Start-up shear of spherocylinder packings: Effect of friction

We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient μ. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus g_{∞}, which is orders of magnitude larger than the modulus g_{0} in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length ℓ of the spherocylinders. One consequence of this motion is that the shear modulus g_{∞} approaches a finite value in the limit ℓ→∞, even though the density of the packings vanishes, ρ∝ℓ^{-2}. By way of contrast, the frictionless modulus decreases to zero, g_{0}∼ℓ^{-2}, in accordance with the behavior of density. Increasing the strain beyond a value γ_{c}∼μ, the packing strain weakens from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a "yield stress" σ_{y}=g_{∞}γ_{c} and the stress behaves as σ=σ_{y}+g_{0}γ. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.