Avalanche contribution to shear modulus of granular materials

Abstract

Shear modulus of frictionless granular materials near the jamming transition under oscillatory shear is numerically investigated. It is found that the shear modulus $G$ satisfies a scaling law to interpolate between $G\sim (\varphi -{\varphi }_J{)}^{1/2}$ and $G\sim {\gamma }_0^{-1/2}(\varphi -{\varphi }_J)$ for a linear spring model of the elastic interaction between contacting grains, where $\varphi$, ${\varphi }_J$, and ${\gamma }_0$ are, respectively, the volume fraction of grains, the fraction at the jamming point, and the amplitude of the oscillatory shear. The linear relation between the shear modulus and $\varphi -{\varphi }_J$ can be understood by slip avalanches.

10 pages, 14 figures

References in corpus (9)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• The Jamming Transition in Granular Systems
• Unified study of glass and jamming rheology in soft particle systems
• Microfluidic rheology of soft colloids above and below jamming
• Scaling properties of granular rheology near the jamming transition
• Critical Scaling of Shearing Rheology at the Jamming Transition of Soft Core Frictionless Disks
• Universal scaling for the jamming transition
• Behavior of pressure and viscosity at high densities for two-dimensional hard and soft granular materials
• Criticality and Scaling Relations in a Sheared Granular Material

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