Chapter 6 - The High-Fidelity Generalized Method of Cells Micromechanics

Abstract

The High-Fidelity Generalized Method of Cells (HFGMC) micromechanics theory is presented. This method is based on a piecewise quadratic displacement field, whereas the displacement fields in the MOC and GMC are piecewise linear. The result is significantly improved local stress and strain field accuracy in HFGMC compared to GMC, but at the expense of computational efficiency. In addition, HFGMC captures the coupling between the normal and shear fields in the composite, and the results exhibit sensitivity to the level of discretization used in defining the composite repeating unit cell—both of which are absent in GMC. As in the previous chapter that described GMC, triply periodic and doubly periodic derivations of the HFGMC theory are provided, along with a reformulation that improves the computational efficiency of the HFGMC theory. A complete isoparametric formulation of HFGMC, which allows non-orthogonal subcells within an RUC, is also presented. A number of application problems are discussed that illustrate the applicability of the HFGMC micromechanics theory to predicting the linear and nonlinear behavior of unidirectional composites, woven composites, open-cell and lattice block materials, and closed-cell foam materials.