Documents published in 2019 : Scipedia

High‐density sphere packing for discrete element method simulations
C. Labra, E. Oñate

Commun. Numer. Meth. Engng (2009). Vol. 25 (7), pp. 837-849; doi: 10.1002/cnm.1193

Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing has resulted in a great number of approaches during the last years. A new algorithm is proposed for high‐density packing using a scheme that minimizes the distance between each particle. Using the support of a finite element mesh, less time is needed in order to achieve a low porosity configuration. In addition, a boundary constraint is introduced. The application of the same optimization scheme is used as a condition to force a good surface definition. The results obtained show a high efficiency for the generation of low porosity packing, achieving values smaller than 10% in 2D cases and 30% in 3D cases.
Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing [...]
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Parallel Delaunay triangulation for particle finite element methods
Y. Fragakis, E. Oñate

Commun. Numer. Meth. Engng (2008). Vol. 24 (11), pp. 1009-1017; doi: 10.1002/cnm.1007

Abstract
Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed‐ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency.
Abstract
Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication [...]
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A simple method for automatic update of finite element meshes
G. Chiandussi, G. Bugeda, E. Oñate

Commun. Numer. Meth. Engng (2000). Vol. 16 (1), pp. 1-19; doi: 10.1002/(SICI)1099-0887(200001)16:1<1::AID-CNM310>3.0.CO;2-A

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to [...]
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An advancing front point generation technique
R. Löhner, E. Oñate

Commun. Numer. Meth. Engng (1998). Vol. 14 (12), pp. 1097-1108; doi: 10.1002/(SICI)1099-0887(199812)14:12<1097::AID-CNM183>3.0.CO;2-7

Abstract
An algorithm to construct boundary‐conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (>106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique.
Abstract
An algorithm to construct boundary‐conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point [...]
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Mixing anisotropic formulation for analysis of composites
S. Oller, E. Oñate, J. Canet

Commun. Numer. Meth. Engng (1996). Vol. 12 (8), pp. 471-482; doi: 10.1002/(SICI)1099-0887(199608)12:8<471::AID-CNM995>3.0.CO;2-6

Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo‐elasto‐plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances [...]
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On the pseudomaterial approach for the analysis of transient forming processes
M. Cruchaga, E. Oñate, S. Idelsohn

Commun. Numer. Meth. Engng (1995). Vol. 11 (2), pp. 137-148; doi: 10.1002/cnm.1640110207

Abstract
A fixed‐mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last zones are identified by a pseudomaterial with relatively small physical parameters. During time processing, the interface between both materials is followed by an arbitrary Lagrangian mesh. This technique appears to be suitable for the treatment of moving surfaces with sharp corners. A particular boundary condition for the Navier‐Stokes equations is also introduced in order to model a porous wall.
Abstract
A fixed‐mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last [...]
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Comparative study of different discrete element models and evaluation of equivalent micromechanical parameters
J. Rojek, C. Labra, O. Su, E. Oñate

Int. J. Solids and Structures (2012). Vol 49 (13), pp. 1497-1517; doi: 10.1016/j.ijsolstr.2012.02.032

Abstract
Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test. Two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used. Macroscopic response produced by different discrete element models has been compared. The main difference between the compared models consists in the evaluation of micromechanical constitutive parameters. Two approaches are compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. The size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair. As geometric scaling parameters, the arithmetic and harmonic means, as well as the minimum of the radii of two contacting particles are considered. Two different models with size dependent contact parameters are formulated. The performance of these models is compared with that of the discrete element model with global uniform contact parameters. Equivalence between the models with size dependent and uniform contact parameters has been checked. In search of this equivalence, different methods of evaluation of global uniform parameters have been studied. The contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii, the geometric parameters used in the evaluation of the contact stiffness in the size-dependent models. The uniform contact strengths have been determined as functions of the averages of radii squares, squares of arithmetic radii means or squares of minimum radii of the contacting pairs. For the more homogenous specimen, the models with local size dependent parameters and models with global uniform parameters give similar response. The models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size-dependent parameters than the models with uniform parameters evaluated according to the particle radii. Simulations using the more heterogenous specimen reveal differences between the considered models. There are significant differences in stress–strain curves as well as in the failure pattern. The models with local size-dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters.
Abstract
Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive [...]
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Numerical simulation of fiber reinforced composite materials––two procedures
E. Car, F. Zalamea, S. Oller, J. Canet, E. Oñate

Int. J. Solids and Structures (2002). Vol. 39 (7), pp. 1967-1986; doi: 10.1016/S0020-7683(01)00240-2

