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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.07388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"90d1a307594d8f686d6b3517dcb11e2f145d06eaf3a716b0900250147e96fbb8","abstract_canon_sha256":"9c83b6333a40d087b144789ce8bbc77d0d76c2fd4e6e7810ef564f7042b7e018"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:45.725474Z","signature_b64":"YI5zSjb5HpPMCTQM+QFfdCipu9b223TNK+tyZinLjiiaC6HX5qBQW1zrnpwxjuKeFdO9BUETPwhOs5QCG/9dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","last_reissued_at":"2026-05-18T01:20:45.724759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:45.724759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\log U$. 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