{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:U2TXMNSWIA4Q5WONEYK4O2GHLY","short_pith_number":"pith:U2TXMNSW","schema_version":"1.0","canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","source":{"kind":"arxiv","id":"1110.4796","version":2},"attestation_state":"computed","paper":{"title":"The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP)","submitted_at":"2011-10-21T14:03:53Z","abstract_excerpt":"Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution $u$ of a Neumann problem near a crack in dimension 2. We consider non smooth cracks $K$ that are merely closed and connected. At any point of density 1/2 in $K$, we show that the blow-up limit of $u$ is the usual \"cracktip\" function $\\sqrt{r}\\sin(\\theta/2)$, with a well-defined coefficient (the \"stress intensity factor\" or SIF). The method relies on Bonnet's monotonicity formula \\cite{b} together with $\\Gamma$-convergence techniques."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1110.4796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"226e0ee0a341b8e48cbcb2868e932a76b7530da82529b8e378953f8bbd0e44a6","abstract_canon_sha256":"4d222d7eb544fb2848e1175868cf44216857411fdc6df8ff9bc09d1740a8171d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.064659Z","signature_b64":"uS7J407RCpf8OxprqH2GJtriYpg7SyPXr+FN8NfmtMvqVgZqEPYJkbKy3WoCzXXbO6L0k8/LDjhy8QIanzCtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","last_reissued_at":"2026-05-18T04:07:05.063975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.063975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP)","submitted_at":"2011-10-21T14:03:53Z","abstract_excerpt":"Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution $u$ of a Neumann problem near a crack in dimension 2. We consider non smooth cracks $K$ that are merely closed and connected. At any point of density 1/2 in $K$, we show that the blow-up limit of $u$ is the usual \"cracktip\" function $\\sqrt{r}\\sin(\\theta/2)$, with a well-defined coefficient (the \"stress intensity factor\" or SIF). The method relies on Bonnet's monotonicity formula \\cite{b} together with $\\Gamma$-convergence techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4796","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1110.4796","created_at":"2026-05-18T04:07:05.064097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.4796v2","created_at":"2026-05-18T04:07:05.064097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4796","created_at":"2026-05-18T04:07:05.064097+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2TXMNSWIA4Q","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2TXMNSWIA4Q5WON","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2TXMNSW","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY","json":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY.json","graph_json":"https://pith.science/api/pith-number/U2TXMNSWIA4Q5WONEYK4O2GHLY/graph.json","events_json":"https://pith.science/api/pith-number/U2TXMNSWIA4Q5WONEYK4O2GHLY/events.json","paper":"https://pith.science/paper/U2TXMNSW"},"agent_actions":{"view_html":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY","download_json":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY.json","view_paper":"https://pith.science/paper/U2TXMNSW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.4796&json=true","fetch_graph":"https://pith.science/api/pith-number/U2TXMNSWIA4Q5WONEYK4O2GHLY/graph.json","fetch_events":"https://pith.science/api/pith-number/U2TXMNSWIA4Q5WONEYK4O2GHLY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/action/storage_attestation","attest_author":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/action/author_attestation","sign_citation":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/action/citation_signature","submit_replication":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/action/replication_record"}},"created_at":"2026-05-18T04:07:05.064097+00:00","updated_at":"2026-05-18T04:07:05.064097+00:00"}