Generalised Voronoi tessellation for generating microstructural finite element models with controllable grain-size distributions and grain aspect ratios

作者：Li Ling; Shen Luming^*; Proust Gwenaelle

来源：International Journal for Numerical Methods in Engineering, 2015, 103(2): 144-156.

DOI：10.1002/nme.4897

• microstructure
• generalised Voronoi tessellation
• grain morphology
• grain size distribution
• finite element method

A generalised Voronoi tessellation is proposed to create three-dimensional microstructural finite element model, which can effectively reproduce the grain size distribution and grain aspect ratio obtained from experiments. This new approach consists of two steps. The first step generates the desired lognormal grain size distribution with a given average grain volume and standard deviation. The second step requires grouping meshed elements to create a specific grain aspect ratio, using the Voronoi generators from the first step. A new concept is introduced to describe the transition from the Poisson-Voronoi tessellation to the centroidal Voronoi tessellation. More importantly, instead of using the conventional way where the Voronoi cells are first generated and then meshed into finite elements, this new approach discretises the pre-meshed specimen with the Voronoi generators. This new technique prevents the presence of high density mesh at the vertices of Voronoi cells, and can tessellate irregular geometry much more easily. Examples of microstructures with different size distributions, non-equiaxed grains and complicated specimen geometries further demonstrate that the proposed approach can offer great flexibility to model various specimen geometries while keeping the process simple and efficient.

• 出版日期2015-7-13