Computationally efficient solution of the High-Fidelity Generalized Method of cells micromechanics relations
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Copyright 2015 by DEStech Publications, Inc. and American Society for Composites. All rights reserved. The High-Fidelity Generalized Method of Cells (HFGMC) is a powerful technique for simulating composite materials and is based on Aboudi's method of cells micromechanics theories. Unlike the original generalized method of cells, the HFGMC uses a higher order approximation for the subcell displacement field. Although this allows for a more accurate determination of the subcell stress/strain fields, the solution to the simultaneous set of equations can become computationally burdensome. In order to overcome expensive computational costs associated with solving large systems of equations, order-reduction techniques have been developed to approximate the solution with an acceptable error. These techniques are widely used in the computational fluid dynamics community and are increasingly being implemented for solving solid mechanics problems involving the finite element method. In this study, the HFGMC global system of equations for doubly-periodic RUCs was reduced in size through the use of Proper Orthogonal Decomposition (POD) with Galerkin projection. Order-reduced models were then implemented within an ABAQUS UMAT and used to perform multiscale analyses. A number of cases were presented that show the computational feasibility of using order-reduction techniques to solve the HFGMC set of simultaneous equations. By simulating composite materials in a more computationally efficient manner, a pathway forward is presented for performing multiscale analyses of composite structures consistent with the Airframe Digital Twin concept.
