{"paper":{"title":"Negative Gaussian curvature from induced metric changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Carl D. Modes, Mark Warner","submitted_at":"2015-02-19T21:26:52Z","abstract_excerpt":"We revisit the light or heat-induced changes in topography of initially flat sheets of solid that elongate or contract along patterned, in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated -- so-called \"anti-cones\". We show that azimuthal material displacements are required for the distorted state to be stretch-free and bend-minimising. The resultant shapes are smooth and aster-like and can become re-entrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, though the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05731","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"}