A scaling law for numerical computation of fracture stress intensity factors
Abstract
Numerical simulations of fracture propagation require accurate computation of stress intensity factors (SIFs) to determine whether a pre-existing fracture will propagate. Even though displacement solutions from well-established numerical methods generally converge with mesh refinement, the convergence behavior of SIF estimates remains less understood. In this work, we propose a scaling law to improve the performance of SIF extraction using two-point displacement correlation methods. This scaling law relates sampling distance from the fracture tip to mesh resolution. It is developed by balancing the asymptotic truncation error against the numerical discretization error. Three numerical discretization methods--standard quadratic finite elements, quadratic finite elements with quarter-point elements, and a multi-point stress approximation finite volume method--are employed to validate the proposed scaling law on fracture benchmark problems under pure-mode and mixed-mode loading. We find that the conventional nearest-tip sampling strategy fails to compute convergent SIF estimates. In contrast, the proposed scaling-based approach yields decreasing errors in the SIF estimates as the mesh is refined. Across all three discretization methods, the proposed scaling law captures the sampling locations required for convergent SIF extraction, suggesting a general numerical characteristic of near-tip SIF extraction.
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BibTeX
@misc{cui2026scaling,
title = {{A scaling law for numerical computation of fracture stress intensity factors}},
author = {Ronghao Cui and Jan Martin Nordbotten and Ivar Stefansson and Inga Berre},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.16850},
eprint = {2611.16850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.16850},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A scaling law for numerical computation of fracture stress intensity factors
AU - Ronghao Cui
AU - Jan Martin Nordbotten
AU - Ivar Stefansson
AU - Inga Berre
PY - 2026
DA - 2026/11/12
PB - arXiv
DO - 10.48550/arxiv.2611.16850
UR - https://arxiv.org/abs/2611.16850
AB - Numerical simulations of fracture propagation require accurate computation of stress intensity factors (SIFs) to determine whether a pre-existing fracture will propagate. Even though displacement solutions from well-established numerical methods generally converge with mesh refinement, the convergence behavior of SIF estimates remains less understood. In this work, we propose a scaling law to improve the performance of SIF extraction using two-point displacement correlation methods. This scaling law relates sampling distance from the fracture tip to mesh resolution. It is developed by balancing the asymptotic truncation error against the numerical discretization error. Three numerical discretization methods--standard quadratic finite elements, quadratic finite elements with quarter-point elements, and a multi-point stress approximation finite volume method--are employed to validate the proposed scaling law on fracture benchmark problems under pure-mode and mixed-mode loading. We find that the conventional nearest-tip sampling strategy fails to compute convergent SIF estimates. In contrast, the proposed scaling-based approach yields decreasing errors in the SIF estimates as the mesh is refined. Across all three discretization methods, the proposed scaling law captures the sampling locations required for convergent SIF extraction, suggesting a general numerical characteristic of near-tip SIF extraction.
ER -