptoms are associated with the presence of anxious symptoms and depressive symptoms in university students of a medical program

Virtual Laboratories as a Strategy for Teaching Improvement in Math Sciences and Engineering in Bolivia

Francisco J. Triveno Vargas — Sun, 10 May 2020 15:38:05 +0200

STEM education is a strategy based on four disciplines (science, technology, engineering and mathematics), integrated in an innovative interdisciplinary approach. Although, the concept of STEM education is more relevant today, the discussion of a teaching model with special attention in the four subjects aforementioned began in the early 2000s. Taking into account this context, the strategy presented in this paper has been disseminated in Bolivia's main universities for the last five years. A country that has not yet managed to associate basic disciplines such as calculus, matrix algebra, and/or differential equations to solve problems of an applicative nature, that is, to establish the link between theory and practice. To establish the connection, it is necessary to deduce differential equations associated with practical problems; solve these equations with numerical methods, appeal to the simulation concept to later introduce programming languages like ''Python/VPython'' to build virtual laboratories. The classical problem addressed for this purpose is the satellite of two degrees of freedom.

Mechanical evaluation of a fire retardant through-thickness reinforced sandwich structure for marine applications

Anthony Comer — Fri, 08 May 2020 22:59:02 +0200

One of the main restrictions in adopting polymer composite materials for primary and secondary structural applications in marine vessels over 50 meters in length is concerns regarding fire retardancy and also a lack of design guidelines in general. The aim of this study is to evaluate the edgewise compression strength and core-shear strength of a fire retardant sandwich structure reinforced with through thickness composite ‘bridges’ under ambient conditions. These properties are important for structural components subjected to in-plane loads such as bulkheads. Core shear strength of the through-thickness reinforced sandwich far exceeded non-reinforced sandwich. However, edgewise compression strength and stiffness of the reinforced case was found to be similar to the unreinforced case.

Crack-path field and strain-injection techniques in computational modeling of propagating material failure

María Jesús Samper — Fri, 08 May 2020 15:50:28 +0200

The work presents two new numerical techniques devised for modeling propagating material failure, i.e. cracks in fracture mechanics or slip-lines in soil mechanics. The first one is termed crack-path-field technique and is conceived for the identification of the path of those cracks, or slip-lines, represented by strain-localization based solutions of the material failure problem. The second one is termed strain-injection, and consists of a procedure to insert, during specific stages of the simulation and in selected areas of the domain of analysis, goal oriented specific strain fields via mixed finite element formulations. In the approach, a first injection, of elemental constant strain modes (CSM) in quadrilaterals, is used, in combination of the crack-path-field technique, for obtaining reliable information that anticipates the position of the crack-path. Based on this information, in a subsequent stage, a discontinuous displacement mode (DDM) is efficiently injected, ensuring the required continuity of the crack-path across sides of contiguous elements. Combination of both techniques results in an efficient and robust procedure based on the staggered resolution of the crack-path-field and the mechanical failure problems. It provides the classical advantages of the "intra-elemental" methods for capturing complex propagating displacement discontinuities in coarse meshes, as E-FEM or X-FEM methods, with the non-code-invasive character of the crack-path-field technique. Numerical representative simulations of a wide range of benchmarks, in terms of the type of material and the failure problem, show the broad applicability, accuracy and robustness of the proposed methodology. The finite element code used for the simulations is open-source and available at http://www.cimne.com/compdesmat/.

PFEM-based modeling of industrial granular flows

María Jesús Samper — Fri, 08 May 2020 15:44:07 +0200

The potential of numerical methods for the solution and optimization of industrial granular flows problems is widely accepted by the industries of this field, the challenge being to promote effectively their industrial practice. In this paper, we attempt to make an exploratory step in this regard by using a numerical model based on continuous mechanics and on the so-called Particle Finite Element Method (PFEM). This goal is achieved by focusing two specific industrial applications in mining industry and pellet manufacturing: silo discharge and calculation of power draw in tumbling mills. Both examples are representative of variations on the granular material mechanical response—varying from a stagnant configuration to a flow condition. The silo discharge is validated using the experimental data, collected on a full-scale flat bottomed cylindrical silo. The simulation is conducted with the aim of characterizing and understanding the correlation between flow patterns and pressures for concentric discharges. In the second example, the potential of PFEM as a numerical tool to track the positions of the particles inside the drum is analyzed. Pressures and wall pressures distribution are also studied. The power draw is also computed and validated against experiments in which the power is plotted in terms of the rotational speed of the drum.

Computational modeling of high-performance steel fiber reinforced concrete using a micromorphic approach

María Jesús Samper — Fri, 08 May 2020 15:35:41 +0200

A finite element methodology for simulating the failure of high performance fiber reinforced concrete composites (HPFRC), with arbitrarily oriented short fibers, is presented. The composite material model is based on a micromorphic approach. Using the framework provided by this theory, the body configuration space is described through two kinematical descriptors. At the structural level, the displacement field represents the standard kinematical descriptor. Additionally, a morphological kinematical descriptor, the micromorphic field, is introduced. It describes the fiber–matrix relative displacement, or slipping mechanism of the bond, observed at the mesoscale level. In the first part of this paper, we summarize the model formulation of the micromorphic approach presented in a previous work by the authors. In the second part, and as the main contribution of the paper, we address specific issues related to the numerical aspects involved in the computational implementation of the model. The developed numerical procedure is based on a mixed finite element technique. The number of dofs per node changes according with the number of fiber bundles simulated in the composite. Then, a specific solution scheme is proposed to solve the variable number of unknowns in the discrete model. The HPFRC composite model takes into account the important effects produced by concrete fracture. A procedure for simulating quasi-brittle fracture is introduced into the model and is described in the paper. The present numerical methodology is assessed by simulating a selected set of experimental tests which proves its viability and accuracy to capture a number of mechanical phenomenon interacting at the macro- and mesoscale and leading to failure of HPFRC composites.

A micromorphic model for steel fiber reinforced concrete

María Jesús Samper — Fri, 08 May 2020 15:29:41 +0200

A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented. The formulation can be considered as a two scale approach, in which the macroscopic model, at the structural level, takes into account the mesostructural phenomenon associated with the fiber-matrix interface bond/slip process. This phenomenon is contemplated by including, in the macroscopic description, a micromorphic field representing the relative fiber-cement displacement. Then, the theoretical framework, from which the governing equations of the problem are derived, can be assimilated to a specific case of the Material Multifield Theory. The balance equation derived for this model, connecting the micro stresses with the micromorphic forces, has a physical meaning related with the fiber-matrix bond slip mechanism. Differently to previous procedures in the literature, addressed to model fiber reinforced composites, where this equation has been added as an additional independent ingredient of the methodology, in the present approach it arises as a natural result derived from the multifield theory. Every component of the composite is defined with a specific free energy and constitutive relation. The mixture theory is adopted to define the overall free energy of the composite, which is assumed to be homogeneously constituted, in the sense that every infinitesimal volume is occupied by all the components in a proportion given by the corresponding volume fraction. The numerical model is assessed by means of a selected set of experiments that prove the viability of the present approach. A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented. The formulation can be considered as a two scale approach, in which the macroscopic model, at the structural level, takes into account the mesostructural phenomenon associated with the fiber–matrix interface bond/slip process. This phenomenon is contemplated by including, in the macroscopic description, a micromorphic field representing the relative fiber–cement displacement. Then, the theoretical framework, from which the governing equations of the problem are derived, can be assimilated to a specific case of the material multifield theory. The balance equation derived for this model, connecting the micro stresses with the micromorphic forces, has a physical meaning related with the fiber–matrix bond slip mechanism. Differently to previous procedures in the literature, addressed to model fiber reinforced composites, where this equation has been added as an additional independent ingredient of the methodology, in the present approach it arises as a natural result derived from the multifield theory. Every component of the composite is defined with a specific free energy and constitutive relation. The mixture theory is adopted to define the overall free energy of the composite, which is assumed to be homogeneously constituted, in the sense that every infinitesimal volume is occupied by all the components in a proportion given by the corresponding volume fraction. The numerical model is assessed by means of a selected set of experiments that prove the viability of the present approach

Strain localization, strong discontinuities and material fracture: matches and mismatches

María Jesús Samper — Fri, 08 May 2020 15:20:49 +0200

The work focuses on the connections of strain localization modeling of material failure and discrete fracture mechanics. It is an attempt to give an answer to the old question of whether the finite element solutions of material failure problems based on strain localization techniques, using standard continuum stress–strain constitutive models equipped with strain softening, have physical sense as solutions of de-cohesive fracture mechanics problems. Based on some well-established links of the Continuum Strong Discontinuity Approach (CSDA) to material failure and cohesive fracture mechanics, some objective indicators are proposed to assess the quality of strain localization results. These indicators are simply derived on the basis of the inelastic strain distribution provided by the strain localization solutions and the direction of propagation of the localization band. They can be computed without knowledge of the exact fracture mechanics solution of the problem, and used as error indicators in a large variety of material failure situations. The proposed indicators are assessed, by means of their application to evaluation of a number of strain localization solutions of benchmark problems. Issues as the influence of the mesh structure and alignment, type of constitutive model and considered finite element techniques are examined. On the light of the obtained results, classical flaws in strain localization solutions, as mesh bias dependence and stress-locking are reinterpreted

On the contact domain method: a comparison of penalty and Lagrange multiplier implementations

María Jesús Samper — Fri, 08 May 2020 14:55:14 +0200

This work focuses on the assessment of the relative performance of the so-called contact domain method, using either the Lagrange multiplier or the penalty strategies. The mathematical formulation of the contact domain method and the imposition of the contact constraints using a stabilized Lagrange multiplier method are taken from the seminal work (as cited later), whereas the penalty based implementation is firstly described here. Although both methods result into equivalent formulations, except for the difference in the constraint imposition strategy, in the Lagrange multiplier method the constraints are enforced using a stabilized formulation based on an interior penalty method, which results into a different estimation of the contact forces compared to the penalty method. Several numerical examples are solved to assess certain numerical intricacies of the two implementations. The results show that both methods perform similarly as one increases the value of the penalty parameter or decreases the value of the stabilization factor (in case of the Lagrange multiplier method). However there seems to exist a clear advantage in using the Lagrange multiplier based strategy in a few critical situations, where the penalty method fails to produce convincing results due to excessive penetration.

