Second gradient effective elastic moduli, and their evolution due to damage and plasticity, of heterogeneous granular solids

A micro-mechanical model is employed to study the second gradient elastic strain energy of heterogeneous granular solids. The granular material is idealized as a collection of particles interacting through inter-particle contacts. To facilitate the derivation of the overall stiffness tensors such an interaction among discrete number of particles has been made continuum in the orientation space. On the basis of this elastic investigation, a damage elastoplastic spring model has been developed in order to consider the evolution of anisotropy of the heterogeneous granular solid. Finally, simple examples will be solved, where the induced anisotropy will be shown.