{"paper":{"title":"The Peridynamic Stress Tensors and the Non-local to Local Passage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Petr Pelech","submitted_at":"2017-11-20T14:18:32Z","abstract_excerpt":"We re-examine the notion of stress in peridynamics. Based on the idea of traction we define two new peridynamic stress tensors $\\mathbf{P}^{\\mathbf{y}}$ and $\\mathbf{P}$ which stand, respectively, for analogues of the Cauchy and 1st Piola-Kirchhoff stress tensors from classical elasticity. We show that the tensor $\\mathbf{P}$ differs from the earlier defined peridynamic stress tensor $\\nu$; though their divergence is equal. We address the question of symmetry of the tensor $\\mathbf{P}^{\\mathbf{y}}$ which proves to be symmetric in case of bond-based peridynamics; as opposed to the inverse Piola"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08445","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"}