Multiscale modeling of heterogeneous material undergoing strain softening poses computational challenges for localization of the microstructure, material instability in the macrostructure, and the computational requirement for accurate and efficient concurrent calculation. In the paper, a stable micro-damage homogenization algorithm is presented which removes the material instability issues in the microstructure with representative volume elements (RVE) that are not sensitive to size when computing the homogenized stress–strain response.
The proposed concurrent simulation framework allows the computation of the macroscopic response to explicitly consider the behavior of the separate constituents (material phases), as well as the complex microstructural morphology. A non-local material length parameter is introduced in the macroscale model, which will control the width of the damage bands and prevent material instability.
The self-consistent clustering analysis (SCA) recently proposed by Liu et al. provides an effective way of developing a microstructural database based on a clustering algorithm and the Lippmann–Schwinger integral equation, which enables an efficient and accurate prediction of nonlinear material response. The self-consistent clustering analysis is further generalized to consider complex loading paths through the projection of the effective stiffness tensor. In the concurrent simulation, the predicted macroscale strain localization is observed to be sensitive to the combination of microscale constituents, showing the unique capability of the SCA microstructural database for complex material simulations.