Multi-scale multi-physics analysis for deterioration of quasi-brittle materials involving micro-crack propagations

This paper presents a multi-scale multi-physics analysis method for aged-deterioration of quasi-brittle materials involving micro-crack propagations. The mathematical homogenization method is applied for connecting the different state variables in micro- and macro-scale, and a weakly coupled solution method is employed for the approximation of bi-directional multi-physics phenomena particularly because of micro-crack propagations. We show the formulation of weakly bi-directional coupled problem, based on the homogenization method, between the diffusion of scalar potential and the deformation of solid. In this paper, the diffusion problem is considered as the heat conduction for the sake of simplicity, and the deformation problem involves crack propagations in micro-scale which can be analyzed by the finite cover analysis. After demonstrating the fundamental validity of the method, we present numerical examples of unsteady micro and macro coupled problems, and discuss the applicability of our method to aged-deterioration problems of quasi-brittle materials.