ABSTRACT
In this paper, explanations are given for 2D case. However, it will be easy to modify them for 3D case.
2 A THEORY ON INDUCED ANISOTROPY
2.1 Measure of induced anisotropy
We begin with the measurement of induced anisotropy in granular assemblies. The induced anisotropy is the anisotropy of contact normal distributed in a granular assembly, and this anisotropy is described by the fabric tensor (Satake, 1982) in the form
where f (θ) is the contact normal density and ni denotes a contact normal with angle θ. f (θ) satisfies
and f (θ) = 1/(2π), when the fabric is isotropic. It follows from Equations (1) and (2) that
As we can assume that Fij is coaxial with the applied stress tensor σij in simple monotonic loadings, we define a parameter α (≥0) called the inductivity degree of anisotropy by the form
where F1, F2(F1 ≥ F2) are principal values of Fij , and σ1, σ2 are those of σij . This equation is also written in the form
where (σα)ij is a tensor having principal values σα1 , σ α 2
and coaxial with σij . It is noted that Equation (5) is applicable both in 2D and 3D cases.
