{"paper":{"title":"A natural requirement for objective corotational rates -- on structure preserving corotational rates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin, Sebastian Holthause, Sergey N. Korobeynikov","submitted_at":"2024-09-29T13:50:56Z","abstract_excerpt":"We investigate objective corotational rates satisfying an additional, physically plausible assumption. More precisely, we require for \\begin{equation*} \\frac{{\\rm D}^{\\circ}}{{\\rm D} t}[B] = \\mathbb{A}^{\\circ}(B).D \\end{equation*} that $\\mathbb{A}^{\\circ}(B)$ is positive definite. Here, $B = F \\, F^T$ is the left Cauchy-Green tensor, $\\frac{{\\rm D}^{\\circ}}{{\\rm D}t}$ is a specific objective corotational rate, $D = {\\rm sym} \\, {\\rm D} v$ is the Eulerian stretching and $\\mathbb{A}^{\\circ}(B)$ is the corresponding induced fourth order tangent stiffness tensor. Well known corotational rates like"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.19707","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/2409.19707/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"}