A finite strain, finite band method for modeling ductile fracture

María Jesús Samper — Fri, 08 May 2020 14:07:54 +0200

We present a finite deformation generalization of the finite thickness embedded discontinuity formulation presented in our previous paper [A.E. Huespe, A. Needleman, J. Oliver, P.J. Sánchez, A finite thickness band method for ductile fracture analysis, Int. J. Plasticity 25 (2009) 2349–2365]. In this framework the transition from a weak discontinuity to a strong discontinuity can occur using a single constitutive relation which is of importance in a range of applications, in particular ductile fracture, where localization typically precedes the creation of new free surface. An embedded weak discontinuity is introduced when the loss of ellipticity condition is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. The methodology is illustrated through several example problems emphasizing finite deformation effects including the development of a cup-cone failure in round bar tension

Finite element modelling of ejection cracks in powder metallurgy die compaction processes: case study

María Jesús Samper — Fri, 08 May 2020 13:56:09 +0200

To date, the modelling of crack formation during the ejection stage in powder metallurgy die compaction processes has fallen outside the scope of conventional finite element studies on this process. In this paper, we attempt to make an exploratory step in this regard by presenting a case study that exemplifies how crack simulations can be harnessed to solve real powder metallurgy manufacturing problems. The part subjected to the study is a multilevel adapter whose design to production process proved problematic to the manufacturer, to the point that simplifications in the geometry of the part were to be made. The goal here is, through finite element simulations, to clarify the reasons behind the difficulties in ejecting free crack compacts, to understand the connection of such difficulties with the geometry modifications introduced in the design and to make recommendations on the prevention of similar problems in other situations

A robust approach to model densification and crack formation in powder compaction processes

María Jesús Samper — Fri, 08 May 2020 13:07:00 +0200

This paper deals with the question of how to efficiently integrate a constitutive model that describes the densification of powders and the potential formation of cracks in Powder Metallurgy (P/M) cold compaction processes. The analyzed model is a large strain, elastoplastic model of the Drucker–Prager/Cap type, refined to cover also the prediction of crack formation, and featuring non-conventional elements such as a density-dependent Von Mises yield surface; a parabolic plastic potential function for the Drucker–Prager envelope; and a softening law whose softening modulus is dependent on the level of densification. The employed integration procedure is a non-conventional hybrid or IMPLicit–EXplicit (IMPL-EX) scheme, whose essence is to solve explicitly for some variables and implicitly for others, with the peculiarity of the ‘explicit’ variables being but extrapolated values of the same quantities computed, at previous time steps, by means of a fully implicit scheme. The return-mapping equations stemming from this implicit scheme are solved using an unconditionally convergent, fractional step method-based iterative procedure. The performance of the IMPL-EX integration algorithm is critically assessed in two different situations: the densification of a cylindrical specimen, and the fracture process in a diametral compression test. Results obtained show conclusively that the proposed hybrid integration strategy offers an efficient solution to the trade-off between robustness and computational time requirements

On the proper characterization of tooling motions and initial conditions in powder die compaction modeling

María Jesús Samper — Fri, 08 May 2020 12:59:51 +0200

The present paper is concerned with the finite element modeling of Powder Metallurgy (P/M) cold die compaction process. Rather than on material constitutive theories or on numerical algorithmic issues, attention is confined exclusively on an scarcely addressed issue in the P/M modeling literature: the proper characterization of the boundary (tooling motions) and initial conditions of the problem. A case study of the compaction of an axially symmetric multilevel adapter in an advanced CNC press machine is used to convey the relevance of the accurate representation of these input data in the quality of model predictions. It is shown that unawareness or deliberate simplification of apparently insignificant details in this respect may cause errors far overshadowing those introduced by deficiencies in either the constitutive model or in the corresponding algorithmic solution procedure. The discussion of this case study serves also to provide useful modeling guidelines; illustrate frequent difficulties, as the unavailability of some information when guessing starting conditions; and reveal subtle, yet relevant for modeling purposes, technical details of advanced CNC press machines.

Flow regime analyses during the filling stage in powder metallurgy processes: experimental study and numerical modelling

María Jesús Samper — Fri, 08 May 2020 12:02:26 +0200

Experimental and numerical studies of powder flow during the die filling stage in powder metallurgy cold compaction processes are presented. An experimental setting consisting of a horizontal pneumatically activated shoe, a vertical die and high-speed video system has been designed. The experiments show the existence of three flow regimes: continuous, transitory and discrete, which are identified in terms of the particle size, the morphology and the speed of the shoe. In the continuous regime the powder flows in a progressive manner but in the discrete one some perturbations appear as a consequence of a shear band formation that forms discrete avalanches. A numerical model, based on a ratedependent constitutive model, via a flow formulation, and in the framework of the particle finite element method (PFEM) is also proposed. For the purpose of this study, the use of the PFEM assumes that the powder can be modelled as a continuous medium. The model, provided with the corresponding characterisation of the parameters, is able to capture the two fundamental phenomena observed during the filling process: (1) the irreversibility of most of the deformation experienced by the material and (2) the quick dissipation of the potential gravitatory energy of the granular system through the inter-particle friction processes, modelled by the plastic dissipation associated with the material model. Experimental and numerical results have been compared in order to study the viability of the proposed model

Simulación numérica del proceso de fractura en concreto reforzado mediante la metodología de discontinuidades fuertes de continuo. Parte II: Aplicación a páneles sometidos a cortante

María Jesús Samper — Fri, 08 May 2020 11:31:03 +0200

En este trabajo se presentan los resultados de la simulación numérica del proceso de fractura en páneles de concreto reforzado sometidos a cortante, utilizando un modelo basado en la metodología de discontinuidades fuertes de continuo (CSDA) y la teoría de mezclas. La CSDA describe la localzación de la deformación y la formación de una discontinuidad asociada con la aparición de una fisura. En cambio, la teoría de mezclas representa el comportamiento de un material compuesto, constituido por una matriz de concreto simple y uno o dos paquetes de barras largas de acero de refuerzo. El comportamiento del concreto simple y el acero se representan mediante un modelo de daño bidimensional y un modelo de plasticidad unidimensional, respectivamente. El modelo se implementa en el método de los elementos finitos considerando estado plano de esfuerzos, deformaciones infinitesimales y cargas estáticas. Se simularon tres páneles reforzados en una o en dos direcciones, los cuales estaban y sometidos principalmente a fuerzas cortantes. Los resultados de la simulación numérica, como la respuesta estructural y el patrón de fisuración, fueron satisfactorios. // The numerical simulation results of the fracture process in reinforced concrete shear panels are presented in this work. The simulation used a model based on the continuum strong discontinuity approach (CSDA) and mixing theory. CSDA describes strain localization and formation of discontinuity associated with the appearance of a crack. On the other hand, mixing theory represents composite material behaviour which is formed by a simple concrete matrix and one or two bundles of long reinforcement bars. The behaviour of simple concrete and steel is represented by a two-dimensional damage model and one-dimensional plasticity model, respectively. The model has been implemented in the finite element method which considers plane stress, infinitesimal strain and static loads. Three panels are simulated, reinforced in one or two ways; they are mainly subjected to shear forces. The numerical simulation results as well as structural response and cracking patterns were satisfactory.

Simulación numérica del proceso de fractura en concreto reforzado mediante la metodología de discontinuidades fuertes de continuo. Parte I: formulación

María Jesús Samper — Fri, 08 May 2020 11:24:40 +0200

En general, las estructuras de concreto reforzado como vigas, columnas y muros están conformadas por entramados complejos de barras de acero embebidas en una matriz de concreto, las cuales exhiben múltiples fisuras ante la aplicación de cargas externas elevadas. Este artículo presenta la formulación de un modelo numérico cuyo objetivo es describir el proceso de fractura en elementos de concreto reforzado a partir de la fracción volumétrica del concreto y del acero. El modelo utiliza un campo enriquecido de la deformación para describir la formación y propagación de fisuras en un material compuesto, tal como lo establecen la metodología de discontinuidades fuertes de continuo y la teoría de mezclas. El material compuesto está constituido por una matriz de concreto y uno o dos paquetes de barras de acero ortogonales entre sí. El acero y el concreto se representan con modelos de plasticidad unidimensional y de daño escalar con tracción y compresión diferenciada, respectivamente. La acción pasador y los efectos del deslizamiento entre las barras y la matriz, se describen con modelos adicionales que relacionan el esfuerzo y la deformación de los materiales componentes. Finalmente, se concluye que el modelo propuesto se puede implementar con facilidad en el método de los elementos finitos, dado que permanecen muchas características del procedimiento numérico no lineal convencional. Asimismo, el modelo permite analizar el problema en la escala macroscópica, lo cual elude la construcción de mallas de elementos finitos de cada material componente y de sus efectos de interacción, reduciendo así el costo computacional. // Reinforced concrete structures generally refers to beams, columns and walls which are constituted by complex lattices of steel bars embedded in a concrete matrix, exhibiting multiple cracks due to high external loads. This paper presents the formulation of a numerical model aimed at describing the fracture process in reinforced concrete, from the volumetric ratio of concrete and steel. Crack formation and propagation in a composite material is described in the model by an enhanced strain field, such as that established in the continuum strong discontinuity approach and mixture theory. The composite material is constituted by a concrete matrix and one or two steel bar orthogonal packages. The steel and concrete are represented by a one-dimensional plasticity model and a scalar damage model having different tension and compression strength, respectively. The dowel action and the bond-slip effects between the bars and the matrix are described with additional models relating component material stress and strain. It is concluded that the proposed model can easily be implemented in the finite element method, due to several conventional nonlinear numerical process characteristics which remain. The model would also allow the problem to be analysed at macroscopic scale, thereby avoiding a finite element mesh having to be constructed for each component material and its interaction effects and reducing computational costs

Mesoscopic model to simulate the mechanical behavior of reinforced concrete members affected by corrosion

María Jesús Samper — Fri, 08 May 2020 11:07:01 +0200

In this contribution, a finite element methodology devised to simulate the structural deterioration of corroded reinforced concrete members is presented. The proposed numerical strategy has the ability to reproduce many of the well-known (undesirable) mechanical effects induced by corrosion processes in the embedded steel bars, as for example: expansion of the reinforcements due to the corrosion product accumulation, damage and cracking patterns distribution in the surrounding concrete, degradation of steel–concrete bond stress transfer, net area reduction in the reinforcements and, mainly, the influence of all these mentioned mechanisms on the structural load carrying capacity predictions.

At the numerical level, each component of the RC structure is represented by means of a suitable FE formulation. For the concrete, a cohesive model based on the Continuum Strong Discontinuity Approach (CSDA) is used. Steel bars are modeled by means of an elasto-plastic constitutive relation. The interface is simulated using contact-friction elements, with the friction degradation as a function of the degree of corrosion attack. Two different (and coupled) mesoscopic analyzes are considered in order to describe the main physical phenomena that govern the problem: (i) an analysis at the cross section level and (ii) an analysis at the structural member level.

