{"paper":{"title":"Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Osterbrink, Johannes Lankeit, Patrizio Neff","submitted_at":"2015-04-29T20:03:35Z","abstract_excerpt":"In this note we extend integrability conditions for the symmetric stretch tensor $U$ in the polar decomposition of the deformation gradient $\\nabla\\varphi=F=R\\,U$ to the non-symmetric case. In doing so we recover integrability conditions for the first Cosserat deformation tensor. Let $F=\\bar R\\,\\bar U$ with $\\bar R:\\Omega\\subset\\mathbb{R}^3\\longrightarrow\\mathrm{SO}(3)$ and $\\bar U:\\Omega\\subset\\mathbb{R}^3\\longrightarrow \\mathrm{GL}(3)$. Then $\\mathfrak{K}:={\\bar R}^T\\mathrm{Grad}\\,{\\bar R}=\\mathrm{Anti}\\Big( \\frac{1}{\\mathrm{det} \\bar U}\\Big[\\bar U(\\mathrm{Curl} \\bar U)^T-\\frac{1}{2} \\mathrm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08003","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":""},"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"}