MULTIPLE SCALE ANALYSIS OF HETEROGENEOUS ELASTIC STRUCTURES USING HOMOGENIZATION THEORY AND VORONOI CELL FINITE-ELEMENT METHOD

This paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with Voronoi cell finite element method (VCFEM) for microstructural modeling. The Voronoi cell finite element model originates from Dirichlet tessellation of a representative material element or a base cell in the microstructure. Homogenized material coefficients for a global displacement finite element model are generated by VCFEM analysis using periodic boundary conditions on the base cell. Following the macroscopic analysis, the local VCFEM analysis is implemented to depict the true evolution of microstructural stresses and strains. Various numerical examples are executed for validating the effectiveness of VCFEM macro-micro modeling of elastic materials. The effect of size, shape, orientation and distribution of heterogeneities on the local and global response are examined.