The resultant mechanical model can be used to simulate generalized reinforcement corrosion. Experimental and previous numerical results, obtained from the available literature, are used to validate the proposed strategy

Numerical modeling of crack formation in powder forming processes

María Jesús Samper — Fri, 08 May 2020 10:56:08 +0200

This paper presents a constitutive model describing the mechanical behavior of metal powders during (uniaxial) cold die compaction processes, placing special emphasis on the modeling of cracks formed during the ejection stage. The constitutive relationships are derived within the general framework of rate-independent, isotropic, finite strain elastoplasticity. The yield condition is determined by three surfaces intersecting non-smoothly in stress space, namely, an elliptical cap and the classical Von Mises and Drucker–Prager yield surfaces. The distinct irreversible processes are described in terms of two internal variables: an internal hardening variable, associated with accumulated compressive (plastic) strains, and an internal softening variable, linked with accumulated (plastic) shear strains. Motivated by both numerical and physical reasons, a parabolic plastic potential function is introduced to characterize the plastic flow on the linear Drucker–Prager failure surface. A thermodynamically consistent calibration procedure is employed to relate the softening modulus to fracture energy values obtained experimentally on Distaloy AE powder specimens. The predictive capability of the constitutive model is checked by simulating three representative cases: a diametral compression test, the ejection of an over-densified thin cylindrical part and the compaction of an axially symmetric multilevel part in an advanced CNC press machine. These simulations demonstrate the ability of the model to detect evidence of macroscopic cracks, clarify and provide reasons for the formation of such cracks, and evaluate, at least qualitatively, the influence of variations in the input variables on their propagation through the green compact

A 3D Frictionless Contact Domain Method for Large Deformation Problems

María Jesús Samper — Fri, 08 May 2020 09:52:17 +0200

This work describes a three-dimensional contact domain method for large deformation frictionless contact problems. Theoretical basis and numerical aspects of this specific contact method are given in [Oliver, Hartmann, Cante, Weyler and Hernández (2009)] and [Hartmann, Oliver, Weyler, Cante and Hernández (2009)] for two-dimensional, large deformation frictional contact problems. In this method, in contrast to many other contact formulations, the necessary contact constraints are formulated on a so-called contact domain, which can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. This contact domain has the same dimension as the contacting bodies. It will be endowed with a displacement field, interpolated from the displacements at the contact surfaces and will be subdivided into a non-overlapping set of contact patches, where the contact constraints will be applied. For the enforcement of these contact constraints a stabilized Lagrange multiplier method is used, which allows the condensation of the introduced Lagrange multipliers, leading to a purely displacement driven problem.

On the numerical resolution of the discontinuous material bifurcation problem

María Jesús Samper — Thu, 07 May 2020 17:11:56 +0200

The work focuses on the numerical resolution of the discontinuous material bifurcation problem as a relevant ingredient in computational material failure mechanics. The problem consists of finding the conditions for the strain localization onset in terms of the so-called bifurcation time, localization directions and localization modes. A numerical algorithm, based on the iterative resolution of a coupled eigenvalue problem in terms of the localization tensor, is proposed for such purpose. The algorithm is shown to be always convergent to the exact solution for the symmetric case (major and minor symmetries of the tangent constitutive operator). In the unsymmetric case (only minor symmetries), the solution is no longer exact, although it is shown that using the symmetric part of the localization tensor in the proposed algorithms provides enough accurate solutions for most of cases. Numerical examples illustrate the benefits of the proposed methodology in terms of accuracy and savings in the computational cost associated with the problem.

A contact domain method for large deformation frictional contact problems. Part 2: Numerical aspects

María Jesús Samper — Thu, 07 May 2020 16:59:30 +0200

This second part of the work describes the numerical aspects of the developed contact domain method for large deformation frictional contact problems. The theoretical basis of this contact method is detailed in the first part of this work. Starting from this, the present contribution focuses on describing important algorithmic details that go along with the finite element implementation for two-dimensional problems. Important aspects are the construction of the contact domain mesh, via a constraint Delaunay triangulation, the linearization of the discretized contact contributions and some important technical aspects about the extrapolation procedure used for the predictive active set strategy. Finally a set of numerical examples is presented to demonstrate the performance of the developed contact strategy. Demanding static and dynamic contact problems in the context of large deformations, including frictional effects as well as self contact, show the wide applicability and the robustness of the proposed method

A finite thickness band method for ductile fracture analysis

María Jesús Samper — Thu, 07 May 2020 16:27:46 +0200

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thickness

A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

María Jesús Samper — Thu, 07 May 2020 16:17:04 +0200

In the first part of this work, the theoretical basis of a frictional contact domain method for two-dimensional large deformation problems is presented. Most of the existing contact formulations impose the contact constraints on the boundary of one of the contacting bodies, which necessitates the projection of certain quantities from one contacting surface onto the other. In this work, the contact constraints are formulated on a so-called contact domain, which has the same dimension as the contacting bodies. This contact domain can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. The introduced contact domain is subdivided into a non-overlapping set of patches and is endowed with a displacement field, interpolated from the displacements at the contact surfaces. This leads to a contact formulation that is based on dimensionless, strain-like measures for the normal and tangential gaps and that exactly passes the contact patch test. In addition, the contact constraints are enforced using a stabilized Lagrange multiplier formulation based on an interior penalty method (Nitsche method). This allows the condensation of the introduced Lagrange multipliers and leads to a purely displacement driven problem. An active set strategy, based on the concept of effective gaps as entities suitable for smooth extrapolation, is used for determining the active normal stick and slip patches of the contact domain.

A mixture theory based method for three-dimensional modeling of reinforced concrete members with embedded crack finite elements

María Jesús Samper — Thu, 07 May 2020 16:03:40 +0200

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

On some topics for the numerical simulation of ductile fracture

María Jesús Samper — Thu, 07 May 2020 15:57:29 +0200

In this work, we analyze some aspects of the macroscopic Gurson–Tvergaard–Needleman (GTN) constitutive model when it is addressed to solve ductile fracture problems by means of numerical simulations: (i) The analytical solutions of the material discontinuous bifurcation problem is performed. Closed and exact formulas are obtained. The so determined critical conditions and the developed strain localization mode are afterward studied and compared in crack growth problems. Even when this methodology of analysis is rather standard at the present, the conclusions drawn from this study differ significantly from that obtained with a similar analysis in quasi-brittle fracture problems. (ii) A new very robust numerical integration method for the GTN model, namely the Impl–Ex Method, is proposed. It is a low computational cost algorithm, equivalent to a linear problem per each integration step, with a reasonable precision for engineering purposes. Its accuracy and convergence rate is assessed by means of an error study applied to a ductile fracture test simulation. (iii) A detailed analysis of a plane strain ductile crack growth problem is performed in a material containing two size-scale of voids. In the analysis, particular attention is given to the mesh size dependence and to the coalescence of the larger void

An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems

María Jesús Samper — Thu, 07 May 2020 15:45:42 +0200

An implicit/explicit integration scheme for non-linear constitutive models is presented. It aims at providing additional computability to those solid mechanics problems were robustness is an important issue, i.e. material failure models equipped with strain softening, soft materials, contact-friction models, etc., although it can also provide important advantages, in terms of computational cost, with respect to purely implicit integration schemes. The proposed scheme is presented based on general families of constitutive models (continuum damage and elasto-plasticity) and its properties, in terms of robustness and accuracy, are analytically derived and computationally assessed by means of numerical simulations. An adaptive time stepping algorithm, based on a priori control of the committed error and the application of the proposed scheme to contact/friction interfaces are also presented.

Three-dimensional analysis of reinforced concrete members via embedded discontinuity finite elements

María Jesús Samper — Thu, 07 May 2020 14:52:59 +0200

This paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuous Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fiber bundles (rebars) oriented in different directions embedded in it. The effects of the rebars are provided by phenomenological constitutive models designed to reproduce the axial non-linear behavior, as well as bond-slip and dowel action. This paper is focused on the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the methodology.

Two-dimensional modelling of material failure in reinforced concrete by means of a continuum strong discontinuity approach

María Jesús Samper — Thu, 07 May 2020 14:25:37 +0200

The paper presents a new methodology to model material failure, in two-dimensional reinforced concrete members, using the Continuum Strong Discontinuity Approach (CSDA). The mixture theory is used as the methodological approach to model reinforced concrete as a composite material, constituted by a plain concrete matrix reinforced with two embedded orthogonal long fiber bundles (rebars). Matrix failure is modeled on the basis of a continuum damage model, equipped with strain softening, whereas the rebars effects are modeled by means of phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond–slip and dowel effects. The proposed methodology extends the fundamental ingredients of the standard Strong Discontinuity Approach, and the embedded discontinuity finite element formulations, in homogeneous materials, to matrix/fiber composite materials, as reinforced concrete. The specific aspects of the material failure modeling for those composites are also addressed. A number of available experimental tests are reproduced in order to illustrate the feasibility of the proposed methodology

Vulnerability analysis of large concrete dams using the continuum strong discontinuity approach and neural networks

María Jesús Samper — Thu, 07 May 2020 14:13:50 +0200

Probabilistic analysis is an emerging field of structural engineering which is very significant in structures of great importance like dams, nuclear reactors etc. In this work a Neural Networks (NN) based Monte Carlo Simulation (MCS) procedure is proposed for the vulnerability analysis of large concrete dams, in conjunction with a non-linear finite element analysis for the prediction of the bearing capacity of the Dam using the Continuum Strong Discontinuity Approach. The use of NN was motivated by the approximate concepts inherent in vulnerability analysis and the time consuming repeated analyses required for MCS. The Rprop algorithm is implemented for training the NN utilizing available information generated from selected non-linear analyses. The trained NN is then used in the context of a MCS procedure to compute the peak load of the structure due to different sets of basic random variables leading to close prediction of the probability of failure. This way it is made possible to obtain rigorous estimates of the probability of failure and the fragility curves for the Scalere (Italy) dam for various predefined damage levels and various flood scenarios. The uncertain properties (modeled as random variables) considered, for both test examples, are the Young’s modulus, the Poisson’s ratio, the tensile strength and the specific fracture energy of the concrete.

