A Two-Step Sequential Hyper-Reduction Method for Efficient Concurrent Nonlinear FE² Analyses

In this paper, we propose a two-step sequential hyper-reduction method to significantly enhance computational efficiency for both macro- and micro-level analyses in concurrent nonlinear FE² multiscale simulations. In general, one of the major computational burdens of nonlinear FE² problems is the repetitive micro-level analysis, which must be performed at all integration points of the macroscopic structure. We propose adopting the discrete empirical interpolation method (DEIM) for both macroscopic and microscopic problems, achieving a significant reduction in the number of integration points in both models. The proposed two-step sequential framework aligns with reduced-order modeling, enabling an efficient multiscale procedure for concurrent nonlinear FE² analysis in the online stage. We verified the accuracy and efficiency of FE² analysis using the proposed method through a simple example.