{"paper":{"title":"The corotational stability postulate: positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aur\\'elien S. Nguetcho Tchakoutio, Nina J. Husemann, Patrizio Neff, Robert J. Martin, Sergey N. Korobeynikov","submitted_at":"2024-11-19T15:10:11Z","abstract_excerpt":"In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that \\begin{equation*}\n  \\langle\\frac{\\mathrm{D}^{\\circ}}{\\mathrm{D} t}[\\sigma] , D \\rangle > 0 \\quad \\forall \\ D \\in \\text{Sym}(3)\\setminus \\{0\\} \\, , \\end{equation*} where $\\frac{\\mathrm{D}^{\\circ}}{\\mathrm{D} t}$ is any corotational stress rate, $\\sigma$ is the Cauchy stress and $D = \\text{Sym} \\, L$, condition $L= \\dot{F} \\, F^{-1}$ is the deformation rate tensor. For $\\widehat{\\sigma}(\\log V) := \\sigma (V)$ it is equivalent to the monotonicity (TSTS-M$^+$) \\begin{equation*}\n  \\langle \\widehat{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12552","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/2411.12552/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"}