Stabilized mixed finite elements with embedded discontinuities for shear bans modelling

María Jesús Samper — Thu, 07 May 2020 14:01:00 +0200

A stabilized mixed finite element with elemental embedded strong discontinuities for shear band modeling is presented. The discrete constitutive model, representing the cohesive forces acting across the shear band, is derived from a rate-independent J(2) plastic continuum material model with strain softening, by using a projection-type procedure determined by the Continuum-Strong Discontinuity Approach. The numerical examples emphasize the increase of the numerical solution accuracy obtained with the present strategy as compared with alternative procedures using linear triangles

Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach

María Jesús Samper — Thu, 07 May 2020 13:49:51 +0200

Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness, two remedies are proposed: (1) the use of an specific symmetric version of the elementary enriched (E-FEM) finite element with embedded discontinuities and (2) a new implicit–explicit integration of the internal variable, in the constitutive model, which renders the tangent constitutive algorithmic operator positive definite and constant. The combination of both developments leads to finite element formulations with constant, in the time step, and non-singular tangent structural stiffness, allowing dramatic improvements in terms of robustness and computational costs. After assessing the convergence and stability properties of the new strategies, three-dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures

A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM

María Jesús Samper — Thu, 07 May 2020 13:14:03 +0200

A comparative study on finite elements for capturing strong discontinuities by means of elemental (E-FEM) or nodal enrichments (X-FEM) is presented. Based on the same constitutive model (continuum damage) and linear elements (triangles and tetrahedra) optimized implementations of both types of enrichments in the same non-linear code are tested for a representative set of 2D and 3D crack propagation examples. It is shown that both methods provide the same qualitative and quantitative results for enough refined meshes. For the performed tests, E-FEM exhibited, in general, a higher accuracy, mostly for coarse meshes, whereas, convergence rate with mesh refinement, which is super-linear, showed slightly higher for X-FEM. As for the computational costs for single crack modelling X-FEM showed, depending on the case, from 1.1 to about 2.5 times more expensive than E-FEM. For multiple cracks, the computational cost of E-FEM keeps constant, whereas the cost associated to X-FEM increases linearly with the number of modelled cracks

On the fracture models determined by the continuum-strong discontinuity approach

María Jesús Samper — Thu, 07 May 2020 13:08:00 +0200

The paper focuses on the Continuum Strong Discontinuity Approach (CSDA) to fracture mechanics, and the traction-separation cohesive laws induced from continuum dissipative models as their projections onto the failure interface. They are compared with the cohesive laws commonly used for the fracture simulation in quasi-brittle materials, typically concrete. Emphasis is placed in the analysis of the mechanical stress-strain states induced by the CSDA into the fracture process zone: first when the damage mechanism is initiated and, after, when the cohesive model determines the crack response. The influence of the material parameters, particularly the fracture energy and the initial continuum softening modulus, in the obtained phenomenological responses is also analyzed. Representative numerical solutions of fracture problems are finally presented

On numerical simulation of powder compaction process: powder transfer modelling and characterisation

María Jesús Samper — Thu, 07 May 2020 12:39:29 +0200

A numerical model for the powder transfer stage in powder metallurgy cold compaction processes, and the corresponding material characterisation procedure, are proposed. They have been designed on the basis of the following requirements: robust and consistent computational mechanics ingredients, reliability of the obtained results for practical processes in powder metallurgy and industrial viability in the sense that characterisation of any mixture doesn't require either much effort or much time of the enduser. The starting point is a previously developed numerical model for powder compaction, formulated in terms of the large plastic deformation theory, which requires calibration of four parameters controlling the evolution of the yield surface. This calibration, which had been successfully carried out in the past in a range of moderate to high densities, is now extended to very low densities in order to make numerical simulations able to deal with compaction processes involving relevant powder transfer stages. To circumvent the difficulties inherent to direct measurements of very low powder densities, a simple apparatus, which allows studying the powder motion in the chamber, has been designed to provide an indirect way of calibration. On this basis, a set of calibration experiments is proposed. The proposed methodology appears to be simple and industrially viable. Although in the work it is applied to the specific constitutive model used by the authors, it also appears available for other families of constitutive models for powder compaction. As a relevant result, this would allow the same constitutive model to be used, via only the appropriated material characterisation, for simulation of densification in powder transfer stages as well as in pure compaction stages

Theoretical and computational issues in modelling material failure in strong discontinuity scenarios

María Jesús Samper — Thu, 07 May 2020 11:25:00 +0200

The paper deals with several aspects related to numerical modelling of material failure in strong discontinuity settings: (a) the onset and development of local material failure in terms of continuum constitutive models equipped with strain softening. Closed forms formulas for the solutions of the discontinuous material bifurcation problem are given for a class of those models; (b) finite elements with embedded discontinuities: nodal and elemental enrichments families are formulated in the continuum strong discontinuity approach (CSDA); (c) instability treatment: a discrete viscous perturbation method at the failure surfaces is presented as a way to substantially improve the robustness of the numerical simulations

Continuum approach to material failure in strong discontinuity settings

María Jesús Samper — Thu, 07 May 2020 11:11:53 +0200

The paper focuses the numerical modelling of material failure in a strong discontinuity setting using a continuum format. Displacement discontinuities, like fractures, cracks, slip lines, etc., are modelled in a strong discontinuity approach, enriched by a transition from weak to strong discontinuities to get an appropriate representation of the fracture process zone. The introduction of the strong discontinuity kinematics automatically projects any standard dissipative constitutive model, equipped with strain softening, into a discrete traction–separation law that is fulfilled at the discontinuity interface. Numerical issues like a global discontinuity tracking algorithm via a heat conduction-like problem are also presented. Some representative numerical simulations illustrate the performance of the presented approach

Computational modeling of cracking of concrete in strong discontinuity settings

María Jesús Samper — Thu, 07 May 2020 11:03:10 +0200

The paper is devoted to present the Continuum Strong Discontinuity Approach (CSDA) and to examine its capabilities for modeling cracking of concrete. After introducing the main ingredients of the CSDA, an isotropic continuum damage model, which distinguishes tension and compression states, is used to implicitly induce a projected traction separation-law that rules the cracking phenomena. Criteria for onset and propagation of material failure and specific finite elements with embedded discontinuities are also briefly sketched. Finally, some representative numerical simulations of cracking, in plain and reinforced concrete specimens, using the CSDA are presented.

On the strong discontinuity approach in finite deformation settings

María Jesús Samper — Thu, 07 May 2020 10:55:31 +0200

Taking the strong discontinuity approach as a framework for modelling displacement discontinuities and strain localization phenomena, this work extends previous results in infinitesimal strain settings to finite deformation scenarios. By means of the strong discontinuity analysis, and taking isotropic damage models as target continuum (stress–strain) constitutive equation, projected discrete (tractions–displacement jumps) constitutive models are derived, together with the strong discontinuity conditions that restrict the stress states at the discontinuous regime. A variable bandwidth model, to automatically induce those strong discontinuity conditions, and a discontinuous bifurcation procedure, to determine the initiation and propagation of the discontinuity, are briefly sketched. The large strain counterpart of a non-symmetric finite element with embedded discontinuities, frequently considered in the strong discontinuity approach for infinitesimal strains, is then presented. Finally, some numerical experiments display the theoretical issues, and emphasize the role of the large strain kinematics in the obtained results

A study on finite elements for capturing strong discontinuities

María Jesús Samper — Thu, 07 May 2020 10:46:39 +0200

The work focuses on the presently existing families of finite elements with embedded discontinuities and explores the possibilities of obtaining symmetric statically consistent finite elements that alleviate the stress-locking problem. For this purpose, mixed (reduced integration) and assumed enhanced strain techniques are applied to the basic symmetric four-noded element. Numerical simulations show the effectiveness of the proposed measures.

From continuum mechanics to fracture mechanics: the strong discontinuity approach

María Jesús Samper — Thu, 07 May 2020 09:39:26 +0200

The paper deals with the strong discontinuity approach and shows the links with the decohesive fracture mechanics provided by that approach. On the basis of 1D continuum damage models it is shown that, by introducing some few ingredients like the strong discontinuity kinematics, discrete constitutive models (traction vs. displacement jumps) are automatically induced. For the general 2D–3D cases it is shown that the weak discontinuity concept is an additional ingredient, necessary in order to fulfill the strong discontinuity conditions, which allows to establish additional links with the fracture process zone concept. Also classical fracture mechanics properties as the fracture energy are related to the continuum model properties in a straightforward manner

On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations

María Jesús Samper — Wed, 06 May 2020 17:23:50 +0200

On the basis of continuum constitutive models (stress vs. strain), the introduction of strong discontinuity kinematics (considering jumps in the displacement fields across a discontinuity interface) induces projected discrete constitutive models (traction-displacement jumps) in a consistent manner. Therefore, this projection provides possible links between the classical continuum strain-localization analysis and the non-linear (decohesive) fracture mechanics techniques. The strong discontinuity analysis shows that (bandwidth based) regularization of the hardening/softening parameter is the crucial modification to be done on the continuum model to achieve such a projection, and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format. The methodology is illustrated on the basis of two classical families of non-linear constitutive models (scalar continuum damage and elasto-plasticity) for which the corresponding discrete constitutive models and the strong discontinuity conditions are derived

Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part II: Numerical simulation

María Jesús Samper — Wed, 06 May 2020 16:43:12 +0200

On the basis of the strong discontinuity analysis of standard local stress–strain constitutive equations, a finite element framework for the simulation of strong discontinuities, which belongs to the family of assumed enhanced strain methods, is presented. Taking the standard linear triangle as the underlying element, an additional incompatible mode leads to the formulation of an enriched strain field which is shown to be able to appropriately capture strong discontinuities. The presented numerical simulations show that mesh size and mesh alignment dependencies can be completely removed

Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part I: fundamentals

María Jesús Samper — Wed, 06 May 2020 16:27:25 +0200

The paper addresses some fundamental aspects about the use of standard constitutive equations to model strong discontinuities (cracks, shear bands, slip lines, etc.) in solid mechanics analyzes. The strong discontinuity analysis is introduced as a basic tool to derive a general framework, in which different families of constitutive equations can be considered, that allows to extract some outstanding aspects of the intended analysis. In particular, a link between continuum and discrete approaches to the strain localization phenomena is obtained. Applications to standard continuum damage and elastoplastic constitutive equations are presented. Relevant aspects to be considered in the numerical simulation of the problem (tackled in Part 2 of the work) are also presented

Continuum modelling of strong discontinuities in solid mechanics using damage models

María Jesús Samper — Wed, 06 May 2020 16:18:34 +0200

Numerical simulation of strong discontinuities by using standard stress-strain constitutive equations including strain-softening is addressed. The concept of strong discontinuity analysis is introduced and driven, as a matter of example, into a standard continuum damage model. Then, the relevant features that make the constitutive equation compatible with the appearance of strong discontinuities are extracted. Those features are used in the design of a specific finite element approach to the strong discontinuity problem which is placed in the framework of the assumed enhanced strain methods. Numerical simulations show that mesh size and mesh alignment dependencies, typical of some continuum approaches, can be removed.

An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids

María Jesús Samper — Wed, 06 May 2020 15:37:52 +0200

Ket qualitative features of solutions exhibiting strong discontinuities in rate-independent inelastic solids are identified and exploited in the design of a new class of finite element approximations. The analysis shows that the softening law must be re-interpreted in a distributional sense for the continuum solutions to make mathematical sense and provides a precise physical interpretation to the softening modulus. These results are verified by numerical simulations employing a regularized discontinuous finite element method which circumvent the strong mesh-dependence exhibited by conventional methods, without resorting to viscosity or introducing additional ad-hoc parameters. The analysis is extended to a new class of anisotropic rate-independent damage models for brittle materials

A consistent characteristic length for smeared cracking models

María Jesús Samper — Wed, 06 May 2020 14:20:54 +0200

A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two-dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.

