{"paper":{"title":"Loss of ellipticity for non-coaxial plastic deformations in additive logarithmic finite strain plasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ionel-Dumitrel Ghiba, Patrizio Neff","submitted_at":"2014-10-08T13:14:53Z","abstract_excerpt":"In this paper we consider the additive logarithmic finite strain plasticity formulation from the view point of loss of ellipticity in elastic unloading. We prove that even if an elastic energy $F\\mapsto W(F)=\\hat{W}(\\log U)$ defined in terms of logarithmic strain $\\log U$, where $U=\\sqrt{F^T\\, F}$, is everywhere rank-one convex as a function of $F$, the new function $F\\mapsto \\widetilde{W}(F)=\\hat{W}(\\log U-\\log U_p)$ need not remain rank-one convex at some given plastic stretch $U_p$ (viz. $E_p^{\\log}:=\\log U_p$). This is in complete contrast to multiplicative plasticity in which $F\\mapsto W("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2819","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}