Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes
Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes
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DOI：
10.1080/14786435.2020.1790053
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发表时间：
2020-07-24
影响因子：
1.6
通讯作者：
Spanjer, W. D. T.
中科院分区：
文献类型：
--
作者：
Bourne, D. P.;Kok, P. J. J.;Spanjer, W. D. T.
我们提出了一种具有给定体积的细胞生成拉盖尔图的快速算法，该算法可用于创建用于计算均质化的多晶材料的rve，或用于将拉盖尔图拟合到金属的EBSD或XRD测量中。给定所需细胞体积的列表，我们解决了一个凸优化问题，以找到这些体积的细胞的拉盖尔图，直到任何规定的公差。该算法建立在计算几何和最优输运理论的工具上，据我们所知，这些工具以前尚未应用于微观结构建模。我们通过在3D中生成具有多达20,000个颗粒的用户定义体积分布的rve来说明该算法的速度和准确性。在标准桌面PC上，我们可以在几分钟内实现小于1%的体积百分比误差。我们还给出了具有带、簇和尺寸梯度的多分散微结构的例子，并将拉盖尔图拟合到中频钢的3D EBSD测量中。
We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling before. We illustrate the speed and accuracy of the algorithm by generating RVEs with user-defined volume distributions with up to 20,000 grains in 3D. We can achieve volume percentage errors of less than 1% in the order of minutes on a standard desktop PC. We also give examples of polydisperse microstructures with bands, clusters and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements of an IF steel.