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We investigate the effective material properties of sand piles of soft convex polygonal particles numerically using the discrete element method (DEM). We first construct two types of sand piles by two different procedures. We then measure averaged stress and strain, thelatter via imposing a 10% reduction of gravity, as well as the fabric tensor. Furthermore, we compare the vertical normal strain tensor between sand piles qualitatively and show how the construction history of the piles affects their strain distribution as well as the stress distribution. In the next step, we determine the elastic constants, assuming Hooke’s law throughout the sand piles, and the correlation between the elastic material conefficients and the fabric tensor. We observe that the bulk modulus of the sand pile, i.e., the stiffness of the granulate is a linear function of the trace of the fabric tensor. We determine the relationship between invariants of the stress and strain tensor, observing that the behaviour is nonlinear which means that we have linear elastic behavior near the centre of the pile and nonlinear behavior announcing the transition to plastic behavior near the surface of the sand piles, the same behavior as was assumed by Cantelaube et al. We find that the macroscopic stress and fabric tensors are not collinear in the sand pile.

Pradip Roul
Alexander Schinner
Klaus Kassner
Granular Matter