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~(φ-φJ)1/2 and G~γ₀^-1/2(φ-φJ) for a linear spring model of the elastic interaction between contacting grains, where φ, φJ, and γ₀ 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 φ-φJ can be understood by slip avalanches.
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Otsuki et al. (2014) studied this question.
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