{"paper":{"title":"The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part I: A general parameter reduction formula and energy-minimizing microrotations in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Fischle, Patrizio Neff","submitted_at":"2015-07-20T13:09:42Z","abstract_excerpt":"In any geometrically nonlinear quadratic Cosserat-micropolar extended continuum model formulated in the deformation gradient field $F := \\nabla\\varphi: \\Omega \\to \\mathrm{GL}^+(n)$ and the microrotation field $R: \\Omega \\to \\mathrm{SO}(n)$, the shear-stretch energy is necessarily of the form \\begin{equation*} W_{\\mu,\\mu_c}(R\\,;F) := \\mu\\,\\left\\lVert{\\mathrm{sym}(R^T F - \\boldsymbol{1})}\\right\\rVert^2 + \\mu_c\\,\\left\\lVert{\\mathrm{skew}(R^T F - \\boldsymbol{1})}\\right\\rVert^2\\;, \\end{equation*} where $\\mu > 0$ is the Lam\\'e shear modulus and $\\mu_c \\geq 0$ is the Cosserat couple modulus. In the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05480","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"}