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The computational cost of micromechanics for heterogeneous materials can bereduced in certain cases where symmetric boundary conditions are applicable. Wederived an eighth symmetric formulation of the Generalized Method of Cells fortriply periodic microstructures. During this endeavor, an inherent symmetry wasdiscovered. This implied that all repeating unit cells may be quarter symmetricrepresentations of other microstructures. Additionally, it was discovered thata repeating unit cell can have columns of subcells swapped with no changes tothe local or global fields. We concluded that first-order micromechanics arenot well suited for capturing detailed or complex microstructures; however,higher-order theories, such as High Fidelity Generalized Method of Cells, canadequately model these microstructures.

Inherent Symmetry and Microstructure Ambiguity in Micromechanics