{"paper":{"title":"The relaxed linear micromorphic continuum: well-posedness of the static problem and relations to the gauge theory of dislocations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Angela Madeo, Ionel-Dumitrel Ghiba, Markus Lazar, Patrizio Neff","submitted_at":"2014-03-13T21:42:09Z","abstract_excerpt":"In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\\in \\mathbb{R}^3$ and the non-symmetric micro-distortion density tensor $P\\in \\mathbb{R}^{3\\times 3}$. In this relaxed theory a symmetric force-stress tensor arises despite the presence of microstructure and the curvature contribution depends solely on the micro-dislocation tensor ${\\rm Curl}\\, P$. However, the relaxed model is able to fully describe rotations of the microstructure and to predict no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3442","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"}