SIMP-ALL: a generalized SIMP method based on the topological derivative concept

María Jesús Samper — Wed, 06 May 2020 13:13:05 +0200

Topology optimization has emerged in the last years as a promising research fieldwith a wide range of applications. One of the most successful approaches, theSIMP method, is based on regularizing the problem and proposing a penaliza-tion interpolation function. In this work, we propose an alternative interpolationfunction, the SIMP-ALL method that is based on the topological derivative con-cept. First, we show the strong relation in plane linear elasticity between theHashin-Shtrikman (H-S) bounds and the topological derivative, providing anew interpretation of the last one. Then, we show that the SIMP-ALL interpo-lation remains always in between the H-S bounds regardless the materials tobe interpolated. This result allows us to interpret intermediate values as realmicrostructures. Finally, we verify numerically this result and we show the con-venience of the proposed SIMP-ALL interpolation for obtaining auto-penalizedoptimal design in a wider range of cases. A MATLAB code of the SIMP-ALLinterpolation function is also provided

A consistent relaxation of optimal design problems for coupling shape and topological derivatives

María Jesús Samper — Wed, 06 May 2020 11:59:27 +0200

In this article, we introduce and analyze a general procedure for approximating a ‘black and white’ shape and topology optimization problem with a density optimization problem, allowing for the presence of ‘grayscale’ regions. Our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem, and on an interpolation scheme, which endows the intermediate density regions with fictitious material properties. Under mild hypotheses on the smoothing operator and on the interpolation scheme, we prove that the features of the approximate density optimization problem (material properties, objective function, etc.) converge to their exact counterparts as the smoothing parameter vanishes. In particular, the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact objective. These results shed new light on the connections between these two different notions of sensitivities for functions of the domain, and they give rise to different numerical algorithms which are illustrated by several experiments

Two-scale topology optimization in computational material design: an integrated approach

María Jesús Samper — Wed, 06 May 2020 11:08:41 +0200

The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the non-conforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya–Babuška–Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.

Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

María Jesús Samper — Wed, 06 May 2020 10:30:54 +0200

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy

Topological sensitivity analysis in heterogeneous anisotropic elasticity problem: theoretical and computational aspects

María Jesús Samper — Wed, 06 May 2020 10:03:36 +0200

The topological sensitivity analysis for the heterogeneous and anisotropic elasticity problem in two-dimensions is performed in this work. The main result of the paper is an analytical closed-form of the topological derivative for the total potential energy of the problem. This derivative displays the sensitivity of the cost functional (the energy in this case) when a small singular perturbation is introduced in an arbitrary point of the domain. In this case, we consider a small disc with a completely different elastic material. Full mathematical justification for the derived formula, and derivations of precise estimates for the remainders of the topological asymptotic expansion are provided. Finally, the influence of the heterogeneity and anisotropy is shown through some numerical examples of structural topology optimization

Computing the Wave-Kernel Matrix Functions

María Jesús Samper — Tue, 05 May 2020 16:10:16 +0200

We derive an algorithm for computing the wave-kernel functions cosh \surd A and sinhc\surd A for an arbitrary square matrix A, where sinhcz = sinh(z)/z. The algorithm is based on Pad\'e approximation and the use of double angle formulas. We show that the backward error of any approximation to cosh \surd A can be explicitly expressed in terms of a hypergeometric function. To bound the backward error we derive and exploit a new bound for \| Ak\| 1/k that is sharper than one previously obtained by Al-Mohy and Higham [SIAM J. Matrix Anal. Appl., 31 (2009), pp. 970-- 989]. The amount of scaling and the degree of the Pad\'e approximant are chosen to minimize the computational cost subject to achieving backward stability for cosh \surd A in exact arithmetic. Numerical experiments show that the algorithm behaves in a forward stable manner in floating-point arithmetic and is superior in this respect to the general purpose Schur--Parlett algorithm applied to these functions.

Energy efficiency, indoor thermal comfort and influence of user habits in retrofitting of social housing blocks: Case study in the Metropolitan Area of Barcelona

María Jesús Samper — Tue, 05 May 2020 15:38:13 +0200

The Mediterranean seaside cities like the towns placed at the Metropolitan region of Barcelona have soft winters and variable summers which change from hot to very hot. Historically, summer comfort in dwellings was reached through passive cooling strategies and reducing the activity of the citizens during the hottest hours (the siesta). At the beginning of the 20th and until the building regulations appear, most of the constructed buildings were designed without any energy saving criteria, therefore, summer and winter passive were scrapped.

L'ús actual de l'energia solar. Aplicacions als edificis

María Jesús Samper — Tue, 05 May 2020 15:26:25 +0200

Monitoring and modelling energy efficiency of municipal public buildings: case study in Catalonia region

María Jesús Samper — Tue, 05 May 2020 15:10:21 +0200

Energy efficiency benchmarking can be used to monitor changes in the overall efficiency of buildings. Benchmarking models, based on energy efficiency indicators, are valuable tools for both public and private stakeholders because they allow an improvement in the building energy management. For the last decade, some governments have used these tools to define their building regulations (Santamouris, M., et al., 2005. Energy performance of residential buildings book. UK: James and James/Earthscan. ISBN: 1-902916-49-2, Chung, W., Hui, Y.V., and Miu Lam, Y., 2006. Benchmarking the energy efficiency of commercial buildings. Applied Energy, 83, 1–14). This paper tries to go further, integrating a benchmarking and a modelling process, into the same energy efficiency analysis. The connections between the energy use intensities (EUIs) and the characteristic building factors are modelled using neural network techniques. The process is divided into two stages: the data acquisition stage and the benchmarking and modelling stage. The benchmarking and modelling stage is focused on the adjustment of these EUIs within the climatic conditions (with a severity climate index method) and the development of a prediction model for calculating the relationship between these climate-adjusted EUIs and the significant factors of a building. In order to validate this methodology, an application to schools in Catalonia is presented. Additionally, the use of the artificial neural network (ANN) benchmark model for predicting potential energy savings from retrofit projects was evaluated. Some of the input variables were modified to reflect potential energy savings from a retrofit project, and the new input set was simulated with the ANN model. The preliminary results show that the developed ANN model can be used to predict energy savings from retrofit projects

Design methodology for low cost tubular digesters

María Jesús Samper — Tue, 05 May 2020 14:18:03 +0200

The aim of this paper is to present a novel, universal, methodology for the design of low cost tubular digesters. This method improves on the established methodology by avoiding assumptions that tend to reduce the final hydraulic retention time (HRT) of digesters once installed. This work recommends designing the digester using trench cross-sectional area and proposes an optimization of the trench dimensions with respect to the angle of the walls and the relationship between the length of the biogas bell and the top width of the trench. The influence of the biogas pressure is considered. A simple geometrical analysis is presented that, by parameterization, can be applied in a wide range of situations.

An outdoor Test Reference Environment for double skin applications of Building Integrated PhotoVoltaic Systems

María Jesús Samper — Tue, 05 May 2020 14:01:14 +0200

This article presents and discusses an outdoor Test Reference Environment (TRE) for double skin applications of Building Integrated PhotoVoltaic (BIPV) Systems.

From the experience gained during the past 20 years in several EC research projects, an experimental tested design for a common Test Reference Environment is proposed. This outdoor test set-up allows the assessment of experimental data for electrical and thermal performance evaluation of photovoltaic systems integrated as double skin applications in the building envelope. The specific design of the Test Reference Environment makes it possible to study in a harmonised way through electrical and thermal energy flow analysis, the impact of different materials for PV modules and construction design of building envelopes. The energy balance for BIPV double skin applications is presented as well.

The experimental data has been used for validation of modelling work by several academic groups which has resulted in an improved knowledge on the heat transfer, in particular the convective heat exchange coefficient for the specific double skin boundary conditions.

Modelling the heat dynamics of a monitored Test Reference Environment for Building Integrated Photovoltaic systems using stochastic differential equations

María Jesús Samper — Tue, 05 May 2020 13:41:31 +0200

This paper deals with grey-box modelling of the energy transfer of a double skin Building Integrated Photovoltaic (BIPV) system. Grey-box models are based on a combination of prior physical knowledge and statistics, which enable identification of the unknown parameters in the system and accurate prediction of the most influential variables. The experimental data originates from tests carried out with an air-based BIPV system installed in a Test Reference Environment. BIPV systems represent an interesting application for achieving the requirements of the EU EPBD Directive. Indeed, these systems could reduce the ventilation thermal losses of the building by pre-heating the fresh air. Furthermore, by decreasing PV module temperature, the ventilation air heat extraction can simultaneously increase electrical and thermal energy production of the building. A correct prediction of the PV module temperature and heat transfer coefficients is fundamental in order to improve the thermo-electrical production.

The considered grey-box models are composed of a set of continuous time stochastic differential equations, holding the physical description of the system, combined with a set of discrete time measurement equations, which represent the data driven part.

In the present work, both one-state and two-state non-linear grey-box models are considered. In order to validate the results, the residuals are analysed for white-noise properties.

Approaches to evaluate building energy performance from daily consumption data considering dynamic and solar gain effects

María Jesús Samper — Tue, 05 May 2020 13:29:56 +0200

A method for determining the total heat loss coefficient, the effective heat capacity and the net solar gain of a building is presented. The method uses a linear regressions approach based on daily energy consumption combined with readily available meteorological data.

The effective heat capacity of the building is evaluated by correlating the energy consumption and outdoor temperature changes from the previous day. The net solar gain of the building is assessed by analysing the data separated into groups by amount of daily solar irradiation. Corrected total heat loss coefficient is determined by explicitly including in the building's energy balance the accumulated heat and the solar gain.

The method has been applied to the analysis of nine public buildings in Spain. An improvement of the estimated heat loss coefficient due to the corrections is observed. The effective heat capacity normalised by the building area is shown to be a useful indicator of the building operation, detecting continuous or intermittent heating.

The estimated parameters in this study can enable specific benchmarking, detecting opportunities for energy savings and evaluating their potential. With the increasing implementation of smart metering technologies, the method is promising for application to the analysis of large building stocks.

