Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy

Granular materials undergoing large deformations exhibit nonlinearity arising from both geometrical and material effects. Here we extend the earlier Granular Micromechanics Approach (GMA)-based continuum models by enriching the grain-pair elastic energy functional and dissipation potential with new tangential terms and a coupling between normal and tangential parameters to better describe these nonlinear effects. These new terms are expected to better represent various deformation mechanisms that grains experience including grain crushing, rearrangement, rotation/rolling, sliding, loss of lateral support, neighborhood densification and strain localization. The elastic energy of a generic grain-pair direction of the GMA is reformulated consisting of a complete quadratic and quartic (duffing) dependencies on normal and tangential relative displacements to capture various nuances of material nonlinearity. Further, the grain-pair dissipation potential formulation is modified by introducing (i) plastic dissipation in the tangential direction and (ii) coupling between the plastic dissipation in tension and compression. It is shown that the coupling of this nonlinear elastic and the damage-plastic behavior yields an apparent molecular-type, such as Lennard-Jones type, potential for the granular system. The GMA framework is exploited to link the grain-scale behavior to the macroscopic response. In this framework, the evolution of grain-scale dissipation parameters is obtained using a hemi-variational principle. To motivate the adoption of GMA framework, we present a brief review of grain-scale deformation mechanisms that lead to the emergent dissipative macroscale behavior and the evolution of induced anisotropy. The enriched model is used to simulate one-dimensional compression of elasto-frictional granular media. Classical behavior of lateral earth pressure coefficient, the ratio of lateral to axial stress, is predicted by the model.The obtained results are expounded with the aid of the evolution of two sets of parameters during the compaction process, one at the grain-scale and the other at the emergent macroscale. At the grain scale, we investigate the directional evolution of elastic energy, damage and plasticity. At the macroscale, we follow the evolution of macroscale induced anisotropy by considering the eigenvalues and harmonic decomposition of equivalent stiffness.