6 - The high-fidelity generalized method of cells (HFGMC) micromechanics theory

Abstract

This chapter presents the high-fidelity generalized method of cells (HFGMC) micromechanics theory. By employing a second-order displacement field in the subcells, the method includes shear coupling that is absent in the method of cells, the generalized method of cells, and analytical models like the Mori-Tanaka method. The presence of shear coupling provides HFGMC predictions with higher-fidelity local stress and strain fields and the ability to account for microstructural effects correctly. However, this increased fidelity comes at the cost of computational efficiency and subcell grid independence. HFGMC therefore represents a step further away from fully analytical micromechanics towards the fully numerical finite element method. The HFGMC theory, including thermomechanical effects, is presented, followed by example problems that highlight the theory's capabilities (for example, consideration of different ordered and disordered fiber-packing arrangements and statistical effective property distributions). HFGMC's predictions are compared to those of the previously presented simpler theories as well as the finite element method.