Numerical analysis of the most appropriate heat transfer correlations for free ventilated double skin photovoltaic façades

María Jesús Samper — Tue, 05 May 2020 13:18:35 +0200

Double skin façades with photovoltaic integrated systems are building components which combine functions of the building envelope with electricity and thermal energy generation. The heat transfer modelling of these components, especially under free convection situations, raises a high complexity and is one of the main drawbacks for a massive dissemination of this technology. Many attempts to fill this gap have been undertaken and some mathematical correlations allowing evaluating average Nusselt numbers and air mass flow rate have been obtained in the last decades. However, very few studies faced a detailed analysis of the valid range of these mathematical expressions and of the restrictions entailed. This paper introduces a methodology to analyse the valid range of the existing mathematical correlations for the convective heat transfer coefficients and for the air mass flow rate in laminar and transition to turbulent free convection, and provides an evaluation of the effect of the asymmetry of the wall boundary conditions. A specific numerical code, based on a stabilized finite element formulation (FEM), is used to solve the incompressible Navier–Stokes equations within the air gap and to determine the accuracy of the existing heat transfer correlations. This evaluation was preceded by an extensive bibliographic research as well as a detailed validation of the physical and numerical hypothesis adopted in the finite element code.

Evaluation of a multi-stage guided search approach for the calibration of building energy simulation models

María Jesús Samper — Tue, 05 May 2020 12:48:22 +0200

This paper is focused on increasing the knowledge on methods for calibrating BES models and to get more insights of different approaches for the optimization of the calibration process. The paper will be centred in the evaluation of a multistage guided search approach. It defines an iterative optimization procedure which starts with the assignment of probabilistic density functions to the unknown parameters, followed by a random sampling and running batch of simulations. It then finishes with an iterative uncertainty and sensitivity analysis combined with a re-assignment of the ranges of variation of the strong parameters. The procedure converges when no new influencing parameters are found. This method is applied to a real case study consisting of an unoccupied office building located in Lleida (Spain). The measured indoor temperature has been used to determine the uncertainty and precision of the method. The effect of the size of the sampling, the number of iterations and the parameters of the global sensitivity method are analyzed in detail. The results of this paper exemplify the degree of accuracy of multistage guided search approaches, and illustrate the reasons how these analyses can contribute to the improvement of more refined calibration methods.

Development of a dynamic model for natural ventilated photovoltaic components and of a data driven approach to validate and identify the model parameters

María Jesús Samper — Tue, 05 May 2020 11:56:33 +0200

In the development of dynamic models for the energy performance evaluation of building integrated natural ventilated PV components there are still many open questions regarding the uncertainty of the estimated parameters of the models. Traditionally, the dynamic models for these complex components are derived from the heat transfer balance equations, and the unknown heat transfer coefficients (convection and radiation), the solar properties of the materials or the pressure coefficients for the air mass flow rate balance, are assigned based on literature or on manufacturer prescriptions. However, there is a lack of systematic methods able to validate the simulation outputs with the measured data, taking into consideration the uncertainty of the parameters and their effect over the results. This research is focused on the development of a dynamic simulation model for a PV ventilated component, and on the application of a data-driven iterative approach to identify the unknown parameters, to evaluate their influence in the simulation outputs and finally, to determine the deviations of the simulations outputs against the measured data. During the identification process, 43 unknown parameters are detected and 13 of them are categorized as strong parameters. The implemented data driven approach is able to achieve high goodness of fit with the measured data and it is recommended to analyses which aim at evaluating the influence of some component parameters or the thermal and electrical energy produced by these natural ventilated PV components.

Influencing factors in energy use of housing blocks: a new methodology, based on clustering and energy simulations, for decision making in energy refurbishment projects

María Jesús Samper — Tue, 05 May 2020 11:31:27 +0200

In recent years, big efforts have been dedicated to identify which are the factors with highest influence in the energy consumption of residential buildings. These factors include aspects such as weather dependence, user behaviour, socio-economic situation, type of the energy installations and typology of buildings. The high number of factors increases the complexity of analysis and leads to a lack of confidence in the results of the energy simulation analysis. This fact grows when we move one step up and perform global analysis of blocks of buildings. The aim of this study is to report a new methodology for the assessment of the energy performance of large groups of buildings when considering the real use of energy. We combine two clustering methods, Generative Topographic Mapping and k-means, to obtain reference dwellings that can be considered as representative of the different energy patterns and energy systems of the neighbourhood. Then, simulation of energy demand and indoor temperature against the monitored comfort conditions in a short period is performed to obtain end use load disaggregation. This methodology was applied in a district at Terrassa City (Spain), and six reference dwellings were selected. Results showed that the method was able to identify the main patterns and provide occupants with feasible recommendations so that they can make required decisions at neighbourhood level. Moreover, given that the proposed method is based on the comparison with similar buildings, it could motivate building occupants to implement community improvement actions, as well as to modify their behaviour.

Hidden Markov Models for indirect classification of occupant behaviour

María Jesús Samper — Tue, 05 May 2020 10:55:23 +0200

Even for similar residential buildings, a huge variability in the energy consumption can be observed. This variability is mainly due to the different behaviours of the occupants and this impacts the thermal (temperature setting, window opening, etc.) as well as the electrical (appliances, TV, computer, etc.) consumption.

It is very seldom to find direct observations of occupant presence and behaviour in residential buildings. However, given the increasing use of smart metering, the opportunity and potential for indirect observation and classification of occupants’ behaviour is possible. This paper focuses on the use of Hidden Markov Models (HMMs) to create methods for indirect observations and characterisation of occupant behaviour.

By applying homogeneous HMMs on the electricity consumption of fourteen apartments, three states describing the data were found suitable. The most likely sequence of states was determined (global decoding). From reconstruction of the states, dependencies like ambient air temperature were investigated. Combined with an occupant survey, this was used to classify/interpret the states as (1) absent or asleep, (2) home, medium consumption and (3) home, high consumption. From the global decoding, the average probability profiles with respect to time of day were investigated, and four distinct patterns of occupant behaviour were observed. Based on the initial results of the homogeneous HMMs and with the observed dependencies, time dependent HMMs (inhomogeneous HMMs) were developed, which improved forecasting. For both the homogeneous and inhomogeneous HMMs, indications of common parameters were observed, which suggests further development of the HMMs as population models.

Comparing time-series clustering approaches for individual electrical load patterns

María Jesús Samper — Tue, 05 May 2020 10:41:36 +0200

This work positions the task of grouping electricity load time series among the vast field of clustering, and highlights corresponding research issues. A selection of the most performant time-series clustering approaches from the signal processing community are compared on the same dataset, composed by domestic electricity load profiles from Spain. The cross-correlation-based distance of Paparrizos and Gravano (2015) is shown to provide the best trade-off between clustering accuracy and CPU times

Using matrix factorisation for the prediction of electrical quantities

María Jesús Samper — Tue, 05 May 2020 10:24:38 +0200

The prediction task is attracting more and more attention among the power system community. Accurate predictions of electrical quantities up to a few hours ahead (e.g. renewable production, electrical load etc.) are for instance crucial for distribution system operators to operate their network in the presence of a high share of renewables, or for energy producers to maximise their profits by optimising their portfolio management. In the literature, statistical approaches are usually proposed to predict electrical quantities. In the present study, the authors present a novel method based on matrix factorisation. The authors' approach is inspired by the literature on data mining and knowledge discovery and the methodologies involved in recommender systems. The idea is to transpose the problem of predicting ratings in a recommender system to a problem of forecasting electrical quantities in a power system. Preliminary results on a real wind speed dataset tend to show that the matrix factorisation model provides similar results than auto regressive integrated models in terms of accuracy (MAE and RMSE). The authors' approach is nevertheless highly scalable and can deal with noisy data (e.g. missing data).

Developing indicators to improve energy action plans in municipalities: An accounting framework based on the fund-flow model

María Jesús Samper — Tue, 05 May 2020 10:00:17 +0200

The main instrument used to implement the EU 2020 objectives at local level is the Covenant of Mayors, which fosters the development of Sustainable Energy Action Plans (SEAPs); these plans aim to reduce CO2 emissions by at least 20% by 2020. These action plans are linked to different municipal promotion tools, and a set of indicators has also been proposed to define and monitor the actions. In general, the adequacy of the main indicators used by the SEAPs is analysed, taking into consideration the representation of the urban system across all scales (city, neighbourhood and building) as well as whether the chosen indicators enable the analyst to consider the influence of human activities (i.e. hours of use) on energy consumption, within the system. In contrast, this paper proposes to apply the fund-flow model as an accounting framework that can be used to develop indicators for energy-efficient urban planning. The energy model behind these indicators was obtained using an innovative procedure for energy simulation which considers the isolated characteristics of the buildings (type of construction, occupation, interior comfort, type of energy system) as well as the interaction with the surrounding buildings (shadows, streets, geometry).The indicators proposed have been developed within the SEMANCO UE project, and we have taken into account their potential as criteria for identifying the most effective actions for energy planning on multilevel scales. An example in Manresa (Spain) is used to test the usability. Our results demonstrate that these indicators are suitable for use in decision-making processes in the field of urban planning and for performing coherent comparisons of actions between urban areas, cities, countries or regions.

EMPOWERING, a smart Big Data framework for sustainable electricity suppliers

María Jesús Samper — Tue, 05 May 2020 09:46:15 +0200

This paper presents the EMPOWERING project, a Big Data environment aimed at helping domestic customers to save electricity by managing their consumption positively. This is achieved by improving the information received about energy bills and offering online tools. The main contributions of EMPOWERING are the creation of a novel workflow in the electricity utility sector regarding the implementation of data analytics for their customers and the fast implementation of data-mining techniques in massive datasets within a Big Data platform to achieve scalability. The results obtained show that EMPOWERING can be of use for customers of electrical suppliers by changing their energy habits to decrease consumption and so increase environmental sustainability.

