Homogenization-based multi-scale damage theory

The research of modern mechanics reveals that the damage and failure of structures should be considered on different scales. The present paper is dedicated to establishing the multi-scale damage theory for the nonlinear structural analysis. Starting from the asymptotic expansion based homogenization theory, the multi-scale energy integration is proposed to bridge the gap between the micro and macro scales. By recalling the Helmholtz free energy based damage definition, the damage variable is represented by the multi-scale energy integration. Hence the damage evolution could be numerically simulated on the basis of the unit cell analysis rather than the experimental data identification. Finally the framework of the multi-scale damage theory is established by transforming the multi-scale damage evolution into the conventional continuum damage mechanics. The agree- ment between the simulated results and the benchmark results indicates the validity and effectiveness of the proposed theory.