Rapid Prediction of Nonlinear Effective Properties of Complex Microstructure Lattice Materials

Lattice materials are renowned for their exceptional mechanical performance and transformative potential for aerospace and structural engineering applications. However, current research primarily focuses on the effective elastic properties of lattice microstructures, whereas there are few studies on the prediction of their effective nonlinear properties, thus limiting the practical application of lattice materials. In addition, the characterization of complex micro structured lattice materials often requires the generation of many elements and performing nonlinear finite element analysis, which involves high computational costs. To address these challenges and enable the efficient prediction of the nonlinear effective properties of complex lattice microstructures in heterogeneous materials, the FEM-Cluster-based Analysis (FCA) approach is proposed. In the offline phase, a reduced-order model and offline database are established. In the online phase, the principle of the cluster minimum complementary energy incremental algorithm is used to rapidly predict the nonlinear effective properties of heterogeneous materials. This method is applied to conduct extensive comparisons with direct numerical simulation across two-dimensional and three-dimensional lattice materials to demonstrate that FCA can achieve similar accuracy while significantly enhancing computational efficiency, thereby offering promising potential for optimizing lattice material design in structural applications.