Abstract
In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented. The first methodology used is a generalized anisotropic large strains elasto-plastic constitutive model for the analysis of multiphase materials. It is based on the mixing theory of basic substance. It is the manager of the several constitutive laws of the different compounds and it allows to consider the interaction between the compounds of the composite materials. In fiber reinforced composite materials, the constitutive behavior of the matrix is isotropic, whereas the fiber is considered orthotropic. So, one of the constitutive model used in the mixing theory needs to consider this characteristic. The non-linear anisotropic theory showed in this work is a generalization of the classic isotropic plasticity theory (A Continuum Constitutive Model to Simulate the Mechanical Behavior of Composite Materials, PhD Thesis, Universidad Politécnica de Cataluña, 2000). It is based in a one-to-one transformation of the stress and strain spaces by means of a four rank tensor. The second methodology used is based on the homogenization theory. This theory divided the composite material problem into two scales: macroscopic and microscopic scale. In macroscopic level the composite material is assuming as a homogeneous material, whereas in microscopic level a unit volume called cell represents the composite (Tratamiento Numérico de Materiales Compuestos Mediante la teorı́a de Homogeneización, PhD Thesis, Universidad Politécnica, de Cataluña 2001). This formulation presents a new viewpoint of the homogenization theory in which can be found the equations that relate both scales. The solution is obtained using a coupled parallel code based on the finite elements method for each scale problem.
Abstract
In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented. The first methodology used is a generalized anisotropic [...]
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A coupled thermomechanical model for the solidification of cast metals
D. Celentano, S. Oller, E. Oñate

Int. J. Solids and Structures (1996). Vol. 33 (5), pp. 647-673; doi: 10.1016/0020-7683(95)00056-G

Abstract
A coupled thermomechanical model to simulate solidification problems in casting is presented. The model is formulated from a phenomenological point of view using a general isotropic thermoelasto-plasticity theory. Generalized phase-change effects accounting for the different thermomechanical behaviour of the solidifying material during its evolution from liquid to solid have been considered. For this purpose, a phase-change function, plastic evolution equations and a temperature-dependent constitutive law have been defined. Full thermomechanical effects as well as variable thermal and mechanical boundary conditions are also taken into account. Particular details concerning the numerical implementation of the model are given, where special emphasis is devoted to the resulting highly non-linear fully coupled finite element equations. The behaviour of this formulation is studied first in a simple quenching problem. Finally, a cylindrical casting test problem including phase-change phenomena, temperature-dependent constitutive properties and contact effects is analysed. Numerical results are compared with laboratory measurements.
Abstract
A coupled thermomechanical model to simulate solidification problems in casting is presented. The model is formulated from a phenomenological point of view using a general [...]
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A plastic damage constitutive model for composite materials
S. Oller, E. Oñate, J. Canet, S. Botello

Int. J. Solids and Structures (1996). Vol. 33 (17), pp. 2501-2518; doi: 10.1016/0020-7683(95)00161-1

Abstract
In this paper a generalized elasto-plastic damage model for the analysis of multiphase frictional composite materials is presented. Details of the derivation of the secant and tangent constitutive equations are given. Mixing theory is used to insert the basic constitutive expressions for each substance on the multiphase composite solid. Details of the numerical implementation of the model into a general non-linear finite element solution scheme are presented. Some examples of linear and non-linear behaviour of composites are given.
Abstract
In this paper a generalized elasto-plastic damage model for the analysis of multiphase frictional composite materials is presented. Details of the derivation of the secant [...]
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A hygro-thermo-mechanical constitutive model for multiphase composite materials
S. Oller, E. Oñate

Int. J. Solids and Structures (1996). Vol. 33 (20-22), pp. 3179-3186; doi: 10.1016/0020-7683(95)00248-0

Abstract
The paper describes a hygro-thermo-mechanical constitutive model appropriate for numerical simulation of multiphase composite material behaviour. The theory is based on the mixture of the basic substances of the composite and allows to evaluate the inter-dependent behaviour between the different compounding constitutive models. The initial anisotropy of each compounding can be taken into account by means of a mapped isotropic plastic formulation. This is a generalization of classic isotropic plasticity theory applied to orthotropic or anisotropic materials. The basic assumption is the existence of a stress and strain real anisotropic spaces and the respective fictitious isotropic spaces where a mapped fictitious problem is solved. Those spaces are related by means of two fourth order transformation tensor. The combination of mixing theory and the mapped isotropic plastic approach provides a powerful constitutive framework for the numerical treatment of bulk-fiber composite materials.
Abstract
The paper describes a hygro-thermo-mechanical constitutive model appropriate for numerical simulation of multiphase composite material behaviour. The theory is based [...]
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A plastic-damage model for concrete
J. Lubliner, X. oliver, S. Oller, E. Oñate

Int. J. Solids and Structures (1989). Vol. 25 (3), pp. 299-326; doi: 10.1016/0020-7683(89)90050-4

Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects. Onset and amount of cracking can be studied by a simple postprocessing of the finite-element plasticity solution. The accuracy of the model is checked with some examples of application.
Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new [...]
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Flow of solids during forming and extrusion: Some aspects of numerical solutions
O. Zienkiewicz, P. Jain, E. Oñate

Int. J. Solids and Structures (1978). Vol. 14 (1), pp. 15-38; doi: 10.1016/0020-7683(78)90062-8

Abstract
In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. The problem thus becomes one of incompressible viscous, non-Newtonian flow with prescribed boundary velocities. Various formulations of such problems (analogous to those of incompressible solid mechanics) are possible, and the paper investigates two basic processes. Details of application to some examples of steady state flow in extrusion, drawing and rolling are given and transient free surface solutions are demonstrated for stretch forming and deep drawing. The formulation is shown to be capable of dealing with boundary friction and strain hardening. The coupling with thermal effects is demonstrated in the last section of the paper, and in addition, some practical problems of elastic spring-back which occur on the removal of load are discussed.
Abstract
In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. The problem thus becomes one of incompressible [...]
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Real-time micro-modelling of city evacuations
E. Haug, R. Löhner, C. Zinggerling, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (1), pp. 71-86; doi: 10.1007/s40571-016-0154-z

Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and archiving from GIS databases, automatic input for pedestrian simulations, as well as scalable pedestrian simulation tools have made it possible to simulate pedestrians at the individual level for complete cities in real time. An example that simulates the evacuation of the city of Barcelona demonstrates that this is now possible. This is the first step towards a fully integrated crowd prediction and management tool that takes into account not only data gathered in real time from cameras, cell phones or other sensors, but also merges these with advanced simulation tools to predict the future state of the crowd.
Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and [...]
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Virtual modeling of polycrystalline structures of materials using particle packing algorithms and Laguerre cells
C. Recarey Morfa, M. Farias, I. Pérez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (2), pp. 213-226; doi: 10.1007/s40571-017-0164-5

Abstract
The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary to generate virtual materials that are statistically equivalent to the microstructure under study, and to connect that geometrical description to the different numerical methods. Herein, the authors present a procedure to model continuous solid polycrystalline materials, such as rocks and metals, preserving their representative statistical grain size distribution. The first phase of the procedure consists of segmenting an image of the material into adjacent polyhedral grains representing the individual crystals. This segmentation allows estimating the grain size distribution, which is used as the input for an advancing front sphere packing algorithm. Finally, Laguerre diagrams are calculated from the obtained sphere packings. The centers of the spheres give the centers of the Laguerre cells, and their radii determine the cells’ weights. The cell sizes in the obtained Laguerre diagrams have a distribution similar to that of the grains obtained from the image segmentation. That is why those diagrams are a convenient model of the original crystalline structure. The above-outlined procedure has been used to model real polycrystalline metallic materials. The main difference with previously existing methods lies in the use of a better particle packing algorithm.
Abstract
The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary [...]
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A three-dimensional FEM–DEM technique for predicting the evolution of fracture in geomaterials and concrete
F. Zárate, A. Cornejo Velázquez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3) , pp. 411-420; doi: 10.1007/s40571-017-0178-z

Abstract
This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301–314, 2015). Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple four-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.
Abstract
This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element [...]
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Pulse fracture simulation in shale rock reservoirs: DEM and FEM–DEM approaches
F. Zárate, A. Cornejo Velázquez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3), pp. 355-373; doi: 10.1007/s40571-017-0174-3

Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM–DEM approaches for the simulation of fracture in shale rock caused by a pulse of pressure. We have studied the evolution of fracture in several fracture scenarios related to the initial stress state in the soil or the pressure pulse peak. Fracture length and type of failure have been taken as reference for validating the models. The results obtained show a good approximation to FEM results from the literature.
Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM–DEM approaches for the simulation of fracture in shale rock caused by a pulse [...]
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Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations
C. Recarey Morfa, L. Cortés, M. Farias, I. Pérez, R. Valera, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3), pp. 319-334; 10.1007/s40571-017-0171-6

Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.
Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension [...]
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Air demand estimation in bottom outlets with the particle finite element method
F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate

Comp. Part. Mech (2017). Vol. 4 (3), pp. 345-356; doi: 10.1007/s40571-016-0117-4

Abstract
Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water flows under the gate lip at high velocity and drags the air downstream of the gate, which may cause damages due to cavitation and vibration. The convenience of installing air vents in dam bottom outlets is well known by practitioners. The design of this element depends basically on the maximum air flow through the air vent, which in turn is a function of the specific geometry and the boundary conditions. The intrinsic features of this phenomenon makes it hard to analyse either on site or in full scaled experimental facilities. As a consequence, empirical formulas are frequently employed, which offer a conservative estimate of the maximum air flow. In this work, the particle finite element method was used to model the air–water interaction in Susqueda Dam bottom outlet, with different gate openings. Specific enhancements of the formulation were developed to consider air–water interaction. The results were analysed as compared to the conventional design criteria and to information gathered on site during the gate operation tests. This analysis suggests that numerical modelling with the PFEM can be helpful for the design of this kind of hydraulic works.
Abstract
Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water [...]
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General advancing front packing algorithm for the discrete element method
C. Recarey Morfa, I. Pérez, M. Farías, E. Oñate, R. Valera, H. Casañas

Comp. Part. Mech (2018). Vol. 5, pp 13–33; doi: 10.1007/s-40571-016-0144-1

Abstract
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.
Abstract
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation [...]
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The Double Hierarchy Method. A parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM
M. Santasusana, J. Irazábal González, E. Oñate, J. Carbonell

Comp. Part. Mech (2016). Vol. 3, pp. 407-428; doi: 10.1007/s40571-016-0109-4

Abstract
In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027–1032, 2001) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.
Abstract
In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are [...]
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A modular, partitioned, discrete element framework for industrial grain distribution systems with rotating machinery
G. Casas, D. Mukherjee, M. Celigueta, T. Zohdi, E. Oñate

Comp. Part. Mech (2017). Vol. 4 (2), pp. 181-198; doi: 10.1007/s40571-015-0089-9

Abstract
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Abstract
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger [...]
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Computation of the stabilization parameter for the finite element solution of advective–diffusive problems
E. Oñate, J. García-Espinosa, S. Idelsohn

