Unilateral interactions in granular packings: a model for the anisotropy modulus

Abstract

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

“…At low compressive loads, stronger anisotropy effects and a greater contribution of the nonaffine motions, which are affected by the PSD, may be observed [42], thus resulting in different F t /F n values. The approximate average values of F t /F n at high compressive loads in all of the simulated packings was strictly related to approximately the same percentage contribution of contacts with nearly fully mobilized friction (F t /F n > 0.38) in all of the samples.…”

“…At low compressive loads, large differences in elastic response of the mixtures with various PSDs were observed. These differences were probably caused by stronger anisotropy effects and greater contribution of the nonaffine motions affected by PSD [42].…”

Local elastic fields in granular solids

“…Calculating these maps enables us to see local structures in the system and study correlations between the elastic constants and other fields. In general, coarse grained fields depend on the coarse graining scale w. To illustrate this dependency, Figure 3 shows the commonly used shear modulus, G = C 1111 + C 2222 − C 1122 − C 2211 , and bulk modulus, E = C 1111 + C 2222 +C 1122 +C 2211 for different coarse graining scales [7]. It shows that the moduli are independent (with deviations less than 5%) of the coarse graining scale for w > 14r.…”

Micro-macro and jamming transition of polydisperse granular materials

“…In particular, recent works [3,73,94,110,222] show that along with the macroscopic properties (stress and volume fraction) [56,94,192,219], also the structure, as quantified by the fabric tensor [120,146,178,222] plays a crucial role, as it characterizes, on average, the geometric arrangement of contacts. Many standard constitutive models, involving elasticity and/or plasticity have been applied to describe the incremental behavior of granular solidssometimes with success, but typically only in a limited range of parameters.…”

“…Granular materials behave differently from usual solids or fluids and show peculiar mechanical properties like dilatancy, history dependence, ratcheting and anisotropy [69,70,73,84,103,104,145,178,190,193,222]. The behavior of these materials is highly non-linear and involves plasticity even at very small strain due to rearrangements of the elementary particles [20,45,65].…”