非線形均質化理論における2変数境界値問題のミクローマクロ非連成近似解法

抄録

We propose a new procedure for approximately solving two-scale boundary value problems (BVPs) that can be derived in the framework of mathematical homogenization method for nonlinear heterogeneous solids. Although the micro- and the macroscopic BVPs are strongly coupled in the original algorithm for nonlinear two-scale BVPs, the proposed method enables us to decouple them without losing the distinct features of the two-scale BVP. That is, in this method, the solution for the macroscopic problem still reflects the mechanical behavior characterized for the microscopic one, and vise versa. We carry out representative numerical analyses for the structure with hyperelastic heterogeneous material and that with polycrystalline metal to demonstrate the capability and availability of the proposed method.