Accompanying dataset for the paper "Mesh Density and Geodesic Tortuosity in Planar Triangular Tesselations Devoted to Fracture Mechanics"

Contributions

Author #1 is the major contributor to the paper writing. Author #1 has created most of the Figures in the paper and has provided all the results concerning the geodesic tortuosity of planar triangular meshes.

Author #2 and Author #3 have provided the results concerning the density of planar triangular meshes.

Funding sources

This work was funded by the French Institute for Radiation Protection and Nuclear Safety (IRSN) and the University of Montpellier, France.

Data structure and information

All the results and figures presented in the paper have been obtained with a python script available in the workflows folder.

Data files processed by that script are provided in the data folder. The pickle files t_{nb}.pkl inside the data/pkl folder contain
lists of tortuosity values computed on a gmsh mesh for several paths containing various number of edges (nb).

pklfiles are produced via a function call to main.py:comp_real_tortuosities(nb)

Data structure and information

workflows/ - folder containing plotting scripts

reproduce.sh - bash script launching python and compressing figures

main.py - python script for figure creation.

/utils - folder containing additional python scripts for figures creation

/figures - folder containing the figures produced by the python script

data/ - data folder

gmsh - folder containing mesh in gmsh information

pkl - folder containing the pickled vectors "t_{nb}.pkl".

Paper Description

In fracture mechanics, the mesh sensitivity is a key issue. It is particularly true concerning cohesive volumetric finite element methods in which the crack path and the overall behavior are respectively influenced by the mesh topology and the mesh density. Poisson-Delaunay tessellations parameters, including the edge length distributions, were widely studied in the literature but very few works concern the mesh density and topology in Delaunay type meshes suitable for finite element simulations, which is of crucial interest for practical use.Starting from previous results concerning Poisson-Delaunay tessellations and studying in detail the Lloyd relaxation algorithm, we propose estimates for the probability density functions of the edge length and triangle top angles sets. These estimates depend both on the intensity of the underlying point process and on an efficiency index associated to the global quality of the mesh. The global and local accuracies of these estimates are checked for various standard mesh generators. Finally the mesh density and geodesic tortuosity are estimated for standard random or structured triangular meshes typically used in finite element simulations.These results provide practical formulas to estimate bias introduced by the mesh density and topology onthe results of cohesive-volumetric finite element simulations.