Formulation of the high-fidelity generalized method of cells with arbitrary cell geometry for refined micromechanics and damage in composites

A new parametric formulation for high-fidelity generalized method of cells (HFGMC) is presented for the micromechanical analysis of multiphase periodic composites. To this end, a linear parametric and geometric mapping is employed to transform arbitrary quadrilateral cell shapes from the physical space to an auxiliary uniform square shapes. A complete quadratic displacement expansion is performed in the mapped space. Thus, a new bilinear term is added to the quadratic displacement expansion; unlike the original HFGMC for regular array of rectangular cells where this term in not required. The continuity of displacements, tractions, together with the periodicity and equilibrium conditions are imposed in the average sense, similar to the original HFGMC formulation, using both the physical and mapping variables. However, the addition of bilinear terms requires the introduction of the first averaged moments of the equilibrium equations. In order to demonstrate the ability the new HFGMC formulation, spatial stress fields are compared with analytical and numerical solutions of circular and elliptical fibers in an infinite medium. Furthermore, two progressive damage methodologies are coupled with the new HFGMC formulation in order to predict the strain softening and elastic degrading behaviors. The first methodology employs a cell extinction approach, while the second uses cohesive interfaces between the cells. Due to the strain softening, both damage methodologies require an iterative solution approach of the governing system nonlinear equations. Damage applications are presented for the transverse loading of composites with square and hexagonal repeating unit-cells (RUC).