Discontinuous change of shear modulus for frictional jammed granular materials

Abstract

The shear modulus of jammed frictional granular materials with the harmonic repulsive interaction under an oscillatory shear is numerically investigated. It is confirmed that the storage modulus, the real part of the shear modulus, for frictional grains with sufficiently small strain amplitude ${\gamma }_0$ discontinuously emerges at the jamming transition point. The storage modulus for small ${\gamma }_0$ differs from that of frictionless grains even in the zero friction limit, while they are almost identical with each other for sufficiently large ${\gamma }_0$, where the transition becomes continuous. The stress-strain curve exhibits a hysteresis loop even for a small strain, which connects a linear region for sufficiently small strain to another linear region for relatively larger strain. We propose a new scaling law to interpolate between the states of small and large ${\gamma }_0$.

10 pages, 13 figures

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• Stress anisotropy in shear-jammed packings of frictionless disks
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• Softening and residual loss modulus of jammed grains under oscillatory shear in an absorbing state
• Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear
• Microscopic Reversibility and Emergent Elasticity in Ultrastable Granular Systems
• Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime
• An exact expression of three-body system for the complex shear modulus of frictional granular materials