Experimental and numerical assessment of local resonance phenomena in 3D-printed acoustic metamaterials

María Jesús Samper — Mon, 04 May 2020 16:49:46 +0200

The so called Locally Resonant Acoustic Metamaterials (LRAM) are a new kind of artificially engineered materials capable of attenuating acoustic waves. As the name suggests, this phenomenon occurs in the vicinity of internal frequencies of the material structure, and can give rise to acoustic bandgaps. One possible way to achieve this is by considering periodic arrangements of a certain topology (unit cell), smaller in size than the characteristic wavelength. In this context, a computational model based on a homogenization framework has been developed from which one can obtain the aforementioned resonance frequencies for a given LRAM unit cell design in the sub-wavelength regime, which is suitable for low-frequency applications. Aiming at validating both the proposed numerical model and the local resonance phenomena responsible for the attenuation capabilities of such materials, a 3D-printed prototype consisting of a plate with a well selected LRAM unit cell design has been built and its acoustic response to normal incident waves in the range between 500 and 2000 Hz has been tested in an impedance tube. The results demonstrate the attenuating capabilities of the proposed design in the targeted frequency range for normal incident sound pressure waves and also establish the proposed formulation as the fundamental base for the computational design of 3D-printed LRAM-based structures

Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework (preprint)

María Jesús Samper — Mon, 04 May 2020 16:41:50 +0200

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the work

Computational design of locally resonant acoustic metamaterials

María Jesús Samper — Mon, 04 May 2020 16:37:50 +0200

The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable for acoustic insulation purposes. This fact has inspired the design of a new kind of lightweight acoustic insulation panels with the ability to attenuate noise sources in the low frequency range (below 5000 Hz) without requiring thick pieces of very dense materials. A design procedure based on different computational mechanics tools, namely, (1) a multiscale homogenization framework, (2) model order reduction strategies and (3) topological optimization procedures, is proposed. It aims at attenuating sound waves through the panel for a target set of resonance frequencies as well as maximizing the associated bandgaps. The resulting design’s performance is later studied by introducing viscoelastic properties in the coating phase, in order to both analyse their effects on the overall design and account for more realistic behaviour. The study displays the emerging field of Computational Material Design (CMD) as a computational mechanics area with enormous potential for the design of metamaterial-based industrial acoustic parts

Strain injection techniques for modeling 3D crack propagation

María Jesús Samper — Mon, 04 May 2020 16:23:17 +0200

This work presents some novel results obtained by using the strain injection techniques for modeling crack propagation in challenging 3D benchmark tests. The techniques were already tested and validated by static and dynamic simulations in 2D [1-4], so the main goal of this paper is to verify if the most important advantages of the method, low computational cost and independence of the results on the finite element mesh, are kept in 3D. The methodology, implemented in the finite element framework, consists essentially in injecting those elements that are going to capture the cracks with some enhanced strain modes for improving the performance of the elements for modeling propagating material failure

Strain-injection and crack-path field techniques for 3D crack-propagation modelling in quasi-brittle materials

María Jesús Samper — Mon, 04 May 2020 16:14:24 +0200

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012); Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014); Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016)] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016)]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenarios

A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling

María Jesús Samper — Mon, 04 May 2020 15:52:29 +0200

A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation

Computational material design for acoustic cloaking

María Jesús Samper — Mon, 04 May 2020 15:26:15 +0200

A topology optimization technique based on the topological derivative and the level set function is utilized to design/synthesize the micro-structure of a pentamode material for an acoustic cloaking device. The technique provides a micro-structure consisting of a honeycomb lattice composed of needle-like and joint members. The resulting metamaterial shows a highly anisotropic elastic response with effective properties displaying a ratio between bulk and shear moduli of almost 3 orders of magnitude. Furthermore, in accordance with previous works in the literature, it can be asserted that this kind of micro-structure can be realistically fabricated. The adoption of a topology optimization technique as a tool for the inverse design of metamaterials with applications to acoustic cloaking problems is one contribution of this paper. However, the most important achievement refers to the analysis and discussion revealing the key role of the external shape of the prescribed domain where the optimization problem is posed. The efficiency of the designed micro-structure is measured by comparing the scattering wave fields generated by acoustic plane waves impinging on bare and cloaked bodies

The domain interface method in non-conforming domain decomposition multifield problemsdomain decomposition multifield problems

María Jesús Samper — Mon, 04 May 2020 15:11:49 +0200

Vademecum-based approach to multi-scale topological material design

María Jesús Samper — Mon, 04 May 2020 14:50:32 +0200

The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques. The goal is then to minimize the structural (macro-scale) compliance by appropriately designing the material distribution (microstructure) at a lower scale (micro-scale), which, in turn, rules the mechanical properties of the material. The specific features of the proposed approach are: (1) The cost function to be optimized (structural stiffness) is defined at the macro-scale, whereas the design variables defining the micro-structural topology lie on the low scale. Therefore a coupled, two-scale (macro/micro), optimization problem is solved unlike the classical, single-scale, topological optimization problems. (2) To overcome the exorbitant computational cost stemming from the multiplicative character of the aforementioned multiscale approach, a specific strategy, based on the consultation of a discrete material catalog of micro-scale optimized topologies (Computational Vademecum) is used. The Computational Vademecum is computed in an offline process, which is performed only once for every constitutive-material, and it can be subsequently consulted as many times as desired in the online design process. This results into a large diminution of the resulting computational costs, which make affordable the proposed methodology for multiscale computational material design. Some representative examples assess the performance of the considered approach

Model Order Reduction in Computational multiscale fracture mechanics

María Jesús Samper — Mon, 04 May 2020 14:12:10 +0200

Nowadays, the model order reduction techniques have become an intensive research eld because of the increasing interest in the computational modeling of complex phenomena in multi-physic problems, and its conse- quent increment in high-computing demanding processes; it is well known that the availability of high-performance computing capacity is, in most of cases limited, therefore, the model order reduction becomes a novelty tool to overcome this paradigm, that represents an immediately challenge in our research community. In computational multiscale modeling for instance, in order to study the interaction between components, a di erent numerical model has to be solved in each scale, this feature increases radically the computational cost. We present a reduced model based on a multi-scale framework for numerical modeling of the structural failure of heterogeneous quasi-brittle materials using the Strong Discontinuity Approach (CSD). The model is assessed by application to cementitious materials. The Proper Orthogonal Decomposition (POD) and the Reduced Order Integration Cubature are the pro- posed techniques to develop the reduced model, these two techniques work together to reduce both, the complexity and computational time of the high-delity model, in our case the FE2 standard model

Strain injection techniques in dynamic fracture modeling

María Jesús Samper — Mon, 04 May 2020 14:03:53 +0200

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localization and strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite element formulation without an increase of the total number of degrees of freedom. Following the Continuum Strong Discontinuity Approach (CSDA), stress–strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to a wide number of continuum mechanics models. The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains. The combination of the above mentioned approaches is envisaged to avoid stress-locking and directional mesh bias phenomena. Dynamic simulations are performed increasing the loading rate up to the appearance of crack branching, and the variation in terms of failure modes is investigated as well as the influence of the strain injection together with the crack path field algorithm. Objectivity of the presented methodology with respect to the spatial and temporal discretization is analyzed in terms of the dissipated energy during the fracture process. The dissipation at the onset of branching is studied for different loading rate conditions and is linked to the experimental maximum velocity observed before branching takes place

The domain interface method: a general-purpose non-intrusive technique for non-conforming domain decomposition problems

María Jesús Samper — Mon, 04 May 2020 13:54:10 +0200

A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach.

Modeling tensile crack propagation in concrete gravity dams via crack-path-field and strain injection techniques

María Jesús Samper — Mon, 04 May 2020 13:45:51 +0200

This work investigates tensile crack propagation in concrete gravity dams by using some recently developed numerical techniques (crack-path field and strain injection techniques). The work carefully addresses aspects related to mesh independence, robustness and computational cost, which are the main issues in fracture modeling. The novel technique consists of a procedure to insert, in the selected domain areas, specific strain fields for enhancing the performance of the underlying finite elements in modeling fracture. Representative numerical simulations of concrete dams show the accuracy and robustness of the methodology

On micro-to-macro connections in domain decomposition multiscale methods

María Jesús Samper — Mon, 04 May 2020 13:40:39 +0200

Micro-to-macro connection techniques constitute a key ingredient in the formulation of multiscale strategies. In this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials. Particularly, these techniques are investigated in a domain decomposition strong coupling multiscale framework. The structural component under analysis is partitioned into a number of non-overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom-in technique. Mesh refinement is employed in the domains where crack coalescence and growth take place. The original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains. Standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links. The influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis

Multiscale domain decomposition analysis of quasi-brittle heterogeneous materials

María Jesús Samper — Mon, 04 May 2020 13:31:46 +0200

A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of nonlinear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the finite element tearing and interconnecting method, are used to partition the material in a number of non-overlapping domains and adaptive refinement is performed at those domains that are affected by damage processes. This refinement is performed in terms of material scale and finite element size. It is verified that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full fine-scale solution procedure.

Computational homogenization for multiscale crack modeling: implementational and computational aspects

María Jesús Samper — Mon, 04 May 2020 13:03:20 +0200

A computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the method.

Domain decomposition techniques for the efficient modeling of brittle heterogeneous materials

María Jesús Samper — Mon, 04 May 2020 12:45:35 +0200

This paper describes a computational tool for the efficient study of failure in brittle heterogeneous materials. By means of several examples, it is demonstrated that the proposed tool is adequate for the analysis of materials that show localized failure modes. This case is particular since the main non-linearities concentrate in a small area compared to the whole specimen. The use of the method is preferred when the mesoscopic structure plays a crucial role during failure processes and needs to be fully taken into account in order to accurately tackle damage growth and propagation in the material. The present strategy is based on a Domain decomposition technique. Its performance is improved by selectively processing inelastic regions and reducing the number of operations in the remaining elastic areas. A four point bending test and the fracturing of a heterogeneous concrete specimen are presented as illustrations. They demonstrate that computational costs can be significantly reduced when the proposed strategy is applied to damage analysis.

Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks

María Jesús Samper — Mon, 04 May 2020 12:05:38 +0200

The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction–separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro-sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method

On the existence of representative volumes for softening quasi-brittle materials: a failure zone averaging scheme

María Jesús Samper — Mon, 04 May 2020 11:31:04 +0200

The concept of the representative volume element (RVE) for softening materials is revised in this contribution. It is demonstrated by means of numerical simulations that there exists a sample which is statistically representative for quasi-brittle materials with random microstructure like concrete. This finding is an important ingredient for homogenization-based multiscale modelling of softening materials.

