A jamming plane of sphere packings

Significance Jamming is a ubiquitous phenomenon that occurs when the viscosity diverges or the rigidity emerges in many soft matter systems, such as granular materials, glasses, foams, colloidal suspensions, emulsions, and polymers. Jamming of frictionless spheres is also closely related to the sphere packing and optimization problems. In practice, jammed packings can be obtained by various ways, among which, compression and shear are two widely employed protocols. Here, we demonstrate that compression and shear-jammed frictionless packings can be described under a unified framework called jamming-plane. Using computer simulations, we show that compression and shear jamming of frictionless spheres can occur at different densities in the limit of large systems, contrary to conventional wisdom, but the jamming criticality is protocol-independent.