Three-dimensional micromechanical model for quasi-brittle solids with residual strains under tension

Presented in this paper is a three-dimensional micromechanical model that enables the simulation of microcrack-weakened quasi-brittle materials with permanent residual strains subjected to tension. The microcracking damage of such a material is described by the concept of domain of microcrack growth. It is thought that the occurrence of residual strains is attributable to two reasons, namely, the release of microscopic residual stresses due to microcracking and the microscopic plastic deformation along microcrack front edges. By introducing the analytical results of the two physical mechanisms into the constitutive relation, a micromechanical damage model is established to describe the effective response of microcrack-weakened quasi-brittle materials such as ceramics and concrete under complex loading/unloading paths. The response of such a material is divided into four stages, namely, the stages of linear elasticity, pre-peak nonlinearity, post-peak stress drop, and strain softening before macroscopic fracture.