Abstract
The numerical solutions of nonlinear multiscale analyses based on the mathematical homogenization theory are studied in the context of the finite element method (FEM). Since the numerical solutions of the microscopic equilibrium problem are evaluated at each Gauss point in a finite element of the overall structure, the macroscopic mechanical behaviors are considered to depend on its spatial discretization. Such a mesh dependency may come from either the usual discretization errors in FE analyses or the mathematical modeling strategy inherent in the homogenization theory. After the motivation and the viewpoints in this study are explained, we shall carry out several numerical experiments in the framework of the homogenization for elastoplasticity. Together with appropriate error estimates, we examine the reliability of numerical solution of the multiple-scale nonlinear homogenization.
