Abstract
The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite-element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8–6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21–38% reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.
Highlights
The High-Fidelity Generalized Method of Cells (HFGMC) is a micromechanics technique that can be used to simulate nonlinear composite materials [1]
The HFGMC is a micromechanics technique used for modeling heterogeneous materials [1] and is an adaptation of classical homogenization theory [22,23,24]
The High-Fidelity Generalized Method of Cells (HFGMC) global system of n × n equations for doubly periodic repeating unit cells (RUCs) comprised of E-glass fibers and a Nylon 12 matrix was reduced in size through the use of Proper Orthogonal Decomposition with Petrov-Galerkin projection
Summary
The High-Fidelity Generalized Method of Cells (HFGMC) is a micromechanics technique that can be used to simulate nonlinear composite materials [1]. In order to generate an order-reduced model using POD, the full solution to a particular problem (often found by solving a set of simultaneous equations) must be known a priori. The goal of POD is to generate a set of basis vectors capable of capturing the dominant components of a system, optimally represent a full set of equations, and provide a mapping relationship between the unreduced and orderreduced domains In this context, an order-reduced POD approach has two main components: (i) approximation of the solution to a set of equations and (ii) projection to the order-reduced domain. This approach was previously shown to yield significant computational savings when applied to the HFGMC equations for linearly elastic materials only [17]. The order-reduced HFGMC models are compared to the traditional HFGMC approach for multiple RUC discretizations in order to assess their accuracy and computational efficiency
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