Geometric aspects of shear jamming induced by deformation of frictionless sphere packings

Abstract

It has recently been demonstrated that shear deformation of frictionless sphere packings leads to structures that will undergo jamming in the presence of friction, at densities well below the isotropic jamming point phi(j) approximate to 0.64, and at high enough strains. Here, we show that the geometric features induced by strain are robust with respect to finite size effects, and include the feature of hyperuniformity, previously studied in the context of jamming, and more recently in driven systems. We study the approach to jamming as strain is increased, by evolving frictionless sheared configurations through frictional dynamics, and thereby identify a critical, or jamming, strain for each density, for a chosen value of the coefficient of friction. In the presence of friction above a certain strain value the sheared frictionless packings begin to develop finite stresses, which marks the onset of shear jamming. At a higher strain value, the shear stress reaches a saturation value after rising rapidly above the onset of shear jamming, which permits identification of the shear jamming transition. The onset of shear jamming and shear jamming are found to occur when the coordination number Z reaches values of Z = 3 and Z = 4 respectively. By considering percolation probabilities for the contact network, clusters of four coordinated and six coordinated spheres, we show that the percolation of four coordinated spheres corresponds to the onset of shear jamming behaviour, whereas the percolation of six coordinated spheres corresponds to shear jamming, for the chosen friction coefficients. At the onset of shear jamming, the force distribution begins to develop a peak at finite value and the force network is anisotropic and heterogeneous. And at the shear jamming transition, the force distribution has a well defined peak close to < f > and the force network is less anisotropic and homogeneous. We briefly discuss mechanical aspects of the jamming behaviour by performing normal mode analysis and computing shear modulus.