Statistical Analysis of Particle Graph of a Granular Assembly Using the Loop Tensor

Abstract

This paper proposes a method of statistical analysis for tensor quantities, which is explained by using the loop tensor defined for the particle graph of a granular assembly. As an example, we analyzed the change of distribution of void shapes in a computer simulation result of a biaxial compression test.
The loop in a particle graph of a granular assembly corresponds to a local void in the two dimensions. Therefore, the loop tensor is considered to quantify the local voids. The loop tensor is decomposed into the scalar and deviatoric part, which are related with the size and anisotropy of a loop, respectively. Applying the statistical analysis to the loop tensor, we obtained an interesting result that the change of inhomogeneity of micro-structure during shear deformation is comparable to that of the volumetric strain in the granular assembly.