Defining shape measures for 3D star-shaped particles: Sphericity, roundness, and dimensions
Defining shape measures for 3D star-shaped particles: Sphericity, roundness, and dimensions
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DOI：
10.1016/j.powtec.2013.08.015
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发表时间：
2013-11-01
影响因子：
5.2
通讯作者：
Garboczi, Edward J.
中科院分区：
文献类型：
--
作者：
Bullard, Jeffrey W.;Garboczi, Edward J.
截断球谐展开用于近似3D星形颗粒的形状，包括广泛的轴对称椭球体，长方体，和超过40.000真实的颗粒从七个不同的材料源。这种数学方法可以计算这些星形粒子的任何几何性质。计算的属性，如体积，表面积，三轴尺寸，最大内接球，和最小封闭球，以及微分几何属性，如表面法线和主曲率，和值进行比较，分析值的良好特征的几何形状。我们发现，颗粒的Krumbein三轴尺寸，广泛应用于沉积地质文献中，基本上是相同的长度，宽度和厚度尺寸，用于表征砾石形状的建筑骨料行业的数值。这些尺寸，我们证明了长度是一个粒子的最小封闭球直径的下限和厚度是其最大内接球直径的上限。我们研究了“真球度”和形状熵，我们还引入了一个新的球度因子的基础上的半径比的最大内接球的最小封闭的球体。该边界球比可以通过数值计算或从宏观尺寸近似计算，其优点是它对表面粗糙度的敏感性低于真实球度。对于圆度，我们将Wadell经典的2D粒子轮廓定义扩展到3D形状，并且我们还引入了一个新的圆度因子，该因子基于整合表面位置单位向量和单位法向量的点积。有限的证据表明，后者的圆度因子更忠实地捕捉基于颗粒形状的视觉感知的圆度的共同概念，并且它比经典的圆度因子更容易计算。由爱思唯尔公司出版
Truncated spherical harmonic expansions are used to approximate the shape of 3D star-shaped particles including a wide range of axially symmetric ellipsoids, cuboids, and over 40.000 real particles drawn from seven different material sources. This mathematical procedure enables any geometric property to be calculated for these star-shaped particles. Calculations are made of properties such as volume, surface area, triaxial dimensions, the maximum inscribed sphere, and the minimum enclosing sphere, as well as differential geometric properties such as surface normals and principal curvatures, and the values are compared to the analytical values for well-characterized geometric shapes. We find that a particle's Krumbein triaxial dimensions, widely used in the sedimentary geology literature, are essentially identical numerically to the length, width, and thickness dimensions that are used to characterize gravel shape in the construction aggregate industry. Of these dimensions, we prove that the length is a lower bound on a particle's minimum enclosing sphere diameter and that the thickness is an upper bound on its maximum inscribed sphere diameter. We examine the "true sphericity" and the shape entropy, and we also introduce a new sphericity factor based on the radius ratio of the maximum inscribed sphere to the minimum enclosing sphere. This bounding sphere ratio, which can be calculated numerically or approximated from macroscopic dimensions, has the advantage that it is less sensitive to surface roughness than the true sphericity. For roundness, we extend Wadell's classical 2D definition for particle silhouettes to 3D shapes and we also introduce a new roundness factor based on integrating the dot product of the surface position unit vector and the unit normal vector. Limited evidence suggests that the latter roundness factor more faithfully captures the common notion of roundness based on visual perception of particle shapes, and it is significantly simpler to calculate than the classical roundness factor. Published by Elsevier B.V.