Scipedia: Journal Papers

On the constitutive modeling of coupled thermomechanical phase-change problems

María Jesús Samper — Wed, 03 Apr 2019 11:24:22 +0200

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.

Simulation of Construction of RCC Dams. II: Stress and Damage

María Jesús Samper — Wed, 03 Apr 2019 10:47:13 +0200

The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-;aaı RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this second part of the paper, the mechanical aspects of the simulation are presented; long-term effects are included by incorporating a creep model that naturally accounts for the aging effects, and the risk of tensile damage is also considered. The methodology determines the stress field inside the dam at any time during the construction and in the following years. Results for the reference case assess the suitability of the adopted design. This is compared to alternative studies considering different construction schedules to conclude that for these cases changes should be introduced in the dam design.

Simulation of Construction of RCC Dams. I: Temperature and Aging

María Jesús Samper — Wed, 03 Apr 2019 10:41:06 +0200

The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-í RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this first part only the thermochemical aspects of the simulation of the construction process are presented. The temperature distribution and evolution inside the dam are obtained before and after the completion of the dam. The evolution of the compressive and tensile strengths and elastic moduli and their final distribution inside the dam can also be predicted. Results from 2D and simplified vertical 1D models are compared to assess the validity of the latter, and several parametric studies are carried out. The simulation and discussion of the mechanical aspects of the construction process are relegated to a companion paper that follows.

Thermo-Chemo-Mechanical Model for Concrete. II: Damage and Creep

María Jesús Samper — Tue, 02 Apr 2019 13:13:26 +0200

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.

Thermo-chemo-mechanical model for concrete. I: Hydration and aging

María Jesús Samper — Tue, 02 Apr 2019 13:09:18 +0200

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.

Strong discontinuities and continuum plasticity models: the strong discontinuity approach

María Jesús Samper — Tue, 02 Apr 2019 12:37:54 +0200

The paper presents the Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models. Kinematics of weak and strong discontinuities are discussed, and a regularized kinematic state of discontinuity is proposed as a mean to model the formation of a strong discontinuity as the collapsed state of a weak discontinuity (with a characteristic bandwidth) induced by a bifurcation of the stress–strain field, which propagates in the solid domain. The analysis of the conditions to induce the bifurcation provides a critical value for the bandwidth at the onset of the weak discontinuity and the direction of propagation. Then a variable bandwidth model is proposed to characterize the transition between the weak and strong discontinuity regimes. Several aspects related to the continuum and, their associated, discrete constitutive equations, the expended power in the formation of the discontinuity and relevant computational details related to the finite element simulations are also discussed. Finally, some representative numerical simulations are shown to illustrate the proposed approach.

On the formulation of coupled thermoplastic problems with phase-change

María Jesús Samper — Tue, 02 Apr 2019 11:50:28 +0200

This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust numerical model, allowing the numerical simulation of solidification processes in the metal casting industry. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. The constitutive behavior has been defined by a thermoelastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. A brief summary of the thermomechanical frictional contact model is included. The numerical model has been implemented into the computational Finite Element code COMET developed by the authors. A numerical assessment of the isentropic and isothermal operator splits, regarding the nonlinear stability behavior, has been performed for weakly and strongly coupled thermomechanical problems. Numerical simulations of solidification processes show the performance of the computational model developed.

Numerical prediction of temperature and density distributions in selective laser sintering processes

María Jesús Samper — Tue, 02 Apr 2019 11:13:23 +0200

A finite element model has been developed for the 3D simulation of the sintering of a single track during a selective laser sintering process (SLS). The model takes into account both the thermal and the sintering phenomena involved in the process. Owing to the continuous movement of the laser beam the model takes also into account the transient nature of the problem. This is transformed into a pseudo‐static one through a transformation of the coordinates system of the equations. Nevertheless, this transformation introduces a convective term into the heat equations that produces instabilities in the solution. These instabilities have been solved by using a stream upwind Petrov Galerkin (SUPG) strategy together with a shock capturing scheme. Finally, a fixed point strategy is used for the solution of the analysis. The model has been tested through the solution of some examples.

Thermo‐mechanical analysis of industrial solidification processes

María Jesús Samper — Thu, 28 Mar 2019 10:20:50 +0100

The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes of industrial metal parts. The proposed constitutive model is defined by a thermo‐visco‐elasto‐(visco)plastic free energy function which includes a contribution for thermal multiphase changes. Mechanical and thermal properties are assumed to be temperature‐dependent, and viscous‐like strains are introduced to account for the variation of the elastic moduli during the cooling process. The continuous transition between the initial fluid‐like and the final solid‐like behaviour of the part is modelled by considering separate viscous and elasto‐plastic responses as a function of the solid fraction. Thermo‐mechanical contact conditions between the mould and the part are specifically considered, assuming that the heat flux is a function of the normal pressure and the thermal and mechanical gaps. A fractional step method arising from an operator split of the governing equations is used to solve the non‐linear coupled system of equations, leading to a staggered product formula solution algorithm suitable for large‐scale computations. Representative simulations of industrial solidification processes are shown, and comparison of computed results using the proposed model with available experimental data is given.

A strain-based plastic viscous-damage model for massive concrete structures

María Jesús Samper — Tue, 02 Apr 2019 10:55:54 +0200

Within the framework of continuum damage mechanics, a new constitutive damage model for massive concrete is presented, mainly intended for the seismic analysis of gravity and arch dams. Consistent with thermodynamic requirements, a straindriven formalism is adopted, improving the algorithmic efficiency as much as required for the analysis of large scale problems to become feasible. Two scalar damage variables are introduced as internal variables, as well as a plastic-strain tensor. An extension to account for the concrete strain-rate dependency, suitable for seismic analysis, is presented at the end. The efficiency of numerical predictions from the constitutive model is illustrated through numerical applications and algorithmic implementation is also detailed.

