Viscoelastic mechanics of two-dimensional granular lattices

Abstract

We study the rate-dependent mechanics of viscoelastic granular packings. Using a two-dimensional, square lattice of particles as a motif mimicking nominally mono-disperse granular packings, we perform a suite of finite element simulations under rate-dependent uniaxial compaction followed by unloading. The focus is on understanding the macroscopic force–displacement relations and the porosity evolution as a function of the viscoelastic relaxation parameters. For the constituent parameters considered here, the force–displacement relations show a two-stage power-law behavior, which is associated with the relative contributions of viscous dissipation and elastic effects at a particular loading rate. For a given loading rate, the nonlinearity of the porosity evolution depends on the constituent parameters and is found to be captured well by a simple analytical model. The heterogeneity of stresses during the compaction and recovery phases provide insights into the emergent complex micromechanics in simple granular motifs. Upon unloading, particles may experience transient tensile pressures, which could have implications on their failure.