A variational effective model for multiscale damage analysis

In the damage analysis of material with complex microstructures, a direct numerical simulation (DNS) could produce huge computational costs. Alternatively, the multiscale modeling is a more effective method by using less degrees of freedom to balance the computational accuracy and cost. In this paper, a new multiscale method for damage analysis is proposed based on the framework of the variational effective model for elastoplastic problems originally presented in author’s previous work. The key idea is to construct variational statement for the free energy and the dissipation potential of a coarse scale model by relating the free energy and the dissipation potential of a fine scale model. In this way, the damage evolution can be directly simulated at the coarse scale solution, resulting in significantly higher computational efficiency compared to the DNS in fine scale. Compared with previous work, a new multiscale computational scheme is derived for damage evolution. In addition, the relaxation damage model is used to effectively avoid ill-posed boundary value problems in damage analysis without using gradient enhanced or integration techniques. Four numerical examples demonstrate the effectiveness of the proposed method in both 2D and 3D problems by comparing its computational accuracy and cost with reference solutions from DNS and FE 2 algorithm.