Abstract
Poisson Voronoi (PV) tessellations as artificial microstructures are widely used in investigations of material deformation behaviors. However, a PV structure usually describes a relative homogeneous field. This work presents a simple numerical method for generating 2D/3D artificial microstructures based on hierarchical PV tessellations. If grains/particles of a phase cover a large size span, the concept of “artificial phases” can be used to create a more realistic size distribution. From case to case, detailed microstructural features cannot be directly achieved by commercial or free softwares, but they are necessary for a deep or thorough study of the material deformation behavior. PV tessellations created in our process can fulfill individual requirements from material designs. Another reason to use PV tessellations is due to the limited experimental data. Concerning the application of PV microstructures, four examples are given. The FE models and results will be presented in consecutive works, i.e. “part II: applications”.
Highlights
To investigate the material behavior, micromechanical material properties are essential, since such features, besides other factors, determine the overall material characteristics
Finite element (FE) simulations play an important role in studying material behaviors
Poisson Voronoi (PV) tessellations are applied as artificial microstructures in finite element (FE) simulations to investigate solid material behaviors
Summary
To investigate the material behavior, micromechanical material properties are essential, since such features, besides other factors, determine the overall material characteristics. Fritzen et al [8] reported a method of generating the 3D meshing of periodic Voronoi structures for polycrystalline aggregates Their process was time efficient, but it required professional programming skills and no hierarchical Voronoi tessellations are included. Based on the minimization of the energy and distance function, a process was presented to dynamically generate the spherical Laguerre Voronoi diagram based on assumptions in the real world [18] Such Voronoi diagram has the corresponding properties of polyhedra as described in [19]. To study the rock strength, a methodology for generating Voronoi tessellations presenting a polycrystalline rock microstructure is proposed to simulate the packing processes and the crystal growth of mineral grains, where the distribution of the poly-crystals (tessellations) varies in shapes and sizes representing different mineral grains [24]. PV tessellations are applied as artificial microstructures in FE simulations to investigate solid material behaviors
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