Pith Number

pith:ZQGBBKRQ

pith:2026:ZQGBBKRQAPEVD6NKORE45PC3P2

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Adaptive isogeometric analysis of high-order phase-field fracture based on THB-splines

A. Reali, H.M. Verhelst, L. Greco

THB-splines enable adaptive high-order phase-field fracture simulations in 2D while cutting computational cost.

arxiv:2602.21685 v2 · 2026-02-25 · math.NA · cs.NA

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Claims

C1strongest 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.

C2weakest 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.

C3one line summary

Adaptive THB-spline isogeometric analysis enables efficient higher-order phase-field fracture simulations in two dimensions.

References

48 extracted · 48 resolved · 0 Pith anchors

[1] 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 1921

[2] G. R. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate (1957) 1957

[3] R. P. Reed, The economic effects of fracture in the United States, volume 647, US Department of Commerce, National Bureau of Standards, 1983 1983

[4] T. Belytschko, T. Black, Elastic crack growth in finite elements with minimal remeshing, International journal for numerical methods in engineering 45 (1999) 601–620 1999

[5] 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 2000

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:23.388994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc0c10aa3003c951f9aa7449cebc5b7e9b163d997a5668fe11daaee7958fa3cf

Aliases

arxiv: 2602.21685 · arxiv_version: 2602.21685v2 · doi: 10.48550/arxiv.2602.21685 · pith_short_12: ZQGBBKRQAPEV · pith_short_16: ZQGBBKRQAPEVD6NK · pith_short_8: ZQGBBKRQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZQGBBKRQAPEVD6NKORE45PC3P2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cc0c10aa3003c951f9aa7449cebc5b7e9b163d997a5668fe11daaee7958fa3cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed29dccc67413a6e221309721472ce7b5de50db23ffbfe75d1cf17ee4d90f5c5",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-02-25T08:38:29Z",
    "title_canon_sha256": "9ad98f1bc69a611ba4ace6cc9837bd1bfa521f86f485d5c1b728b6b3cbf48b3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.21685",
    "kind": "arxiv",
    "version": 2
  }
}