A field boundary element formulation for damage mechanics

Abstract

In this paper, two typical and representative elastoplastic damage mechanic models are presented in the context of a field boundary element formulation. In particular, the damage models of Lemaitre and Gurson are considered. Lemaitre's model is based on more phenomenological considerations, whereas Gurson's model describes the failure mechanism on a micromechanic level by means of initiation, growth and coalescence of voids. The special requirements of implementing both models into a field boundary element code are investigated. The formulation is based on thermodynamics of irreversible processes and the concept of internal variables. Kinematic and isotropic hardening, isotropic damage evolution and arbitrary uniaxial stress-strain relations are considered to describe the nonlinear material behaviour at small strains. The theoretical background of both models as well as the field boundary element formulation are presented. This includes the evaluation of hypersingular boundary integrals and a consistent regularization of strongly singular domain integrals for arbitratry domain elements. The strain-space formulations of the constitutive equations are presented first in 3D and the applied to 2D examples, in order to demonstrate the validity of the proposed method.