FEM-Cluster based reduction method for efficient numerical prediction of effective properties of heterogeneous material in nonlinear range

Abstract A novel FEM-Cluster based reduced order method or FEM-Cluster based Analysis method (FCA) which enables efficient numerical prediction of effective properties of heterogeneous material in nonlinear range is proposed. The cluster concept initially presented in the work by WK Liu et al. is introduced and extended to derive a full FEM multi-scale formulation of the Representative Unit Cell (RUC) to circumvent the heavy burden due to huge computational efforts required for a direct numerical simulation (DNS) of the high-fidelity RUC. The proposed FEM-Cluster based reduced order method is formulated in a consistent framework of finite element method. The offline clustering process with construction of the cluster-interaction matrix derived under the assumption of the linear elasticity is carried out by the devised FE procedure of RUC. The online elasto-plastic process is performed by the incremental non-linear FE analysis using the constant cluster-interaction matrix, which plays a role in the present work conceptually similar to the initial elastic modular matrix used in the ”initial stiffness method” for the traditional incremental elasto-plastic analysis. Accurate and efficient numerical prediction of effective properties of heterogeneous material in nonlinear range are developed in a consistent way. The performances of the proposed reduced order model and its numerical implementation are studied and demonstrated. Several numerical examples show its efficiency and applicability.