Micromechanical Modeling of Material Cross-anisotropy

Micromechanical behavior of granular materials is an important aspect for various engineering fields like soil mechanics, powder technology and mineral processing. The anisotropic material structure of the granular deposits is generally represented by a fabric tensor which takes into account the distribution of normal vectors at the interparticle contacts. In this regard, a truncated spherical harmonic function, restricted up to second-order terms, is often used to define the fabric tensor; however, this constrains the generic description of material anisotropy. While getting deposited under gravity, granular solids often exhibit a cross-anisotropic fabric structure with a preferential particle contact orientation favored by the direction of deposition. In the present study, the stiffness tensor of a cross-anisotropic fabric structure has been explored taking into account both the second and fourth order truncation of the spherical harmonic function. It has been noticed that the fourth order truncation gives a better control in capturing the cross-anisotropic nature of the granular fabric. Further, the bounds on fabric parameters are examined along with the influence of their respective magnitudes on the elastic stiffness moduli of the granular packing.