{"paper":{"title":"Geometry of logarithmic strain measures in solid mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bernhard Eidel, Patrizio Neff, Robert J. Martin","submitted_at":"2015-05-08T22:38:46Z","abstract_excerpt":"We consider the two logarithmic strain measures\\[\\omega_{\\rm iso}=\\|\\mathrm{dev}_n\\log U\\|=\\|\\mathrm{dev}_n\\log \\sqrt{F^TF}\\|\\quad\\text{ and }\\quad \\omega_{\\rm vol}=|\\mathrm{tr}(\\log U)|=|\\mathrm{tr}(\\log\\sqrt{F^TF})|\\,,\\]which are isotropic invariants of the Hencky strain tensor $\\log U$, and show that they can be uniquely characterized by purely geometric methods based on the geodesic distance on the general linear group $\\mathrm{GL}(n)$. Here, $F$ is the deformation gradient, $U=\\sqrt{F^TF}$ is the right Biot-stretch tensor, $\\log$ denotes the principal matrix logarithm, $\\|.\\|$ is the Frob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02203","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"}