Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm

In this article, we propose a three‐dimensional meshing algorithm for discrete models combining the lattice approach with the polyhedral particle approach. Our aim is to be able to leverage readily available, well‐supported meshers to handle various geometries. We use them to generate a tetrahedral mesh, which our mesher then converts to a polyhedral mesh. The input mesh serves as geometrical support to generate the nodes of the discrete mesh. The desired shape is obtained with an assembly of convex polyhedral particles—without having to clip them. We show that this approach enables meshing convex or concave geometries with sharp edges, curved features, and more. Several three‐dimensional geometries are presented to support this claim and illustrate the capabilities of the mesher. We provide a detailed analysis of its isotropy. The geometric isotropy is studied by analyzing the orientation of the generated beams. The mechanical isotropy is verified by assessing the properties of the elasticity tensor. Finally, we show that the new mesh retains its ability to be a good support for the generation of realistic cracking patterns.

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Mesh generation of complex three‐dimensional geometries for beam‐particle modeling of fracture

Rima

Oliver-Leblond

Bonhomme

et al. 2022

Numerical Meth Engineering

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VoroCrust

et al. 2020

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Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface, circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.

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Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm

Cited by 2 publications

References 40 publications

Mesh generation of complex three‐dimensional geometries for beam‐particle modeling of fracture

Mesh generation of complex three‐dimensional geometries for beam‐particle modeling of fracture

VoroCrust

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