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**A new method for the generation of arbitrarily shaped 3D random polycrystalline domains.**
*(English)*
Zbl 1309.74058

Summary: In this paper a new method for the generation and meshing of arbitrarily shaped three-dimensional polycrystalline models is presented. The discretization is based on Voronoi tessellation, which is shown to be statistically representative of the microstructure of polycrystalline materials. An original approach is introduced to define any possible (concave or convex) shape of the final domain, independently from the initial configuration of the aggregate. Firstly the Voronoi cells are cropped along arbitrarily oriented planes to generate a convex domain, and then an arbitrary number of cuts are performed along planar surfaces to generate the final concave domain. Finally the grains are discretised separately and assembled together to create a finite element model. Several examples are presented to show the capability of generated virtual samples to simulate the behaviour of real polycrystalline materials. The macroscopic elastic properties of polycrystals consisting of anisotropic (trigonal) grains and the stress intensity factor at the tip of a sharp notch are evaluated and compared both with analytical calculations and experimental evidences, showing excellent agreement.

### MSC:

74N15 | Analysis of microstructure in solids |

05C90 | Applications of graph theory |

74S05 | Finite element methods applied to problems in solid mechanics |

### Keywords:

Voronoi tessellation; 3D polycrystalline microstructures; finite element method; concave domains
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\textit{S. Falco} et al., Comput. Mech. 54, No. 6, 1447--1460 (2014; Zbl 1309.74058)

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