Anisotropic Elastic-Brittle-Damage and Fracture Models Based on Irreversible Thermodynamics

Abstract

Anisotropic damage evolution and crack propagation in elastic-brittle materials is analyzed by the concepts of Continuum Damage Mechanics (CDM) and Finite Element Method FEM (ABAQUS). The original total formulation of the Murakami-Kamiya (MK) model of elastic-damage material is extended and used for damage anisotropy and fracture prediction in concrete. The incremental formulation of the stress-strain equations is developed by the use of the tangent elastic-damage stiffness. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The Local Approach to Fracture (LAF) by FEM is applied to both the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modeled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress-strain curves are reached. Another way to model crack consists in releasing of the kinematic constrains in the nodes. The developed constitutive model is capable of capturing anisotropic damage evolution and crack growth in 2D structure subjected to the quasistatic or cyclic mechanical or thermal loadings. Different damage evolution in tension or compression, as well as the corresponding fracture modes may be analysed.