{"paper":{"title":"Plates with incompatible prestrain of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Annie Raoult, Diego Ricciotti, Marta Lewicka","submitted_at":"2015-03-30T20:31:12Z","abstract_excerpt":"We study the effective elastic behaviour of the incompatibly prestrained thin plates, characterized by a Riemann metric $G$ on the reference configuration. We assume that the prestrain is \"weak\", i.e. it induces scaling of the incompatible elastic energy $E^h$ of order less than $h^2$ in terms of the plate's thickness $h$.\n  We essentially prove two results. First, we establish the $\\Gamma$-limit of the scaled energies $h^{-4}E^h$ and show that it consists of a von K\\'arm\\'an-like energy, given in terms of the first order infinitesimal isometries and of the admissible strains on the surface is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08845","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"}