{"paper":{"title":"Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ionel-Dumitrel Ghiba, Jendrik Voss, Patrizio Neff, Robert J. Martin","submitted_at":"2019-03-01T19:39:55Z","abstract_excerpt":"In this note, we provide an explicit formula for computing the quasiconvex envelope of any real-valued function $W\\colon\\operatorname{SL}(2)\\to\\mathbb{R}$ with $W(RF)=W(FR)=W(F)$ for all $F\\in\\operatorname{SL}(2)$ and all $R\\in\\operatorname{SO}(2)$, where $\\operatorname{SL}(2)$ and $\\operatorname{SO}(2)$ denote the special linear group and the special orthogonal group, respectively. In order to obtain our result, we combine earlier work by Dacorogna and Koshigoe on the relaxation of certain conformal planar energy functions with a recent result on the equivalence between polyconvexity and rank"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00508","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"}