Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Mesh Density and Geodesic Tortuosity in Planar Triangular Tesselations Devoted to Fracture Mechanics

Abstract : 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 details 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 on the results of cohesive-volumetric finite element simulations.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03703549
Contributor : Joffrey Lhonneur Connect in order to contact the contributor
Submitted on : Friday, June 24, 2022 - 9:42:31 AM
Last modification on : Friday, August 5, 2022 - 3:03:55 PM

File

MeshDensity_JTCAM.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03703549, version 1

Citation

Joffrey Lhonneur, Nawfal Blal, Yann Monerie. Mesh Density and Geodesic Tortuosity in Planar Triangular Tesselations Devoted to Fracture Mechanics. 2022. ⟨hal-03703549⟩

Share