Hierarchical rve-based multiscale modeling of nonlinear heterogeneous materials using the finite volume method

This paper describes the development of a hierarchical multiscale procedure within the finite volume (FL) OpenFOAM framework for modeling the mechanical response of nonlinear heterogeneous solid materials. This is a first development of the hierarchical multiscale model for solid mechanics using the FL discretization method. In this computational procedure, the information is passed between the macro-and microscales using representative volume elements (RVEs), allowing for general, nonperiodic microstructures to be considered. An RVE with the prescribed microstructural features is assigned to each computational point. The overall macro response accounts for the microstructural effects through the coupling of macro-and microscales, i.e., the macro deformation gradient is passed to the RVE and, in turn, the homogenized micro stress-strain response is passed back to the macroscale. The incremental total Lagrangian formulation is used to represent the equilibrium state of the solid domain at both scales, and its integral equilibrium equation is discretized using the cell-centered (colocated) FV method in OpenFOAM. The verification of the model is demonstrated using both two-and three-dimensional simulations of perforated elastic-plastic plates subjected to tensile loading.