{"paper":{"title":"Hypo-elasticity, Cauchy-elasticity, corotational stability and monotonicity in the logarithmic strain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Adam Sky, Davide Bernardini, Ionel-Dumitrel Ghiba, Marco Valerio D'Agostino, Patrizio Neff, Robert J. Martin, Sebastian Holthausen","submitted_at":"2024-09-30T07:56:15Z","abstract_excerpt":"We combine the rate-formulation for the objective, corotational Zaremba-Jaumann rate\n  \\begin{align}\n  \\frac{{\\rm D}^{\\rm ZJ}}{{\\rm D} t} [\\sigma] = \\mathbb{H}^{\\rm ZJ}(\\sigma).D, \\qquad D = {\\rm sym} {\\rm D} v\\,,\n  \\end{align} operating on the Cauchy stress $\\sigma$, the Eulerian strain rate $D$ and the spatial velocity $v$ with the novel \\enquote{corotational stability postulate} (CSP)\\begin{equation}\n  \\Bigl\\langle \\frac{{\\rm D}^{\\rm ZJ}}{{\\rm D} t}[\\sigma], D \\Bigr\\rangle > 0 \\qquad \\forall \\, D\\in{\\rm Sym}(3)\\setminus\\{0\\} \\end{equation} to show that for a given isotropic Cauchy-elastic c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.20051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}