Numerical benchmark to assess sensitivity to spatial discretization in quasi-static fracture simulations : Application to phase-field models
Abstract
Numerous numerical methods based on Linear Elastic Fracture Mechanics (LEFM), such as phase-field fracture models, enable the solution of crack propagation problems. Despite established mathematical properties (e.g., Γ-convergence), their numerical discretization can introduce systematic biases that persist even with spatial mesh refinement, such as artificial anisotropy in fracture properties at the element scale. Although acknowledged, these biases remain underexplored in practice. To address this gap, this work introduces a numerical benchmark for quantitatively evaluating discretization-induced biases. The benchmark focuses on the propagation of an off-centered crack in a band subjected to a sliding tensile load, where the crack follows an exponentially decaying trajectory toward the band center. This path is verified against a sharp crack LEFM reference solution. This non-trivial yet well-characterized crack path offers a robust basis for the quantitative assessment and the comparison of different crack propagation solvers. To illustrate this benchmark, we assess two phase-field implementations: one based on the finite element method and another on the finite difference method. These simulations reveal that discretization indeed introduces local artificial anisotropy. For structured meshes, crack path curvature is not captured, even for element sizes considered small enough in classical practice. For unstructured meshes, while the path is well-captured at smaller sizes, oscillations in the predicted trajectory are observed. Used here to assess the discretization biases of two specific numerical methods, this benchmark test is intended to evaluate other numerical methods for simulating crack propagation.
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BibTeX
@misc{zembra2026numerical,
title = {{Numerical benchmark to assess sensitivity to spatial discretization in quasi-static fracture simulations : Application to phase-field models}},
author = {Edgar Zembra and Flavien Loiseau and Véronique Lazarus and Hervé Henry},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05755195v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Numerical benchmark to assess sensitivity to spatial discretization in quasi-static fracture simulations : Application to phase-field models
AU - Edgar Zembra
AU - Flavien Loiseau
AU - Véronique Lazarus
AU - Hervé Henry
PY - 2026
DA - 2026/09/18
PB - HAL
UR - https://hal.science/hal-05755195v1
AB - Numerous numerical methods based on Linear Elastic Fracture Mechanics (LEFM), such as phase-field fracture models, enable the solution of crack propagation problems. Despite established mathematical properties (e.g., Γ-convergence), their numerical discretization can introduce systematic biases that persist even with spatial mesh refinement, such as artificial anisotropy in fracture properties at the element scale. Although acknowledged, these biases remain underexplored in practice. To address this gap, this work introduces a numerical benchmark for quantitatively evaluating discretization-induced biases. The benchmark focuses on the propagation of an off-centered crack in a band subjected to a sliding tensile load, where the crack follows an exponentially decaying trajectory toward the band center. This path is verified against a sharp crack LEFM reference solution. This non-trivial yet well-characterized crack path offers a robust basis for the quantitative assessment and the comparison of different crack propagation solvers. To illustrate this benchmark, we assess two phase-field implementations: one based on the finite element method and another on the finite difference method. These simulations reveal that discretization indeed introduces local artificial anisotropy. For structured meshes, crack path curvature is not captured, even for element sizes considered small enough in classical practice. For unstructured meshes, while the path is well-captured at smaller sizes, oscillations in the predicted trajectory are observed. Used here to assess the discretization biases of two specific numerical methods, this benchmark test is intended to evaluate other numerical methods for simulating crack propagation.
ER -