Micromechanical Damage Models for Brittle Solids. Part I: Tensile Loadings

Abstract

Three‐dimensional micromechanical anisotropic damage models for microcrack‐weakened brittle solids are presented. The self‐consistent method is employed together with analytical solutions for weakly interacting elliptical microcracks in anisotropic media. The microcrack‐induced inelastic compliances are systematically derived in terms of anisotropic microcrack opening displacements. The sizes, orientations and densities of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of fracture mechanics stability criteria and microcrack geometry within a representative volume element. Thus, the proposed models have constitutive predictive capability. This general framework is then applied to analyze the constitutive behavior of concrete under uniaxial or triaxial tension loading/unloading stress paths. Simple and efficient computational algorithm as well as uniaxial experimental validation are given to illustrate the potential capability of the proposed framework. It is emphasized that no fitted phenomenological material parameter is employed in the proposed damage models.