Amorphous sphere packings have been intensely investigated to understand mechanical and flow behaviour of dense granular matter and to explore universal aspects of the jamming transition, from fluid to structurally arrested states. Considerable recent research has focused on anisotropic packings of frictional grains generated by shear deformation leading to shear jamming 1-5 , occurring below the jamming density for isotropic packings of frictionless grains 6-11 . Here, with the aim of disentangling the role of shear-deformation-induced structures and friction in generating shear jamming, we computationally study sheared assemblies of frictionless spheres, over a wide range of densities. We demonstrate that shear deformation alone leads to the emergence of geometric features characteristic of jammed packings, with the increase of shear strain. We also show that such emergent geometry, together with friction, leads to mechanically stable, shear-jammed, packings above a threshold density that lies well below the isotropic jamming point.The transition from a fluid to a rigid, or jammed, state occurs and is of interest in a wide variety of condensed matter, with glasses, granular packings and colloidal suspensions being wellknown examples. Understanding the transition, occurring variously when temperature or applied stress is lowered, or the density raised, requires knowledge of interconnected changes in structure, thermodynamics, dynamics of structural relaxation and rheology. A unified and definitive picture of this jamming transition, has been an actively pursued goal with implications in diverse areas of research 6 . Random packings of frictionless hard and soft spheres have been studied in this general context 6-9 , and in particular as an idealized or reference model for granular materials. Much attention has been focused on behaviour as the jamming point, identified 7,8 to occur as a packing fraction of about 64%, is approached. Although the density at which random close packing occurs is understood not to be unique (see, for example, refs 6,9,10 and references therein), many aspects of behaviour suggesting the jamming point (denoted henceforth as φ J ) to be a critical point 11 , are robust 6 . Real granular materials studied experimentally inevitably deviate from this idealization, and how these deviations influence their jamming behaviour has been an active subject of recent research [1][2][3][4][5]12 . In particular, jamming of frictional grains under shear deformation, or shear jamming, has been shown to arise 3 over a range of stresses, and of densities below φ J , resulting in a density-stress phase diagram that is substantially different from the frictionless case 13 . An extended range of jamming densities has also been discussed earlier in the context of random loose packing 7,8,14 , protocol dependence and memory effects 15,16 , and specifically for frictional packings 1,2 .Given that the structural changes and organization resulting from the shear deformation, as well as friction are likely to pla...

The formation of self-organised structures that resist shear deformation have been discussed in the context of shear jamming and thickening [1][2][3], with frictional forces playing a key role. However, shear induces geometric features necessary for jamming even in frictionless packings [4]. We analyse conditions for jamming in such assemblies by solving force and torque balance conditions for their contact geometry. We demonstrate, and validate with frictional simulations, that the isostatic condition for mean contact number Z = D + 1 (for spatial dimension D = 2, 3) holds at jamming for both finite and infinite friction, above the random loose packing density. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems [5]. We perform rigidity percolation analysis [6,7] for D = 2 and find that rigidity percolation precedes shear jamming, which however coincides with the percolation of overconstrained regions, leading to the identification of an intermediate phase analogous to that observed in covalent glasses [8].Jamming is the process by which disordered assemblies of particles become rigid and resist externally imposed stresses, for instance when their density becomes large enough. It has been widely investigated, both as a phenomenon that occurs in granular matter, and as a particular aspect of the emergence of rigidity in disordered matter, e. g. colloidal suspensions, foams, glass formers and gels and to understand the rheological properties of thermal and athermal driven systems [1-3, 5, 9, 10]. The jamming of frictionless sphere assemblies is particularly well studied and occurs at a packing fraction of φ J ≈ 0.64, referred to as random close packing (RCP) or the jamming point. In the presence of friction, jamming is expected to occur down to a significantly lower density, which is ∼ 0.54 (in 3D) [11,12] in the isotropic case, also known as the random loose packing density (RLP), but strong dependences on friction and protocol lead to a wide range of estimates of this density, [0.54 − 0.61]. A rather different scenario was envisaged by Cates et al [13] for jamming in systems subjected to external stress, in which the application of external stress itself leads to a self organisation of particles that could resist stress, and thus lead to jamming. Such a scenario of shear jamming has been studied recently experimentally and theoretically [1,10,14,15] for sheared granular packings in the presence of friction, but also in the case of frictionless spheres [16][17][18][19]. However, our understanding is yet incomplete concerning various central issues, such as: (i) the range of densities over which shear jamming may occur, and the corresponding conditions, (ii) the differences and similarities between shear jamming and the isotropic frictionless as well as frictional jamming, (iii) a geometric description of the self organization of particles that lead to jamming behaviour, and (iv) the origins of the geometric organisation observed...

Self-organization, and transitions from reversible to irreversible behaviour, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behaviour is related to yielding of amorphous solids, jamming, and memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behaviour, and transitions between them, we investigate computationally the response of soft sphere assemblies to athermal cyclic shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic shear deformation induces transitions from reversible to irreversible behaviour in both unjammed and jammed soft sphere packings. Well above isotropic jamming density (φ J ), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher density limit we designate φ cyc J , an unjammed phase emerges between a localised, absorbing phase, and a diffusive, irreversible phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing, and opens a window where shear jamming becomes possible for frictionless packings. Below φ J , two distinct localised states, termed point and loop reversibile, are observed. We characterise in detail the different regimes and transitions between them, and obtain a unified density-shear amplitude phase diagram. arXiv:1907.08503v1 [cond-mat.soft]