{"paper":{"title":"On the variational limits of lattice energies on prestrained elastic bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marta Lewicka, Pablo Ochoa","submitted_at":"2014-03-06T22:31:40Z","abstract_excerpt":"We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\\Omega$. When the mesh size of the discrete lattice in $\\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1611","kind":"arxiv","version":2},"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"}