Two-scale Modeling of Composites damage with Voronoi cell finite element method for microscale computation

Abstract

This paper develops an adaptive two-level computational model that includes macro and microscope analysis. Traditional displacement based finite element is used for macroscopic analysis, while Voronoi cell finite element model is used for computations of arbitrary heterogeneous domains. For an adaptive analysis, when local area may be destructive, VCFEM mesh is used instead of corresponding finite element for damage analysis. Because VCFEM model and finite element are all taken the nodal displacements as field variables, therefore, based on the idea of multigrid by the adaptive mesh adjustment, let finite element edge length and VCFEM edge length are basically the same, two kinds of elements were connected together through the use of shared nodes and use the order of the edge displacement interpolation. This formed a two-scale model of the coexistence of macro structure and micro structure. For microscale analysis, three Voronoi cell finite models (VCFEM) are build including perfect interface bonding model, interface debonding model and multiple matrix cracks model. Numerical example is executed for validating the effectiveness of the two-scale model method.