Fast effective strength prediction of heterogeneous materials by FCA-based basis reduction method and periodic Green’s function

Abstract

The effective strength prediction of heterogeneous materials under varying loading conditions is crucial but highly challenging, especially considering the stress redistribution during repeated loading and unloading. The data-driven FEM-Cluster based Analysis basis reduction method for Shakedown Analysis (FCA-SA) has been proven to be an efficient approach. Based on the clustering idea, this method divides elements of the Representative Volume Element (RVE) with similar mechanical response into clusters to construct the reduced-order model (ROM) of RVE, and applies cluster eigenstrains on ROM to obtain cluster-based self-equilibrium element stress (SEES) bases for shakedown analysis. However, construction of the cluster-based SEES bases needs multiple time-consuming FEM analysis if the number of clusters is large. To address this issue, this paper proposes a novel method that utilizes the FCA-based Green’s function, which relates the stress at a point on homogeneous materials and the eigenstrain at periodically distributed points for fast constructing cluster-based SEES bases for RVE of heterogeneous materials. To justify the method, we first show that for the given discretized FE model of RVE, the SEES bases obtained under one material distribution remain valid after the material distribution changes. Further, the cluster-based SEES space of homogeneous materials is demonstrated to be an effective approximation to the cluster-based SEES space of heterogeneous materials. Thus, the analytical expression of FCA-based Green’s function is employed to efficiently construct cluster-based SEES bases of heterogeneous material. Combined with FCA-SA, this method enables the effective strength surface of 2D and 3D heterogeneous materials to be accurately predicted under different proportional loading conditions. Compared to our unmodified method, the computational efficiency of the SEES bases has been improved by an average of two orders of magnitude. Numerical examples demonstrate the effectiveness and efficiency of the proposed method.