The High-Fidelity Generalized Method of Cells with arbitrary cell geometry and its relationship to the Parametric Finite-Volume Micromechanics

This contribution is motivated by the recent IJSS article titled “Formulation of the High-Fidelity Generalized Method of Cells with Arbitrary Cell Geometry for Refined Micromechanics and Damage in Composites” by Haj-Ali and Aboudi. In the present discussion, we critically compare these authors’ approach with the Parametric Finite-Volume Direct Averaging Micromechanics (FVDAM) theory developed in a sequence of papers dating to 2004. We show that the extension proposed by Haj-Ali and Aboudi follows the framework of the parametric FVDAM theory, and not the original HFGMC model as claimed. Just as importantly, we demonstrate that the proposed extension is fundamentally flawed as it violates accepted principles which every mechanics theory must satisfy, namely correct reducibility and coordinate frame indifference. Direct comparison of predictions generated by the parametric FVDAM theory, the proposed extension called HFGMC with arbitrary cell geometry and finite-element method demonstrates no need for the extension carried out in the specific manner proposed by Haj-Ali and Aboudi, which in fact produces inferior results.