{"paper":{"title":"The exponentiated Hencky-logarithmic strain energy. Improvement of planar polyconvexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ionel-Dumitrel Ghiba, Miroslav Silhavy, Patrizio Neff","submitted_at":"2015-01-27T14:50:27Z","abstract_excerpt":"In this paper we improve the result about the polyconvexity of the energies from the family of isotropic volumetric-isochoric decoupled strain exponentiated Hencky energies defined in the first part of this series, i.e. $$\n  W_{_{\\rm eH}}(F)= \\left\\{\\begin{array}{lll} \\frac{\\mu}{k}\\,e^{k\\,\\|{\\rm dev}_n\\log U\\|^2}+\\frac{\\kappa}{2\\,\\widehat{k}}\\,e^{\\widehat{k}\\,[(\\log {\\rm det} U)]^2}&\\text{if}& {\\rm det}\\, F>0,\\\\ +\\infty &\\text{if} &{\\rm det} F\\leq 0\\,, \\end{array}\\right. $$ where $F=\\nabla \\varphi$ is the gradient of deformation, $U=\\sqrt{F^T F}$ is the right stretch tensor and ${\\rm dev}_n\\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06780","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":""},"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"}