Eugenio Oñate's Journal Papers (2019). 1

Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite size domains was presented. This provides an expression for the element stabilization parameter in terms of the solution residual and its first derivatives in a kind of iterative or adaptative manner. Details of the application of this procedure to 1D and 2D advective- diffusive problems are given. Some examples of applications showing the potential of the new approach are presented.
Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite [...]
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A Comparison of two objective stress rates in object-oriented codes
A. Rodríguez-Ferran, A. Huerta

Monograph CIMNE (1994). M26

Abstract
An object-oriented code, CASTEM2000, has provided the framework for algorithmic development and numerical testing. In these codes, information is stored and manipulated as objects which represent the entitiesrelevant to a finite element method computation.
Abstract
An object-oriented code, CASTEM2000, has provided the framework for algorithmic development and numerical testing. In these codes, information is stored and manipulated as [...]
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Lagrangian finite element model for the 3D simulation of glass forming processes
P. Ryzhakov, J. García-Espinosa, E. Oñate

Computers and Structures (2016). Vol. 177, pp. 126-140; doi: 10.1016/j.compstruc.2016.09.007

Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product’s wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.
Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we [...]
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A rate dependent plastic-damage constitutive model for large scale computational in concrete structures
R. Faria, J. Oliver

Monograph CIMNE (1993). M17
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Composite materials non-linear modelling for long fibre-reinforced laminates: Continuum basis, computational aspects and validations
F. Rastellini, S. Oller, O. Salomon, E. Oñate

Computers and Structures (2008). Vol. 86 (9), pp. 879-896; doi: 10.1016/j.compstruc.2007.04.009

Abstract
An innovative computational methodology is proposed for modelling the material non-linearmechanical behaviour of FRP structures. To model a single unidirectional composite lamina, a serial–parallel (SP) continuum approach has been developed assuming that components behave as parallel materials in the fibres alignment direction and as serial materials in orthogonal directions. The model is based on the appropriate management of the constitutive models of the component materials, by making use of suitable ‘closure equations’ that characterize the composite micro-mechanics [Rastellini F. Modelización numérica de la no-linealidad constitutiva de laminados compuestos. PhD thesis. ETSECCPB, Politechnical University of Catalonia, Barcelona, March, 2006. [in Spanish]]. Classical lamination theory is combined with the SP model to describe multidirectional laminates. The methodology is validated through several numerical analyses, which are contrasted against benchmark tests and experimental data taken from the world-wide failure exercise [Hinton MJ, Soden PD. Predicting failure in composite laminates: The background to the exercise. Comp Sci Technol 1998; 58:1001–10].
Abstract
An innovative computational methodology is proposed for modelling the material non-linearmechanical behaviour of FRP structures. To model a single unidirectional composite [...]
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An integration of a low cost adaptive remeshing strategy in the solution of structural shape optimization problems using evolutionary methods
G. Bugeda, J. Ródenas, E. Oñate

Computers and Structures (2008). Vol. 86 (13-14), pp. 1563-1578; doi: 10.1016/j.compstruc.2007.05.010

Abstract
Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural analysis of an important number of different designs, this making the computational cost of the analysis of each design a critical issue. For this reason, each design must be analyzed at a minimum computational cost but ensuring a minimum quality of the results. It is well known that the cheapest mesh for producing a solution with a fixed quality at minimum cost is an adapted one. Nevertheless, traditional adapted meshes are obtained from adaptive remeshing strategies, where each design has to be analyzed more than once, thereby also causing a high computational cost. This work presents a new strategy that allows generating an adapted mesh for each design without the necessity of performing a full adaptive remeshing procedure for each of them. It is based on the use of sensitivity analysis of all magnitudes related with adaptive remeshing (location of nodes, error estimation, etc.) with respect to the design variables. This sensitivity analysis is performed only once using a geometry of reference and it is used to project the results of the corresponding analysis to all other designs to be analyzed. The projected information allows generating an appropriate adapted mesh for each new design in one shot, greatly reducing the computational cost compared with standard strategies.
Abstract
Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural [...]
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Análisis de problemas de choque e impacto entre sólidos deformables por el Método de los Elementos Finitos.
J. Miquel, E. Oñate, C. Garino, S. Botello, F. Flores, J. Rojek

Monograph CIMNE (1994). M25

Abstract
El trabajo que se expone ha hecho uso de los últimos avances en mecánica computacional, métodos numéricos, visualización y algoritmos de cálculo para obtener un programa de ordenador para simulación de problemas de choque e impacto de interés práctico para una amplia variedad de sectores industriales. En particular, el objetivo del proyecto SIMPACT ha sido el desarrollo de un paquete de software para análisis de problemas de dinámica rápida y análisis no lineal procesable en una amplia variedad de ordenadores, con aplicación a choques de vehículos, impacto en estructuras aeroespaciales, defensa y problemas de conformado, entre otros.
Abstract
El trabajo que se expone ha hecho uso de los últimos avances en mecánica computacional, métodos numéricos, visualización y algoritmos de [...]
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Estructuras de edificación con aislaminto antisísmico
L. Jané, A. Barbat

Monograph CIMNE (1992). M13
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Estimación y corrección del error en el análisis estructural por el MEF
G. Bugeda

