{"paper":{"title":"An ellipticity domain for the distortional Hencky-logarithmic strain energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin","submitted_at":"2015-07-27T12:52:34Z","abstract_excerpt":"We describe ellipticity domains for the isochoric elastic energy $ F\\mapsto \\|{\\rm dev}_n\\log U\\|^2=\\bigg\\|\\log \\frac{\\sqrt{F^TF}}{(\\det F)^{1/n}}\\bigg\\|^2 =\\frac{1}{4}\\,\\bigg\\|\\log \\frac{C}{({\\rm det} C)^{1/n}}\\bigg\\|^2 $ for $n=2,3$, where $C=F^TF$ for $F\\in {\\rm GL}^+(n)$. Here, ${\\rm dev}_n\\log {U} =\\log {U}-\\frac{1}{n}\\, {\\rm tr}(\\log {U})\\cdot 1\\!\\!1$ is the deviatoric part of the logarithmic strain tensor $\\log U$. For $n=2$ we identify the maximal ellipticity domain, while for $n=3$ we show that the energy is Legendre-Hadamard elliptic in the set $\\mathcal{E}_3\\bigg(W_{_{\\rm H}}^{\\rm i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07388","kind":"arxiv","version":2},"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"}