{"paper":{"title":"A constitutive condition for idealized isotropic Cauchy elasticity involving 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":"2024-09-03T11:45:16Z","abstract_excerpt":"Following Hill and Leblond, the aim of our work is to show, for isotropic nonlinear elasticity, a relation between the corotational Zaremba-Jaumann objective derivative of the Cauchy stress $\\sigma$, i.e.\n  \\begin{equation}\n  \\frac{{\\rm D}^{\\rm ZJ}}{{\\rm D} t}[\\sigma] = \\frac{{\\rm d}}{{\\rm d}{t}}[\\sigma] - W \\, \\sigma + \\sigma \\, W, \\qquad W = {\\rm skew}(\\dot F \\, F^{-1})\n  \\end{equation} and a constitutive requirement involving the logarithmic strain tensor. Given the deformation tensor $F ={\\rm D} \\varphi$, the left Cauchy-Green tensor $B = F \\, F^T$, and the strain-rate tensor $D = {\\rm sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01811","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/2409.01811/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"}