Monograph CIMNE (1991). M9

Abstract
En los últimos años se han desarrollado diversas técnicas para resolver el problema de la estimación y la corrección del error. De hecho, la mayoría de los avances que se han realizado dentro del campo de los elementos finitos se pueden entender como formas distingas de minimizar el error existente en las soluciones. En esta monografía se hablará de dos técnicas distintas para la corrección de errores: Técnicas de refinamiento y técnicas de remallado.
Abstract
En los últimos años se han desarrollado diversas técnicas para resolver el problema de la estimación y la corrección del error. De hecho, [...]
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Modelización numérica de materiales friccionales
S. Oller

Monograph CIMNE (1991). M10

Abstract
La presente monografía trata el problema del comportamiento de los materiales friccionales, especialmente del hormigón, más allá de su límite elástico. Estudia los problemas de aplastamiento y fractura y describe un modelo constitutivo amplio que permite una muy adecuada simulación de estos fenómenos.
Abstract
La presente monografía trata el problema del comportamiento de los materiales friccionales, especialmente del hormigón, más allá de su límite [...]
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A Finite Element formulation for the numerical solution of the convection-diffusion equation
R. Codina

Monograph CIMNE (1993). M14

Abstract
In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, tha is, when diffusion is very small. The basic finite element formulation employed here is the Streamline-Upwind-Petrov-Galerkin (SUPG). A thorough description of this approach is presented in Chapter 1. Chapter 2 deals with the application of the generalized trapezoidal rule to advance in time for the transient equation. A complete stability and accuracy analysis is performed for the explicit Euler scheme, both using linear and quadratic finite elements. Chapter 3 is concerned with the problem of removing the localized oscillations that remain about abrupt layers of the solution.
Abstract
In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, tha is, when diffusion is very [...]
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Mechanics of a continuum medium. Vol. III
A. Fusco

Monograph CIMNE (1993). M20

Abstract
This work presents the fundamental assumptions and the successive mathematical developments which allow to establish the complete field equations of a continuum. The aim is to be sufficiently general and self-content using, however, mathematical procedures which can be always understook by an engineer with a common background of Linear Algebra and elementary Differential Calculus.
Abstract
This work presents the fundamental assumptions and the successive mathematical developments which allow to establish the complete field equations of a continuum. The aim is [...]
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A Finite Element formulation for viscous incompressible flows
R. Codina

Monograph CIMNE (1993). M16
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Modelado de la fisuración en estructuras de hormigón
J. Oliver

Monograph CIMNE (1993). M15

Abstract
En este trabajo, se presenta una perspectiva general de los modelos de fisuración existentes y de algunas aportaciones de la línea de investigación que se desarrollan, tanto en el dominio de la formulación teórica de dichos modelos como de su aplicación práctica.
Abstract
En este trabajo, se presenta una perspectiva general de los modelos de fisuración existentes y de algunas aportaciones de la línea de investigación que [...]
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Particle finite element method in fluid-mechanics including thermal convection-diffusion
S. Idelsohn, R. Aubry, E. Oñate

Computers and Structures (2005). Vol. 83 (17-18), pp. 1459-1475; doi: 10.1016/j.compstruc.2004.10.021

Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed.
Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due [...]
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A Lagrangian meshless finite element method applied to fluid–structure interaction problems
S. Idelsohn, E. Oñate, F. Del Pin

Computers and Structures (2003). Vol. 81 (8-11), pp. 655-671; doi: 10.1016/S0045-7949(02)00477-7

Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.
Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are [...]
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Lectures on nonlinear finite element analysis of concrete shells
E. Oñate

Monograph CIMNE (1991). M7

Abstract
This monograph presents 4 lectures on non linear analysis of concrete shells by the finite element method. The lectures were prepared by the author for the course on "Non linear analysis of shells by finite elements" held at the International Center for Mechanics Sciences in Udine, Italy on June 24-28th 1991. The content of the lectures presents an overview of the different aspects involved in the analysis of concrete shells by finite elements. Thus, Lecture 1 introdeuces the basic concepts of the analysis of reinforced concrete shell structures using flat shell and curved degenerated layered shell finite elements. Both the geometric and kinematic assumptions are described in detail together with the respective finite element formulation and the numerical algorithm for non linear elasto-plastic analysis including the effect of moderately large displacements. Lecture 2 presents an overview of the constitutive behaviour of concrete and steel in a form suitable for numerical computations using the finite element models described in previous lecture. The reinforcing steel bars are modelled with a simple elasto-plastic model. Hovewer, two conceptualy different concrete models are presented. The first model is based on elasto-plastic theory to describe the compressive behaviour of concrete, whereas a linear orthotropic elasto-brittle model is used for modelling the cracking behaviour under tensile conditions. This ``elasto-platic-brittle model has been extensively used by Owen and Figueiras and most of the concepts presented emanate from reference [18] of this chapter. The second model is based on the assumptions that both the tensile and compressive behaviour of concrete can be treated under the unified framework of elasto-plasticity theory. This model termed ``plastic-damage model has ben proposed by Lubliner, Oller, Oliver and O\~nate in different publications which main concepts are summarized in the lecture (see refs. [33-38] of this chapter). In Lecture 3 the basic finite element formulation for the analysis of stiffened concrete shells via the use of eccentric beams is described. Finally, in Lecture 4 some examples of applications of the finite element formulations presented to the non-linear analysis of different reinforced concrete shell structures analyzed by different authors are described. Examples included range from the analysis of plain and pre-stressed concrete deep beams, to more sophisticated shell type structures including the nonlinear behaviour of a composite steel-concrete girder bridge and a cryogenic concrete liquid gas tank under severe thermal conditions. This monograph has been written exclusively with didactic purposes. Most of the ideas included in the text have been extracted from research publications by the author and many others. The interested reader will be able to find details on the different subjects treated in the many references included at the end of each chapter.
Abstract
This monograph presents 4 lectures on non linear analysis of concrete shells by the finite element method. The lectures were prepared by the author for the course on "Non [...]
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Análisis dinámico de presas
J. Canet, E. Oñate, J. Buil, E. Herrero

