Copyright © 2010 SciRes. ENG Isotropic Elastoplasticity Fully Coupled with Non-Local Damage

This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equivalence hypothesis, fully coupled constitutive equations are used to describe the non local damage in-duced softening leading to a mesh independent solution. An additional partial differential equation governing the evolution of the non local isotropic damage is added to the classical equilibrium equations and associated weak forms derived. This leads to discretized IBVP governed by two algebric systems. The first one, associ-ated with equilibrium equations, is highly non linear and can be solved by an iterative Newton Raphson method. The second one, related to the non local damage, is a linear algebric system and can be solved di-rectly to compute the non local damage variable at each load increment. Two fields, linear interpolation tri-angular element with additional degree of freedom is terms of the non local damage variable D is con-structed. The non local damage variable D is then transferred from mesh nodes to the quadrature (or Gauss) points to affect strongly the elastoplastic behavior. Two simple 2D examples are worked out in order to in-vestigate the ability of proposed approach to deliver a mesh independent solution in the softening stage