{"paper":{"title":"Adaptive isogeometric analysis of high-order phase-field fracture based on THB-splines","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"THB-splines enable adaptive high-order phase-field fracture simulations in 2D while cutting computational cost.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"A. Reali, H.M. Verhelst, L. Greco","submitted_at":"2026-02-25T08:38:29Z","abstract_excerpt":"In recent decades, the study of fracture propagation in solids has increasingly relied on phase-field models. Several recent contributions have highlighted the potential of this approach in both static and dynamic frameworks. However, a major limitation remains the high computational cost. Two main strategies have been identified to mitigate this issue: the use of locally refined meshes and the adoption of higher-order models. In this work, leveraging Truncated Hierarchical B-splines (THB-splines), we introduce adaptive simulations of higher-order phase-field formulations (AT1 and AT2), focusi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Leveraging Truncated Hierarchical B-splines (THB-splines), we introduce adaptive simulations of higher-order phase-field formulations (AT1 and AT2), focusing primarily on two-dimensional fracture problems.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That THB-splines combined with high-order phase-field models will deliver substantial computational savings while preserving the accuracy of fracture path predictions in the adaptive setting.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Adaptive THB-spline isogeometric analysis enables efficient higher-order phase-field fracture simulations in two dimensions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"THB-splines enable adaptive high-order phase-field fracture simulations in 2D while cutting computational cost.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8d98c0a4119a78333b6b77a789881bd06004604596dc4923c6a74a8e686bfaa2"},"source":{"id":"2602.21685","kind":"arxiv","version":2},"verdict":{"id":"b9f9a051-7e1e-4093-b2a5-85faa860b2b7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T19:44:09.734893Z","strongest_claim":"Leveraging Truncated Hierarchical B-splines (THB-splines), we introduce adaptive simulations of higher-order phase-field formulations (AT1 and AT2), focusing primarily on two-dimensional fracture problems.","one_line_summary":"Adaptive THB-spline isogeometric analysis enables efficient higher-order phase-field fracture simulations in two dimensions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That THB-splines combined with high-order phase-field models will deliver substantial computational savings while preserving the accuracy of fracture path predictions in the adaptive setting.","pith_extraction_headline":"THB-splines enable adaptive high-order phase-field fracture simulations in 2D while cutting computational cost."},"references":{"count":48,"sample":[{"doi":"","year":1921,"title":"A. A. Griffith, G. I. Taylor, Vi. the phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Char","work_id":"7f69bfc5-0849-4a4a-8215-315626fa3761","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1957,"title":"G. R. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate (1957)","work_id":"c69863a5-4b3e-40a8-8222-016c9cff6150","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1983,"title":"R. P. Reed, The economic effects of fracture in the United States, volume 647, US Department of Commerce, National Bureau of Standards, 1983","work_id":"2e73fc50-8cf3-45d3-9697-be0611d84974","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"T. Belytschko, T. Black, Elastic crack growth in finite elements with minimal remeshing, International journal for numerical methods in engineering 45 (1999) 601–620","work_id":"29801f19-5bcc-4557-8798-56f28d8a9f4f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"B. Bourdin, G. Francfort, J.-J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids 48 (2000) 797–826","work_id":"6ed28ef8-5195-466e-9ad5-1eae2ab88f79","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":48,"snapshot_sha256":"881eead9fc4f3e887f9d796cd95d2d8532e7063fb02c31ebaded176cf4f184f7","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8b4bc66396cb101fe7c9ea64d3a793632105cbdaa1503cf16c43890a40454965"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}