Elasto-Plastic Analysis of Composite Materials Using the Homogenization Method. 1st Report. Formulation.

Abstract

The homogenization method is applied to the analysis of a composite material whose constituents reveal elastoplastic character as well as finite deformation. Since the updating Lagrangian scheme with rate forms guarantees the linearity of the governing equations, it is possible to use the separation of variables in the two-scale asymptotic expansion of the solution. Furthermore, the updating scheme also enables us to utilize the microscopic stress field, which is obtained in a localization process, in the judgement of plastic failure. A review of the general procedure for the asymptotic homogenization method supports our present discussion. Although the large deformation and small strain are assumed as the mechanical responses of both macro and microscopic structures of a composite, the periodicity assumption is not violated in a local region. Thus the total deformation of the composite can be obtained as accumulation of a series of instantaneous solutions.