VCFEM-Based Two-scale Simulation For Particle Reinforced Polymer

Composites are used more and more widely in the aerospace, automotive and ordnance industries because of their superior properties compared to conventional structural materials. In order to analyze, design and optimize the composites, multi-scale computational models must be introduced to analyze the impact of mesostructure on the macroscopic mechanical properties. Homogenization method is an important means for multi-scale analysis of material properties. It can combine meso-scale with macro-scale to get the macroscopic effective property parameters as well as the microscopic stress and stratin.Homogenization method based on the simple cell model, which is assumed to arrange with periodic, is often employed in traditional research. Actually, different points on the macro-structure of composites may have different microstructure morphology. So more accurate micromechanical models must be developed. VCFEM model can accurately describe the size, shape and random spatial distribution of the microstructure of composites. It can construct a base cell with arbitrary shape as a representative unit of the microstructure features at different points of the macro-structure of composites.This paper combines homogenization method and Voronoi cell finite element method to study the effective mechanical properties of particle reinforced polymer on the macro and meso scale. At the mesoscopic scale, the Voronoi base cell is used to describe the mesostructure. At the same time, the hybrid stress element is used to form the finite element formulation which is based on asymptotic homogenization method and complimentary energy functional. At last, the calculation model of microscopic stress field and the equivalent elastic constants is obtained. At the macroscopic scale, commercial finite element software ANSYS is used to simulate the distribution of macroscopic stress based on the equivalent elastic constants got from microscopic.The program with Visual C++ is made for the microscopic homogenization method based on VCFEM which simulates the micro stress field with stress function of 7 coefficients. We use this program to calculate the equivalent elastic constants of Silica/Epoxy Resin composites where the volume fraction of Silica is 10%. The calculation result is consistent with the literature. The result shows that:the homogenization method based on VCFEM is very practical compared to traditional homogenization method.