{"paper":{"title":"Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"primary_cat":"physics.class-ph","authors_text":"Dominik K. Klein, Maximilian P. Wollner, Patrizio Neff","submitted_at":"2026-06-10T16:33:07Z","abstract_excerpt":"We study constitutive conditions of hyperelastic potentials for incompressible material behavior in three dimensions. By means of a counterexample, we show that polyconvexity does not imply true-stress-true-strain monotonicity. Thus, polyconvexity alone is not strong enough to guarantee a physically reasonable response for idealized elasticity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06568","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/2607.06568/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"}