{"paper":{"title":"The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part II: Non-classical energy-minimizing microrotations in 3D and their computational validation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andreas Fischle, Patrizio Neff","submitted_at":"2015-09-21T14:22:44Z","abstract_excerpt":"In any geometrically nonlinear, isotropic and quadratic Cosserat micropolar extended continuum model formulated in the deformation gradient field $F = \\nabla\\varphi : \\Omega \\to GL^+(n)$ and the microrotation field $R: \\Omega \\to SO(n)$, the shear-stretch energy is necessarily of the form\n  $$W_{\\mu,\\mu_c}(R;F) = \\mu\\, \\| sym(R^T F - 1) \\|^2 + \\mu_c\\, \\| skew(R^T F - 1) \\|^2 .$$\n  We aim at the derivation of closed form expressions for the minimizers of $W(R;F)$ in $SO(3)$, i.e., for the set of optimal Cosserat microrotations in dimension $n = 3$, as a function of $F \\in GL^+(n)$. In a previou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06236","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"}