Monograph CIMNE (1991). M5

Abstract
Se desarrolla en este trabajo un estudio numérico-experimental acerca del comportamiento dinámico de las presas bóvedas considerando su interacción con el agua del embalse. Para ello, se ha realizado un análisis de los factores que inciden más directamente en el comportamiento dinámico de tales tipos de estructuras. Dicho análisis se realiza mediante e lmétodo de los elementos finitos, estudiando distintas alternativas de formulación. Asimismo, se ha realizado un esayo a escala real de una presa bóveda existente, mediante una serie de explosiones y midiendo la respuesta obtenida.
Abstract
Se desarrolla en este trabajo un estudio numérico-experimental acerca del comportamiento dinámico de las presas bóvedas considerando su interacción [...]
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Simulación Numérica de Patologías en Presas de Hormigón
M. Cervera, J. Oliver, M. Galindo

Monograph CIMNE (1991). M4
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Stress, strain and energy splittings for anisotropic elastic solids under volumetric constraints
C. Felippa, E. Oñate

Computers and Structures (2003). Vol. 81 (13), pp. 1343-1357; doi: 10.1016/S0045-7949(03)00060-9

Abstract
We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.
Abstract
We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, [...]
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A finite element methodology for local/global damage evaluation in civil engineering structures
A. Hanganu, E. Oñate, A. Barbat

Computers and Structures (2002). Vol. 80 (20-21), pp. 1667-1687; doi: 10.1016/S0045-7949(02)00012-3

Abstract
The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and global damage in civil engineering structures using the finite element method and a continuum damage model, is presented. The method is adequate for the computation of the limit load in reinforced concrete (RC) structures and for the prediction of the failure mechanisms. Details of the applied damage model are given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications of the methodology to the nonlinear analysis of a range of RC structures, are presented.
Abstract
The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and [...]
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Some algorithms to correct a geometry in order to create a finite element mesh
R. Ribó, G. Bugeda, E. Oñate

Computers and Structures (2002). Vol. 80 (16-17), pp. 1399-1408; doi: 10.1016/S0045-7949(02)00105-0

Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non-proper geometrical definitions coming from CAD systems. Typically, CAD systems do not take care of the proper definition of the geometries for the analysis purposes. In addition, the use of standard CAD files (IGES, VDA, …) for the transfer of geometries between different systems introduce some additional difficulties. In this work, a collection of algorithms to repair and/or to improve the geometry definitions are provided. The aim of these algorithms is to make as easy as possible the generation of a mesh over complex geometries given some minimum requirements of quality and correctness. The geometrical model will be considered as composed of a set of NURBS lines and trimmed surfaces. Some examples of application of the algorithms and of the meshes generated from the corrected geometry are also presented in this work.
Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non-proper geometrical definitions coming from CAD systems. Typically, [...]
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A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation
R. Scotta, R. Vitaliani, A. Saetta, E. Oñate, A. Hanganu

Computers and Structures (2001). Vol. 79 (7), pp. 737-755; doi: 10.1016/S0045-7949(00)00178-4

Abstract
A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.
Abstract
A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. [...]
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A finite point method for elasticity problems
E. Oñate, F. Perazzo, J. Canet

Computers and Structures (2001). Vol. 79 (22-25), pp. 2151-2163; doi: 10.1016/S0045-7949(01)00067-0

Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.
Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization [...]
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A layer-wise triangle for analysis of laminated composite plates and shells
S. Botello, E. Oñate, J. Canet

Computers and Structures (1999). Vol. 70 (6), pp. 635-646; doi: 10.1016/S0045-7949(98)00165-5

Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of dierent laminate plate and shell structures
Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation [...]
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Plate bending elements with discrete constraints: New triangular elements
O. Zienkiewicz, R. Taylor, P. Papadopoulos, E. Oñate

Computers and Structures (1990). Vol. 35 (4), pp. 505-522; doi: 10.1016/0045-7949(90)90072-A

Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have proved to be very effective, however their relation to straightforward mixed approximations has not been clear. In this paper this relationship is discussed and the reasons for their success explained. This allows new and effective triangular elements to be developed. The presentation shows the close relationships with the DKT (Discrete Kirchhoff Theory) element previously available only for thin plates and allows extension of their applications.
Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have [...]
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Dynamic analysis of structures using a Reissner-Mindlin finite strip formulation
J. Canet, B. Suarez, E. Oñate

Computers and Structures (1989). Vol. 31 (6), pp. 967-975; doi: 10.1016/0045-7949(89)90281-2

Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of the relevant strip matrices for a variety of structures using the simple two node linear strip element are given. Examples of the good performance of the linear strip element for free and forced vibration analysis of plates, bridges and axisymmetric shells are presented.
Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of [...]
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A comparison of the linear, quadratic and cubic mindlin strip elements for the analysis of thick and thin plates
E. Oñate, B. Suarez

Computers and Structures (1983). Vol. 17 (3), pp. 427-439; doi: 10.1016/0045-7949(83)90134-7

Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques are used to ensure the good behaviour of the elements when dealing with thin plates. Numerical results showing the convergence and accuracy of the elements for the analysis of plates of a wide range of thicknesses are given. The general performance of the three elements is discussed in detail. In particular, the linear element with a single integration point seems to be the best value strip element for practical purposes.
Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective [...]
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A unified approach for the analysis of bridges, plates and axisymmetric shells using the linear mindlin strip element
E. Oñate, B. Suarez

Computers and Structures (1983). Vol. 17 (3), pp. 407-426; doi: 10.1016/0045-7949(83)90133-5

Abstract
In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.
Abstract
In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified [...]
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2D particle contact-based meshfree method in CDEM and its application in geotechnical problems
C. Feng, S. Li, E. Oñate

Engineering Computations (2015). Vol. 32 (4), pp. 1080-1103; doi: 10.1108/EC-04-2014-0095

Abstract
Purpose – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) and FEM. When simulating large deformation problems, such as cutting, blasting, water-like material flowing, the distortion of elements will lead to no convergence of the numerical system. To solve the convergence problem, a particle contact-based meshfree method (PCMM) is introduced in. The paper aims to discuss this issue. Design/methodology/approach – PCMM is based on traditional particle DEM, and use particle contacts to generate triangular elements. If three particles are contact with each other, the element will be created. Once elements are created, the macroscopic constitutive law could be introduced in. When large deformation of element occurs, the contact relationship between particles will be changed. Those elements that do not meet the contact condition will be deleted, and new elements that coincide with the relationship will be generated. By the deletion and creation of elements, the convergence problem induced by element distortion will be eliminated. To solve FEM and PCMM coupled problems, a point-edge contact model is introduced in, and normal and tangential springs are adopted to transfer the contact force between particles and blocks. Findings – According to the deletion and recreation of elements based on particle contacts, PCMM could simulate large deformation problems. Some numerical cases (i.e. elastic field testing, uniaxial compression analysis and wave propagation simulation) show the accuracy of PCMM, and others (i.e. soil cutting, contact burst and water-like material flowing) show the rationality of PCMM. Originality/value – In traditional particle DEM, contact relationships are used to calculate contact forces. But in PCMM, contact relationships are adopted to generate elements. Compared to other meshfree methods, in PCMM, the element automatic deletion and recreation technique is used to solve large deformation problems.
Abstract
Purpose – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) [...]
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Simple and efficient numerical tools for the analysis of parachutes
F. Flores, E. Ortega, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2019). 19

Abstract
Purpose – The purpose of this paper is to describe a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluid-structural solver for unsteady simulations of ram-air type parachutes. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique. Design/methodology/approach – For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly nonlinear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness. Findings – A simple and effective numerical tool for the analysis of parachutes has been developed. Originality/value – An analysis code has been developed which addresses the needs of ram-air parachute designers. The software delivers reasonably accurate results in a short time using modest hardware. It can therefore assist the design process, which nowadays relies on empirical methods
Abstract
Purpose – The purpose of this paper is to describe a set of simple yet effective, numerical method for the design and evaluation of parachute-payload [...]
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Validation of the particle finite element method (PFEM) for simulation of free surface flows
A. Larese, R. Rossi, E. Oñate, S. Idelsohn

Engineering Computations (2008). Vol. 25 (3-4), pp. 385-425; doi: 10.1108/02644400810874976

Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach – A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature. Findings – Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution. Originality/value – Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.
Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach [...]
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Non‐linear explicit dynamic analysis of shells using the BST rotation‐free triangle
E. Oñate, P. Cendonya, J. Canet

Engineering Computations (2002). Vol. 19 (5-6), pp. 662-706; doi: 10.1108/02644400210439119

Abstract
The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.
Abstract
The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. [...]
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A residual correction method based on finite calculus
E. Oñate, R. Taylor, O. Zienkiewicz, J. Rojek

Engineering Computations (2003). Vol. 20 (5-6), pp. 629-658; doi: 10.1108/02644400310488790

Abstract
In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar convection‐diffusion problem and the problem of elasticity at the incompressible or quasi‐incompressible limit. The formulation permits the use of equal interpolation for displacements and pressure on linear triangles and tetrahedra as well as any low order element type. To add additional stability in the solution, pressure gradient corrections are introduced as suggested from developments of sub‐scale methods. Numerical examples are included to demonstrate the performance of the method when applied to typical test problems.
Abstract
In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar [...]
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Direct computation of instability points with inequality constraints using the FEM
H. Tschöpe, P. Wriggers, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 611-628; doi: 10.1108/02644400310488781

Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.
Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical [...]
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Direct computation of instability points with inequality constraints using the FEM
H. Tschöpe, P. Wriggers, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2019). 29

Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.
Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical [...]
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The extended Delaunay tessellation
N. Calvo, S. Idelsohn, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 583-600; doi: 10.1108/02644400310488763

Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.
Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï [...]
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Numerical modelling and simulation of frictional contact using a generalised coulomb law
A. Heege, P. Alart, E. Oñate

Engineering Computations (1995). Vol. 12 (7), pp. 641-656; doi: 10.1108/02644409510799820

Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.
Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach [...]
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An anisotropic elastoplastic model based on an isotropic formulation
S. Oller, S. Botello, J. Canet, E. Oñate

Engineering Computations (1995). Vol. 12 (3), pp. 245-262; doi: 10.1108/02644409510799587

Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.
Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of [...]
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Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle
E. Oñate, M. Cervera

Engineering Computations (1993). Vol. 10 (6), pp. 543-561; doi: /10.1108/eb023924

Abstract
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.
Abstract
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 [...]
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Analysis of some partitioned algorithms for fluid-structure interaction
R. Rossi, E. Oñate

Engineering Computations (2010). Vol. 27 (1), pp. 20-56; doi: 10.1108/02644401011008513

Abstract
The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different approaches developed over recent years the general solution of FSI problems remains however far from being closed. This paper addresses the theoretical analysis of a several partitioned solution schemes for FSI. This is achieved by choosing a simple but representative model problem which allows to obtain analytical results. A loose coupling partitioned procedure is presented first. An iterative version of the same algorithm is presented next together with an analysis of its convergence properties and a brief discussion of a possible acceleration strategy. Finally a new iterative strategy based on solving a modified equation is described. Some examples of application of the partitioned algorithms considered are presented including the aeroelastic analysis of a bridge.
Abstract
The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different [...]
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A study of mesh optimality criteria in adaptive finite element analysis
E. Oñate, G. Bugeda

Engineering Computations (1993). Vol. 10 (4), pp. 307-321; doi: 10.1108/eb023910

Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.
Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error [...]
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Combination of the critical displacement method with a damage model for structural instability analysis
E. Oñate, P. Wriggers

Engineering Computations (2001). Vol. 18 (3-4), pp. 642-662; doi: 10.1108/02644400110387190

Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non-linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load-displacement relationship accounting for material non-linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.
Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with [...]
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Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method
B. Suarez, J. Canet, E. Oñate

Engineering Computations (1988). Vol. 5 (2), pp. 158-164; doi: 10.1108/eb023734

Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.
Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin [...]
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A constitutive model for cracking of concrete based on the incremental theory of plasticity
E. Oñate, S. Oller, X. oliver, J. Lubliner

Engineering Computations (1988). Vol. 5 (4), pp. 309-319; doi: 10.1108/eb023750

Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.
Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters [...]
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A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics
I. Iaconeta, A. Larese, R. Rossi, E. Oñate

Computational Mechanics (2018). Published online; doi: 10.1007/s00466-018-1647-9

Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.
Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with [...]
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Accurate modelling of the elastic behavior of a continuum with the Discrete Element Method
M. Celigueta, S. Latorre, F. Garcia, E. Oñate

Computational Mechanics (2017). Vol. 60 (6), pp. 997-1010; doi: 10.1007/s00466-017-1453-9

Abstract
The Discrete Element Method (DEM) has been used for modelling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range.
Abstract
The Discrete Element Method (DEM) has been used for modelling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear [...]
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A new formulation for air-blast fluid–structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations
Y. Bazilevs, K. Kamran, G. Moutsanidis, D. Benson, E. Oñate

Computational Mechanics (2017). Vol. 60 (1), pp. 83-100; doi: 10.1007/s00466-017-1394-3

Abstract
In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.
Abstract
In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, [...]
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A-posteriori error estimation for the finite point method with applications to compressible flow
E. Ortega, R. Flores, E. Oñate, S. Idelsohn

Computational Mechanics (2017). Vol. 60 (2), pp. 219-233; doi: 10.1007/s00466-017-1402-7

Abstract
An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.
Abstract
An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained [...]
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An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus
M. Kouhi, E. Oñate

Computational Mechanics (2015). Vol. 56 (1), pp. 113-129; doi: 10.1007/s00466-015-1161-2

Abstract
A new implicit stabilized formulation for the numerical solution of the compressible Navier–Stokes equations is presented. The method is based on the finite calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors Kouhi, Oñate (Int J Numer Methods Fluids 74:872–897, 2014). In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier–Stokes equations using an implicit scheme is presented.
Abstract
A new implicit stabilized formulation for the numerical solution of the compressible Navier–Stokes equations is presented. The method is based on the finite calculus [...]
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A unified monolithic approach for multi-fluid flows and fluid–structure interaction using the Particle Finite Element Method with fixed mesh
P. Becker, S. Idelsohn, E. Oñate

Computational Mechanics (2015). Vol. 55 (6), pp. 1091-1104; doi: 10.1007/s00466-014-1107-0

Abstract
This paper describes a strategy to solve multi-fluid and fluid–structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2–2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
Abstract
This paper describes a strategy to solve multi-fluid and fluid–structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) [...]
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Numerically stable formulas for a particle-based explicit exponential integrator
P. Nadukandi, E. Oñate

Computational Mechanics (2015). Vol. 55 (5), pp. 903-920; doi: 10.1007/s00466-015-1142-5

Abstract
Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.
Abstract
Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential [...]
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