Kinematically Correct Formulation for Two-scale Finite Deformation Problems

Abstract

The finite deformation kinematics for two-scale modeling of heterogeneous media is originally described in this paper based on our own developments of the multi-scale computational strategy. With the help of three-field variational formulation and the convergence results, we derive the kinematically correct formulation for two-scale finite deformation problems and provide a clear distinction between ours and the ones with two-scale asymptotic expansions with rate formulation. Then the tangential homogenization process is naturally arises as a consistent linearization in the context of two-scale modeling. During the course of this development, the notion of two-scale kinematics is required to properly describe the micro-macro coupling behaviors inherent to this kind of modeling strategies. By using a simple numerical example, we explain our basic idea toward the mathematical modeling based on the homogenization theory.