A rate-dependent isotropic damage model for the seismic analysis of concrete dams

María Jesús Samper — Tue, 02 Apr 2019 10:49:15 +0200

In this paper a rate‐dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown to incorporate two features essential for seismic analysis: stiffness degradation and stiffness recovery upon load reversals and strain‐rate sensitivity. The issue of mesh objectivity is addressed using the concept of the ‘characteristic length’ of the fracture zone, to show that both the softening modulus and the fluidity parameter must depend on it to provide consistent results as the computational mesh is refined. Some aspects of the numerical implementation of the model are also treated, to show that the model can be easily incorporated in any standard non‐linear finite element code. The application of the proposed model to the seismic analysis of a large gravity concrete dam shows that the structural response may vary significantly in terms of the development of damage. The inclusion of rate sensitivity is able to reproduce the experimental observation that the tensile peak strength of concrete can be increased up to 50 percent for the range of strain rates that appear in a structural safety analysis of a dam subjected to severe seismic actions.

On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled Problems

María Jesús Samper — Tue, 02 Apr 2019 10:30:10 +0200

Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Aims to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end, deals with two well-known coupled problems of computational mechanics – the fluid-structure interaction problem and thermally-driven flows of incompressible fluids. Demonstrates the possibility of coupling the block-iterative loop with the nonlinearity of the problems through numerical experiments which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. Discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. Explains also the need for online synchronized communication between the different codes used as is the description of the master code which will control the overall algorithm.

Seismic evaluation of concrete dams via continuum damage models

María Jesús Samper — Tue, 02 Apr 2019 10:14:44 +0200

In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) and arch dams (3D representation). The method allows for non‐linear material behaviour of the dam, ‘transparent fictitious boundaries’ for dealing properly with in‐coming and out‐going seismic waves, and an efficient procedure to deal with dam‐soil‐fluid interaction. The mechanical behaviour of concrete is modelled using an isotropic damage model which allows for tension and compression damage, and exhibits stiffness recovery upon load reversals. Emphasis is placed in the treatment of fluid‐structure interaction, regarding both formulation and efficiency aspects. A gravity dam and an arch dam are analysed subjected to artificially generated earthquakes of different intensities, and the results are used to study the degree of (un)safety of the dams.

Numerical analysis of stereolithography processes using the finite element method

María Jesús Samper — Mon, 21 Jan 2019 13:47:29 +0100

Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time savings with respect to traditional manufacturing processes. One of the main sources of error in the final dimensions of the prototype is the curl distortion effect owing to the shrinkage of the resin during the SLA process. Presents a study of the influence of different constructive and numerical parameters in the curl distortion, an analysis which was made using the computer code stereolithography analysis program, developed to model SLA processes using the finite element method. Also briefly presents this code.

A finite volume format for structural mechanics

María Jesús Samper — Tue, 11 Dec 2018 13:59:57 +0100

A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non‐Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.

A penalty finite element method for non‐Newtonian creeping flows

María Jesús Samper — Tue, 11 Dec 2018 13:48:54 +0100

In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.

Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle

María Jesús Samper — Fri, 04 Jan 2019 12:24:58 +0100

A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.

The intrinsic time for the streamline upwind Petrov-Galerkin formulation using quadratic elements

María Jesús Samper — Mon, 10 Dec 2018 13:24:19 +0100

In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic elements. Some related issues such as the computation of the characteristic element length and the introduction of source terms in the one-dimensional model problem are also addressed.

Numerical Analysis of Dams with Extensive Cracking due to Concrete Hydration: Simulation of a Real Case

María Jesús Samper — Mon, 01 Apr 2019 12:18:47 +0200

The paper presents the computational model developed to study an existing large gravity dam suffering from observed "pathological behavior" resulting concrete hydration. The combined effect of water intrusion and chemical and numerical studies. The present study was undertaken to simulate numerically the observed phenomenon and to predict future developments. Concrete is modelled using an isotropic continuum damage model including visco-elastic effects. The triggering of the volumetric expansion resulting from water intrusion is linked to the onset of damage at each a point, assuming that water enters dam mostly through the damaged areas. Transversal construction joints are modelled using smeared joints. Temperature and porewater pressure effects are included using assumed distributions based on available field data. Results are presented which match reasonably well with the available filed measurements.

A computational model for progressive cracking in large dams due to the swelling of concrete

María Jesús Samper — Mon, 21 Jan 2019 12:31:58 +0100

The paper presents a computational model for the analysis of large concrete gravity dams subjected to severe damage due to internal actions. It has been observed in several operating concrete dams that the combined effects of water intrusion and concrete expansion produce a time-advancing deteriorating process that may endanger the global stability of the construction. The present study was undertaken to simulate numerically the observed phenomena and to enable to predict future developments. Tensile cracking of the concrete is modelled using an elasticfracturing constitutive model. The model is able to simulate in a realistic manner the phenomena of primary and secondary crack initiation, elastic degradation, crack closing and reopening. The triggering of the volumetric expansion due to water intrusion is linked to the onset of cracking at each point, assuming that water enters the dam mostly through the cracks. Temperature and pore-water pressure effects are included using assumed distributions based on available field data. Construction joints are modelled using a frictional joint element, although a “constitutive alternative” is outlined. Close surveillance of the behaviour of a dam that presented this sort of problem was used to calibrate the numerical model and to confirm the obtained results.