Mean field homogenization schemes for composites with prolate and oblate spheroids: use of the orientation tensors and computation of the strain second-moments

Antoine Martin

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arXiv · 2607.09213

Mean field homogenization schemes for composites with prolate and oblate spheroids: use of the orientation tensors and computation of the strain second-moments

Antoine Martin

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Abstract

In this document we provide the homogenized stiffnesses from Mori-Tanaka scheme and Ponte-Casta{\~n}eda and Willis scheme applied to composites with spheroidal inclusions. The inclusions can be prolate spheroids ('fibers') or oblate spheroids ('penny-shapes'). We show how to compute the homogenized stiffnesses for particular distribution of spheroid orientations, using the second-order and fourth-order orientation tensors. We also provide formulas to compute the derivatives of these quantities w.r.t. the material parameters, which is of particular interest for computing the second-moments of the strains.

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Antoine Martin. 2026-07-10. Mean field homogenization schemes for composites with prolate and oblate spheroids: use of the orientation tensors and computation of the strain second-moments. https://arxiv.org/abs/2607.09213

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