Fully implicit formulation of elastoplastic homogenization problem for two-scale analysis

In this study, using a virtual work equation, a micro-/macro-kinematic relation and a linearized constitutive relation, a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two-scale analysis. It is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells, and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields. The computational algorithm developed is then examined by performing a two-scale analysis of a holed plate with an elastoplastic micro-structure, subjected to tensile loading. This demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells.