{"paper":{"title":"The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"David Steigmann, Ionel-Dumitrel Ghiba, Johannes Lankeit, Patrizio Neff, Robert Martin","submitted_at":"2014-08-17T12:16:58Z","abstract_excerpt":"We consider a family of isotropic volumetric-isochoric decoupled strain energies $$ F\\mapsto W_{\\rm eH}(F):=\\widehat{W}_{\\rm eH}(U):=\\left\\{\\begin{array}{lll} \\frac{\\mu}{k}\\,e^{k\\,\\|{\\rm dev}_n\\log {U}\\|^2}+\\frac{\\kappa}{2\\hat{k}}\\,e^{\\hat{k}\\,[{\\rm tr}(\\log U)]^2}&\\text{if}& {\\rm det}\\, F>0,\\\\ +\\infty &\\text{if} &{\\rm det} F\\leq 0, \\end{array}\\right.\\quad $$ based on the Hencky-logarithmic (true, natural) strain tensor $\\log U$, where $\\mu>0$ is the infinitesimal shear modulus, $\\kappa=\\frac{2\\mu+3\\lambda}{3}>0$ is the infinitesimal bulk modulus with $\\lambda$ the first Lam\\'{e} constant, $k,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4430","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"}