Quasi-micromechanical damage model for brittle solids with interacting microcracks

Abstract

The combination of phenomenological and micromechanical damage mechanics is a promising path to construct an applicable damage model with firm physical foundation. In this paper, a quasi-micromechanical model is presented for microcrack-weakened brittle or quasi-brittle materials. The microcracking damage is characterized in terms of the orientation domain of microcrack growth (DMG) as well as a scalar microcrack density parameter. The DMG describes the complex damage and its evolution associated with microcrack growth, while the scalar microcrack density factor defining the isotropic part of damage yields an easy calculation of the effects of microcrack interaction on effective elastic moduli. The conventional methods for estimating the effective moduli of microcracked solids, based on the concept of effective medium or effective field, are formulated in a universal framework. A novel and efficient scheme is suggested to calculate the microcrack interaction effects on the effective elastic moduli in a very convenient manner. Thereby, a quasi-micromechanical model is established to simulate the constitutive response of microcrack-weakened brittle or quasi-brittle materials under complex loading. Considering various micromechanisms of microcracking damage, the overall effective constitutive relation for different stages including linear elasticity, pre-peak non-linear hardening, stress drop and strain softening are expressed in a unified form.