{"paper":{"title":"Mean field homogenization schemes for composites with prolate and oblate spheroids: use of the orientation tensors and computation of the strain second-moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Antoine Martin (IRESNE)","submitted_at":"2026-07-10T09:02:35Z","abstract_excerpt":"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 t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09213","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09213/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}