Formulation of homogenization method applied to large deformation problem for composite materials

In order to analyze the mechanical behaviors of composite materials under large deformation, the formulation of the homogenization method is described. In this formulation, assuming that the microstructures in a local region of the global structure are deformed uniformly and that consequently the microscopic periodicity remains in the local region under large deformation, the microscopic deformation is precisely defined by the perturbed displacement and product of macroscopic displacement gradient and microscopic coordinates. Finally, microscopic and macroscopic equations are obtained. The above mentioned assumption of the periodicity of microstructures is experimentally validated. The computer program is also developed according to this formulation, and the large deformation is analyzed for the unidirectional fiber reinforced composite material and the knitted fabric composite material.