Increasing understanding and confidence in THM simulations of engineered barrier systems

María Jesús Samper — Mon, 04 May 2020 10:41:01 +0200

Previous studies on the modelling of coupled thermo-hydro-mechanical (THM) processes in bentonite-based engineered barrier systems (EBSs) showed the sensitivity of the output quantities to changes in the input parameters. To investigate the effects of uncertainties on the modelling results, to improve the understanding of the coupled processes active in the repository near field and to gain in-depth understanding of model uncertainties of different codes, a sensitivity analysis and code comparison of EBS simulations was performed within the Task Force on Engineered Barrier Systems. The analysis included variations in material parameter values, boundary and initial conditions, considered physical processes and model geometries, amounting to 60 different cases. This in-depth analysis helped evaluate the influence of parameter and conceptual uncertainties on the results of coupled THM simulations and to identify key parameters and processes. The cross-code comparison encouraged a fruitful exchange among modelling teams and led to very good agreements between the results of the different codes. Serving as a benchmark example for THM-coupled simulations of bentonite-based EBSs, the study helped increase the confidence in the modelling capabilities of several codes used for safety evaluations of repositories for spent fuel and high-level radioactive waste

Characterisation of the multi-scale fabric features of high plasticity clays

María Jesús Samper — Mon, 04 May 2020 10:26:57 +0200

An investigation of the microstructural features of a high-plasticity clay, in both its natural conditions and reconstituted in the laboratory, is described. Scanning electron microscopy is used here to characterise the fabric at different magnifications, while image processing of the micrographs delivers a quantitative assessment of the fabric orientation. The results of energy-dispersive X-ray spectroscopy and swelling tests, as reported in a previous study by the authors, are used to characterise the bonding nature and strength, as well as mercury intrusion porosimetry to investigate clay porosimetry. Despite their identical composition, the natural and the reconstituted clay have experienced different deposition and loading history, generating different microstructural features that are shown to underlie their differences in state. For both clays, one-dimensional (1D) compression to medium–high pressures is seen to determine a well-oriented medium magnification fabric. However, larger-scale observations and the corresponding image processing results reveal non-uniform local fabric features, hence making fabric characterisation dependent on the scale of analysis and bringing about the issue of identifying the clay micro-scale representative element volume relating to the clay macro-behaviour. The micro-REV is identified for the clays under study and its connection with the macro-behaviour characterised. The microstructural evolution induced by 1D compression to very high pressures is shown to concern mainly the clay porosity and porosimetry, the fabric orientation being steady, thus explaining the isotropic hardening observed in laboratory tests.

Discussion on 'Effects of particle breakage and stress reversal on the behaviour of sand around displacement piles'

María Jesús Samper — Mon, 04 May 2020 10:02:46 +0200

Micromechanical inspection of incremental behaviour of crushable soils

María Jesús Samper — Mon, 04 May 2020 09:49:53 +0200

In granular soils grain crushing reduces dilatancy and stress obliquity enhances crushability. These are well-supported specimen-scale experimental observations. In principle, those observations should reflect some peculiar micromechanism associated with crushing, but which is it? To answer that question the nature of crushing-induced particle-scale interactions is here investigated using an efficient DEM model of crushable soil. Microstructural measures such as the mechanical coordination number and fabric are examined while performing systematic stress probing on the triaxial plane. Numerical techniques such as parallel and the newly introduced sequential probing enable clear separation of the micromechanical mechanisms associated with crushing. Particle crushing is shown to reduce fabric anisotropy during incremental loading and to slow fabric change during continuous shearing. On the other hand, increased fabric anisotropy does take more particles closer to breakage. Shear-enhanced breakage appears then to be a natural consequence of shear-enhanced fabric anisotropy. The particle crushing model employed here makes crushing dependent only on particle and contact properties, without any pre-established influence of particle connectivity. That influence does not emerge, and it is shown how particle connectivity, per se, is not a good indicator of crushing likelihood

Conceptual uncertainties in modelling the interaction between engineered and natural barriers of nuclear waste repositories in crystalline rocks

María Jesús Samper — Thu, 30 Apr 2020 18:01:55 +0200

Nuclear waste disposal in geological formations relies on a multi-barrier concept that includes engineered components – which, in many cases, include a bentonite buffer surrounding waste packages – and the host rock. Contrasts in materials, together with gradients across the interface between the engineered and natural barriers, lead to complex interactions between these two subsystems. Numerical modelling, combined with monitoring and testing data, can be used to improve our overall understanding of rock–bentonite interactions and to predict the performance of this coupled system. Although established methods exist to examine the prediction uncertainties due to uncertainties in the input parameters, the impact of conceptual model decisions on the quantitative and qualitative modelling results is more difficult to assess. A Swedish Nuclear Fuel and Waste Management Company Task Force project facilitated such an assessment. In this project, 11 teams used different conceptualizations and modelling tools to analyse the Bentonite Rock Interaction Experiment (BRIE) conducted at the Äspö Hard Rock Laboratory in Sweden. The exercise showed that prior system understanding along with the features implemented in the available simulators affect the processes included in the conceptual model. For some of these features, sufficient characterization data are available to obtain defensible results and interpretations, whereas others are less supported. The exercise also helped to identify the conceptual uncertainties that led to different assessments of the relative importance of the engineered and natural barrier subsystems. The range of predicted bentonite wetting times encompassed by the ensemble results were considerably larger than the ranges derived from individual models. This is a consequence of conceptual uncertainties, demonstrating the relevance of using a multi-model approach involving alternative conceptualizations.

Standard penetration testing in a virtual calibration chamber

María Jesús Samper — Thu, 30 Apr 2020 17:47:41 +0200

The virtual calibration chamber technique, based on the discrete element method, is here applied to study the standard penetration test (SPT). A macro-element approach is used to represent a rod driven with an impact like those applied to perform SPT. The rod is driven into a chamber filled with a scaled discrete analogue of a quartz sand. The contact properties of the discrete analogue are calibrated simulating two low-pressure triaxial tests. The rod is driven changing input energy and controlling initial density and confinement stress. Energy-based blowcount normalization is shown to be effective. Results obtained are in good quantitative agreement with well-accepted experimentally-based relations between blowcount, density and overburden. It is also shown that the tip resistance measured under impact dynamic penetration conditions is close to that under constant velocity conditions, hence supporting recent proposals to relate CPT and SPT results

Sphericity measures of sand grains

María Jesús Samper — Thu, 30 Apr 2020 17:27:42 +0200

The sphericity of a grain should measure the similitude of its shape with that of a sphere. Sphericity is a shape descriptor of long-standing interest for sedimentology. Now it has gained also interest to facilitate discrete element modelling of granular materials. True sphericity was initially defined by a surface ratio that requires three-dimensional (3D) grain surface measurement. That kind of measurement has been practically impossible until recently and, as a consequence, a number of alternative 3D measures and 2D proxies were proposed. In this work we present results from a study of grain shape based on x-ray tomography of two different sand specimens, containing more than 110.000 particles altogether. Sphericity measures were systematically obtained for all grains. 2D proxy measures were also obtained in samples of oriented and not-oriented grains. It is shown that the 2D proxy best correlated with true sphericity is perimeter sphericity, whereas the traditional Krumbein-Sloss chart proxy is poorly correlated. 2D measures acquired through minor axis projection are more closely related to 3D measures than those acquired using random projections.

Clays in natural and engineered barriers for nuclear waste disposal

María Jesús Samper — Thu, 30 Apr 2020 16:50:04 +0200

Argillaceous rocks and expansive clays play a key role in many scenarios of the deep geological disposal of nuclear waste.

Grading evolution and critical state in a discrete numerical model of Fontainebleau sand

María Jesús Samper — Thu, 30 Apr 2020 16:37:07 +0200

Granular materials reach critical states upon shearing. The position and shape of a critical state line (CSL) in the compression plane are important for constitutive models, interpretation of in situ tests and liquefaction analyses. It is not fully clear how grain crushing may affect the identification and uniqueness of the CSL in granular soils. Discrete-element simulations are used here to establish the relation between breakage-induced grading evolution and the CSL position in the compression plane. An efficient model of particle breakage is applied to perform a large number of tests, in which grading evolution is continuously tracked using a grading index. Using both previous and new experimental results, the discrete-element model is calibrated and validated to represent Fontainebleau sand, a quartz sand. The results obtained show that, when breakage is present, the inclusion of a grading index in the description of critical states is advantageous. This can be simply done using the critical state plane (CSP) concept. A CSP is obtained for Fontainebleau sand.

Numerical simulation of the undrained stability of slopes in anisotropic fine-grained soils

María Jesús Samper — Thu, 30 Apr 2020 16:26:24 +0200

The undrained stability of slopes in anisotropic fine-grained soils is studied in this paper using the finite element method (FEM). A constitutive model is presented, able to account for the observed variation of undrained strength with loading direction. The model is able to encompass the different strength distributions observed in normally, slightly overconsolidated and heavily overconsolidated soils. A series of stability analyses have been performed to explore the effect of the type of undrained strength anisotropy on the stability and failure mechanisms of slopes of different inclinations. In addition, a real case study of the failure of an underwater slope is analysed with the numerical approach presented. It suggests that, by considering undrained strength anisotropy, the failure can be satisfactorily explained.

SDMT-based numerical analyses of deep excavation in soft soil

María Jesús Samper — Thu, 30 Apr 2020 16:19:38 +0200

The paper explores the application of conventional (DMT) and seismic (SDMT) dilatometer tests to an important case of deep excavation design. The work presents finite-element analyses simulating a deep excavation close to Barcelona (Spain). A thick layer of soft interbedded sandy and silty soils made characterization based on laboratory testing very difficult. SDMT offered an alternative for estimating the soil stiffness and its stress-strain dependency. Numerical results and high-quality monitoring data show quite close agreement for most phases of the construction process, supporting the use of seismic dilatometer tests in numerical analyses of deep excavations. The paper also indicates the importance of incorporating stiffness data at low strains. FE analyses involved some uncertainties derived from the presence of jet-grouting soil treatments. On this point, a parametric study illustrates the effects of different modeling approaches.

Nonlocal plasticity modelling of strain localisation in stiff clays

María Jesús Samper — Thu, 30 Apr 2020 15:52:08 +0200

The paper addresses the numerical simulation of strain localisation in stiff clays that exhibit softening behaviour. An elastoplastic constitutive model developed to incorporate key features of stiff clay behaviour is described first. A non-local formulation is then introduced for the regularisation of the analysis of localisation. A series of analyses were conducted to explore relevant aspects of the numerical simulation of localisation. A 3D analysis was also performed to assess the suitability of the approach presented for 3D applications. Finally, application to the simulation of a laboratory test on Beaucaire marl results in an excellent reproduction of experimental observations.

On the choice of stress–strain variables for unsaturated soils and its effect on plastic flow

María Jesús Samper — Thu, 30 Apr 2020 15:43:52 +0200

The net stress plus suction and the average skeleton stress plus modified suction are two alternative sets of energetically consistent stress variables for modelling the hydro-mechanical behaviour of unsaturated soils. When used in conjunction with their work-conjugate strains, both sets of stress variables correctly calculate the first-order term of the hydro-mechanical work input into a soil element subjected to infinitesimal changes of deformation and water content. They therefore also correctly calculate the increment of internal energy along a given stress–strain path, that is the integral of the first-order term of the infinitesimal work input. This paper shows, however, that the above two sets of stress variables lead to different values of the second-order term of the hydro-mechanical work input. They are therefore no longer equivalent with respect to other aspects of material behaviour governed by the second-order work such as the flow rule of elasto-plastic models. The flow rule assumes the normality between plastic strains and equipotential surfaces defined in the conjugate stress–strain space. This normality is however lost when an elasto-plastic model originally formulated in terms of net stress plus suction is recast in terms of average skeleton stress plus modified suction (or vice versa) by means of standard mapping relationships between stress variables. To restore normality in both stress spaces, it is necessary to impose specific forms of elastic and plastic behaviour.