Authors: Joffrey Lhonneur ^1,2; Nawfal Blal ³; Yann Monerie ^1,4

• 1 Laboratoire de micromécanique et intégrité des structures
• 2 Bureau d’étude et de modélisation des effets des armes et explosifs
• 3 Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
• 4 Mécanique Théorique, Interface, Changements d’Echelles

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 on the results of cohesive-volumetric finite element simulations.