In this study, we focus on the modeling of solid structures that include microstructures observed in particle-dispersed composites. The finite element modeling can be used to clarify how the macroscopic behaviors of solid structures are influenced by the microstructures. In such a case, if the whole structure including the microstructures is modeled by the finite elements, an enormous number of finite elements and enormous amount of computational time are required. To overcome such difficulties, we propose a new method for modeling microstructures. In this method, an explicit form of the stress-strain relation covering both elastic and elastic-plastic regions is derived from the equivalent inclusion method proposed by Eshelby that provides mathematical solutions for stress and strain at an arbitrary point inside and outside the inclusion. The derived elastic-plastic constitutive equation takes account of the microstructures, so that the effect of microstructures on the macroscopic behaviors can be obtained from the conventional finite element method by using such a constitutive equation without modeling microstructures in the finite element analysis. The effectiveness of the proposed constitutive equation is verified for a simple problem by comparing the results of the one-element finite element analyses using the proposed constitutive equation with those of the detailed finite element analyses using multi-element finite element modeling.
Quantum Finite Elements for Lattice Field Theory