Michio Otsuki (Osaka University)

Shear modulus of granular materials near jamming transition

Granular materials have rigidity above a critical density [1]. It is well-known that frictionless spheres under infinitesimal strain exhibit a continuous transition of the shear modulus G. The accessible shear strain in the experiment [29], however, is too large, and it is impossible to remove contact friction in real dry granular materials.

In this talk, we present our recent numerical results on the shear storage modulus of granular materials under oscillatory shear. For finite strain, recent studies have revealed that the storage modulus of frictionless grains decreases with increasing strain as a result of slip avalanches. The present authors have proposed a scaling law of the storage modulus to interpolate between the states of small and large shear strain [1]. We also investigate the storage modulus of frictional grains. The storage modulus for sufficiently small strain exhibits a discontinuous transition, while the transition becomes asymptotically continuous as the shear strain increases due to the Coulomb criterion for the tangential friction between grains [2]. We also discuss the effect of the grainsf shape on the storage modulus.

[1] M. Otsuki and H. Hayakawa, Phys. Rev. E 90, 042202 (2014).
[2] M. Otsuki and H. Hayakawa, Phys. Rev. E 95, 062902 (2017).