This dataset accompanies the paper \"The single edge notch fracture test for viscoelastic elastomers\" by Kamarei, Sozio, and Lopez-Pamies, published in the Journal of Theoretical, Computational and Applied Mechanics (JTCAM, 2026). The dataset contains the numerical results needed to reproduce the figures and findings of that paper.
\n\n\nNote on a related prior work: The Griffith criticality condition employed in the simulations was introduced in a separate earlier publication — Shrimali, B. and Lopez-Pamies, O. (2023), Extreme Mechanics Letters 58: 101944 — which is a distinct paper from the JTCAM article this dataset supports. The Extreme Mechanics Letters paper establishes the theoretical foundation; the JTCAM paper applies and extends it to a comprehensive parametric study of the SEN fracture test for viscoelastic elastomers, including direct comparisons against experiments.
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The results combine a parametric study with direct comparisons against experiments, revealing how non-Gaussian elasticity, nonlinear viscosity, and intrinsic fracture energy interact to govern fracture nucleation from a pre-existing crack.
\nThe simulation code used to generate this dataset is publicly available at:
\n\n\nhttps://github.com/farhadkama/FEniCSx_Kamarei_Sozio_Lopez-Pamies
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All data files use a consistent set of SI-compatible mechanical units throughout:
\n| Quantity | \nUnit | \nNotes | \n
|---|---|---|
| Force | \nN | \nNewton | \n
| Length | \nmm | \nMillimeter | \n
| Mass | \ntonne (t) | \n1 t = 10\u2076 g; ensures stress in MPa = N/mm² | \n
| Time | \ns | \nSecond | \n
| Stress / Modulus | \nMPa = N/mm² | \nDerived unit consistent with the above | \n
| Energy | \nN·mm = mJ | \nDerived unit (force × length) | \n
| Energy per unit length | \nN·mm/mm = N | \nStored energy normalized by a reference length (e.g., specimen thickness); used in fracture energy post-processing | \n
The data is organized into three categories based on the type of viscosity model:
\nConstant_viscosity/)Shear_thinning_viscosity/)Deformation_dependent_viscosity/)Within each viscosity category, results are provided across a range of loading rates spanning from $10^{-6}$ to $10^{6}$. For each rate, three sub-categories characterize the growth behavior of the non-equilibrium energy:
\nE — Equal growth of non-equilibrium energyW — Weaker growth of non-equilibrium energyS — Stronger growth of non-equilibrium energyWithin each sub-category, two data files are provided corresponding to two different pre-existing crack sizes, which together are sufficient for post-processing and reproducing the results of the paper. Each data file contains columns representing the following quantities: time, displacement (the applied displacement of the specimen), stretch (the corresponding macroscopic stretch), and psiEq (the equilibrium stored elastic energy). These quantities are sufficient to carry out the post-processing
\n{viscosity_type}/
\n\u2514\u2500\u2500 rate_{value}/
\n\u251c\u2500\u2500 E/ \u2502
\n\u251c\u2500\u2500 crack_size_1.ssv
\n\u2514\u2500\u2500 crack_size_2.ssv
\n\u251c\u2500\u2500 W/
\n\u251c\u2500\u2500 crack_size_1.ssv
\n\u2514\u2500\u2500 crack_size_2.ssv
\n\u2514\u2500\u2500 S/
\n\u251c\u2500\u2500 crack_size_1.ssv
\n\u2514\u2500\u2500 crack_size_2.ssv
\nThe simulation code depends on the FEniCSx finite element library, version 0.10.0, deployed via a Singularity/Apptainer container on an HPC cluster. The complete software environment is specified in pkg.txt.
ghcr.io/fenics/dolfinx/dolfinx:v0.10.0fenics-dolfinx 0.10.0, petsc4py, mpi4py, numpy, scipy, h5pymatplotlib (optional, for figure generation)To reproduce the numerical results of the paper, clone the simulation source code from GitHub, adjust the material parameters, crack size, and loading rate for the desired case directly in the Python script, then run using the Singularity container as described in reproduce.sh.
The material parameters for each case (constant viscosity, shear thinning, deformation dependent) are documented in the JTCAM paper. The two crack sizes used per case are listed in the paper's parametric study section.
\nThis repository contains computational data and figure files for the research paper \"The single edge notch fracture test for viscoelastic elastomers\" by Kamarei, Sozio, and Lopez-Pamies, Journal of Theoretical, Computational and Applied Mechanics (2026).
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