Multiscale damage analysis based on the variational effective model

Abstract In the damage analysis of material with complex microstructures, a full‐scale direct numerical simulation (DNS) could produce huge computational costs. Alternatively, multiscale modeling is a more effective method by using less degrees of freedom to balance the calculation accuracy and cost. In this paper, a new multiscale damage modeling method is proposed based on the framework of the variational effective model originally presented by Jezdan et al. and the relaxation damage model presented by Junker et al. A variational statement for the free energy and the dissipation potential for a coarse scale model is constructed by relating the free energy and dissipation potential of the fine scale model. In this way, the coarse scale damage variable is defined instead of directly solving in the fine scale model; therefore, the computational efficiency can be increased. Besides, the relaxation damage model can effectively avoid ill‐posed boundary value problems in damage analysis without use of gradients or integration techniques. Two numerical examples are provided to demonstrate the effectiveness of the proposed method.