A new anisotropic elasto-plastic-damage model for quasi-brittle materials using strain energy equivalence

Abstract

An anisotropic elasto-plastic-damage model is developed for quasi-brittle materials within the thermodynamics framework. The anisotropic damage is characterized by second-order damage tensors that are different under tensile and compressive loadings. The hypothesis of strain energy equivalence is adopted with two components, including the hypothesis of elastic strain energy equivalence and the hypothesis of plastic strain energy equivalence. The hypothesis of plastic strain energy equivalence is extended from metals to quasi-brittle materials so as to derive the relations of hardening stresses, which are previously assumed between the undamaged and damaged configurations for quasi-brittle materials. A plastic yield criterion is adopted simultaneously with a damage criterion to account for the coupled elasto-plastic-damage behavior under different loadings. The damage criterion can capture larger axial damage in uniaxial tension and smaller axial damage in uniaxial compression as compared with the lateral damage. The Helmholtz free energy functions are derived for three components: elastic, plastic, and damage. The constitutive laws are derived for three scenarios: the elastoplastic behavior without further damage evolution, the damage behavior without further plasticity evolution, and the coupled elasto-plastic-damage behavior. The anisotropic elasto-plastic-damage model is implemented in ABAQUS as a user material (UMAT) subroutine. The coupled constitutive laws in the continuum domain are implemented in an uncoupled way in the discrete domain with three steps, elastic predictor, plastic corrector, and damage corrector. The UMAT is validated in different conditions, including uniaxial, biaxial, and three-point bending tests. The advantage of considering the plastic free energy in anisotropic damage is illustrated through the strength envelope in biaxial loadings. The numerical results generally agree with experimental results, including the stress-strain curves in uniaxial tests, strength envelope in biaxial tests, and load-deflection curves in three-point bending tests.