Theoretical Formulation of a Coupled Elastic—Plastic Anisotropic Damage Model for Concrete using the Strain Energy Equivalence Concept

An anisotropic damage constitutive model for concrete is developed within the framework of elastoplasticity and continuum damage mechanics. The transformation from the effective (undamaged) to the damaged configuration in the elastic regime is obtained by using the hypothesis of elastic strain energy equivalence. Damage in plasticity is accounted for by developing a new formulation relating the plastic strains rate tensors in the effective and damaged configurations. Two anisotropic damage criteria are introduced to account for the different concrete behavior effects under tensile and compressive loadings. The total stress is decomposed into tensile and compressive components in order to satisfy these damage criteria. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and will be used simultaneously with the damage criteria. The transformation of stresses from the effective to the damaged configuration is achieved by using a fourth order transformation tensor that is based on second order tensile and compressive damage tensors. Expressions are derived for the elastoplastic tangent operator in the effective and damaged configurations. The formulations are derived consistently based on sound thermodynamic principles.