Compression- and shear-driven jamming of U-shaped particles in two dimensions

Abstract

We carry out numerical simulations of soft, U-shaped, frictionless particles in d = 2 dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction φ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction φJ than observed in compression. A growing relaxation time and translational correlation length is found as φ increases towards φJ . We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as φ increases to φJ . At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as φ increases, saturating to a plateau just below φJ , but then increasing again as φ increases above φJ .[The final publication is available at Springer via http://dx.

Athermal shearing of frictionless cross-shaped particles of varying aspect ratio

“…The non-convex shape of the crosses allows for particles to interlock and create gear-like effects in their interactions. We study the rotational motion of such particles and their orientational ordering in the shear flow, making comparison to previous work we have done on non-convex U-shaped particles ("staples") [4] and convex elongated rods [5][6][7]. We will see that the lack of convexity plays a significant role in such particle orientational effects.…”

“…Here the second sum is over all contacts with spherocylinder component a of particle i with spherocylinder b of particle j, and we consider only the elastic forces as that gives the dominant contribution to the stress at loẇ γ. For our overdamped model with a dissipative drag force, the rheology is Newtonian [4,6,10]. At lowγ below φ J one has p ∼γ, while above φ J one has [10] a finite yield stress with p ∼ p 0 + cγ b .…”

“…Particles i and j will overlap if r ia,jb < D ij = (D i + D j )/2. In that case there is a harmonic repulsion between the particle with an elastic force [4,6],…”

“…the error bars on the data points denotes the value of φ 2 , while the lower limit gives φ 1 . For comparison we also include our earlier results for a system of N = 1024 monodisperse staples [4] (as in Fig. 1b), and for N = 1024 spherocylinders of asphericity α = 4 [6] (as in Fig.…”

“…6 we plot the average particle rotational veloc- ity, scaled by the strain rate, − θ i /γ vs φ for crosses with aspect ratio β = 0.25, 0.5, and 1. For comparison we include our earlier results for staples [4] and spherocylinders with α = 4 [5,7]. In each case, here and in subsequent Figs.…”