{"paper":{"title":"The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ionel-Dumitrel Ghiba, Jendrik Voss, Oliver Sander, Patrizio Neff, Robert J. Martin","submitted_at":"2018-12-31T22:28:27Z","abstract_excerpt":"We consider conformally invariant energies $W$ on the group $\\operatorname{GL}^+(2)$ of $2\\times2$-matrices with positive determinant, i.e. $W\\colon\\operatorname{GL}^+(2)\\to\\mathbb{R}$ such that \\[W(AFB) = W(F) \\qquad\\text{for all }\\; A,B\\in\\{aR\\in\\operatorname{GL}^+(2) \\,|\\, a\\in(0,\\infty)\\,,\\; R\\in\\operatorname{SO}(2)\\}\\,,\\] where $\\operatorname{SO}(2)$ denotes the special orthogonal group, and provide an explicit formula for the (notoriously difficult to compute) quasiconvex envelope of these functions. Our results, which are based on the representation $W(F)=h(\\frac{\\lambda_1}{\\lambda_2})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00058","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"}