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== Abstract ==
 
== Abstract ==
  
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Este artículo presenta formulaciones mixtas no lineales para simular el proceso de falla de materiales en sólidos mediante sus aproximaciones con elementos finitos. Las formulaciones presentadas son las correspondientes al trabajo virtual producido por los desplazamientos y esfuerzos virtuales y al trabajo virtual producido por los desplazamientos y deformaciones virtuales. Ambas formulaciones se derivan del trabajo virtual que incluye cuatro variables independientes. El comportamiento de los materiales se determina por un modelo de daño isotrópico continuo, el cual requiere de dos variables internas en cada punto de integración. En la implementación numérica, la aproximación desplazamiento-esfuerzo presenta problemas numéricos cuando el comportamiento del material se aproxima al daño total, por lo que solamente la formulación desplazamiento-deformación fue implementada. Se discuten las ventajas de la aproximación desplazamiento- deformación sobre una formulación típica de desplazamientos para simular el proceso de falla de materiales con modelos de daño como localización de deformaciones. Para mostrar la validez e ilustrar la efectividad de la formulación desplazamiento-deformación, se presentan los resultados de algunos ejemplos numéricos representativos. Summary This paper presents nonlinear mixed formulations to simulate the material failure process in solids by its finite element approximation. The formulations presented are the corresponding virtual work by the virtual stresses and displacements and the virtual work by displacements and strains. Both formulations presented are derived from the principle of virtual work with four independent variables. The beha- viour of the material is governed by an isotropic continuum damage model equipped with two internal variables at each integration point. In the numerical implementation, the displacement-stress formulation presents numerical problems when the behaviour of the material approaches complete damage, thus only the displacement-strain formulation was implemented. The advantage of the strain-displacement over a typical displacement formulation to simulate the material failure process with damage models as strain concentrations is discussed. To show the validity and illustrate the effectiveness of the displacement-strain formulation, results from some representative numerical examples are presented and discussed within the framework of continuum approximations.
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This paper presents nonlinear mixed formulations to simulate the material failure process in solids by its finite element approximation. The formulations presented are the corresponding virtual work by the virtual stresses and displacements and the virtual work by displacements and strains. Both formulations presented are derived from the principle of virtual work with four independent variables. The beha- viour of the material is governed by an isotropic continuum damage model equipped with two internal variables at each integration point. In the numerical implementation, the displacement-stress formulation presents numerical problems when the behaviour of the material approaches complete damage, thus only the displacement-strain formulation was implemented. The advantage of the strain-displacement over a typical displacement formulation to simulate the material failure process with damage models as strain concentrations is discussed. To show the validity and illustrate the effectiveness of the displacement-strain formulation, results from some representative numerical examples are presented and discussed within the framework of continuum approximations.
  
 
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== Full document ==
 
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Latest revision as of 10:56, 14 June 2017

Abstract

This paper presents nonlinear mixed formulations to simulate the material failure process in solids by its finite element approximation. The formulations presented are the corresponding virtual work by the virtual stresses and displacements and the virtual work by displacements and strains. Both formulations presented are derived from the principle of virtual work with four independent variables. The beha- viour of the material is governed by an isotropic continuum damage model equipped with two internal variables at each integration point. In the numerical implementation, the displacement-stress formulation presents numerical problems when the behaviour of the material approaches complete damage, thus only the displacement-strain formulation was implemented. The advantage of the strain-displacement over a typical displacement formulation to simulate the material failure process with damage models as strain concentrations is discussed. To show the validity and illustrate the effectiveness of the displacement-strain formulation, results from some representative numerical examples are presented and discussed within the framework of continuum approximations.

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Published on 01/07/10
Accepted on 01/07/10
Submitted on 01/07/10

Volume 26, Issue 3, 2010
Licence: CC BY-NC-SA license

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