{"paper":{"title":"On deformation-gradient tensors as two-point tensors in curvilinear coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"physics.class-ph","authors_text":"Andrey Melnikov, Michael A. Slawinski","submitted_at":"2018-07-07T02:44:20Z","abstract_excerpt":"We derive a general expression for the deformation-gradient tensor by invoking the standard definition of a gradient of a vector field in curvilinear coordinates. This expression shows the connection between the standard definition of a gradient of a vector field and the deformation gradient tensor in continuum mechanics. We illustrate its application in the context of problems discussed by Ogden [1997]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04624","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"}