Smooth Hysteretic Formulation for Damage Modeling

Abstract

A smooth hysteretic formulation for modeling of damage is presented, emanating from damage mechanics and classical theory of plasticity. This generalized smooth, rate-independent three-dimensional (3D) Bouc–Wen type model is intended for nonlinear static and dynamic analysis of structures and is expressed in tensorial form. The hysteretic model embodies the modified von Mises yield criterion that takes into account damage evolution and nonlinear hardening laws. Based on these considerations, elastic finite elements are extended considering the plastic strains as additional hysteretic degrees of freedom together with the variables for damage and isotropic hardening as well as the back-stresses. These variables are considered at the integration points of the finite elements, and their evolution is described by the Bouc–Wen-type equations. The developed hysteretic finite element allows for geometric nonlinear analysis, assuming small strains. Numerical examples are presented, attesting to the generality of the proposed approach as well as the efficacy and accuracy.