无序细观结构在体积中与截面上尺度分布函数之间的关系的统计诠释

STATISTICAL INTERPRETATION ON THE RELATIONSHIP BETWEEN THE VOLUMETRIC AND SECTIONAL SIZE DISTRIBUTIONS OF DISORDERED MESO-STRUCTURES

研究材料中的无序细观微结构在体积中的尺度分布函数与在截面上观测到的尺度分布函数之间的变换关系,导出了变换方程,并阐明了对它应作统计解释。还给出了分布函数的矩的变换关系,讨论了粗糙面分维数与它和截面的交的分维数之间的关系。

In this paper the transformation between the volumetric and sectional size distribution of the disordered meso-structures is studied. An integral equation governing this transformation for the cases of spheres or parallel penny shaped cracks is derived. The statistical interpretation on the transformation equation is emphasized. Furthermore, the transformations for moments of distribution function and for fractal dimension are discussed.