Computationally efficient High-Fidelity Generalized Method of Cells micromechanics via order-reduction techniques

Abstract

The High-Fidelity Generalized Method of Cells (HFGMC) is a powerful technique for simulating composite materials. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for accurate determination of the subcell stress/strain fields. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic RUCs was reduced in size through the use of Proper Orthogonal Decomposition. Accurate order-reduced HFGMC models were then implemented within a special-purpose finite element user material subroutine and used to perform multiscale composite analyses. A number of cases were presented that demonstrate the computational feasibility of using order-reduction techniques to solve solid mechanics problems with complex microstructures. By simulating composite materials in a more computationally efficient manner, a pathway forward is presented for performing high-fidelity multiscale analyses of composite structures.