14. The Parametric HFGMC Micromechanics

The parametric high-fidelity generalized method of cells (HFGMC) is thoroughly developed and reviewed starting from the HFGMC formulation with regular array of subcells. The HFGMC is shown to be an effective micromechanical analysis method for linear, nonlinear, and multi-physics problems involving heterogeneous materials with periodic microstructure. This chapter deals with two (2D) and three-dimensional (3D) HFGMC applied for multiphase periodic composites suited for nonlinear and evolving damage. A new average virtual work formulation is also introduced in order to generate a symmetric stiffness matrix formulation for the nonlinear iterative solution of the HFGMC system of equations. This approach allows the application of classical direct iterative solution techniques and tremendously enhances the computational efficiency. A review of noteworthy recent HFGMC applications for composite materials is also given. The HFGMC micromechanics is well suited for integrating the nonlinear and damage response of composites and predicting the fiber-matrix spatial local fields including progressive damage effects.