| Abstract: | This paper presents a Gibbs potential-based granular micromechanics approach capable of modelingmaterialswith complete anisotropy. The deformation energy of each grain–pair interaction is taken as a functionof the inter-granular forces. The overall classical Gibbs potential of a material point is then defined as thevolume average of the grain–pair deformation energy. As a first-order theory, the inter-granular forces arerelated to the Cauchy stress tensor using a modified static constraint that incorporates directional distributionof the grain–pair interactions. Further considering the conjugate relationship of the macroscale strain tensorand the Cauchy stress, a relationship between inter-granular displacement and the strain tensor is derived.To establish the constitutive relation, the inter-granular stiffness coefficients are introduced considering theconjugate relation of inter-granular displacement and forces. Notably, the inter-granular stiffness introducedin this manner is by definition different from that of the isolated grain–pair interactive. The integral formof the constitutive relation is then obtained by defining two directional density distribution functions; onerelated to the average grain–scale combined mechanical–geometrical properties and the other related to purelygeometrical properties. Finally, as the main contribution of this paper, the distribution density function isparameterized using spherical harmonics expansion with carefully selected terms that has the capability ofmodeling completely anisotropic (triclinic) materials. By systematic modification of this distribution function,different elastic symmetries ranging from isotropic to completely anisotropic (triclinic) materials are modeled.As a comparison, we discuss the results of the present method with those obtained using a kinematic assumptionfor the case of isotropy and transverse isotropy, wherein it is found that the velocity of surface quasi-shearwaves can show different trends for the two methods. |
