{"paper":{"title":"One-dimensional von K\\'arm\\'an models for elastic ribbons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Freddi, Maria Giovanna Mora, Peter Hornung, Roberto Paroni","submitted_at":"2017-01-10T18:32:53Z","abstract_excerpt":"By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\\'arm\\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found starting from the \"linearized\" von K\\'arm\\'an energy corresponds to that of a linearly elastic beam that can twist but can deform in just one plane; while the model found from the von K\\'arm\\'an energy is a non-linear model that comprises stretching, bendings, and twisting. The \"constrained\" von K\\'arm\\'an energy, instead, leads to a new Sadowsky type of mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02721","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"}