Differences in plasticity between hard and soft spheres

Contact changes in packings of sheared hard spheres invariably trigger instabilities and irreversible rearrangements, providing an archetypal scenario for plasticity of disordered media. Here we show that the plasticity of jammed soft spheres at any finite pressure follows a different scenario, with only 14% of contact changes leading to irreversible rearrangements, irrespective of pressure, size, dimension or interaction potential. Moreover, we find that for sheared soft spheres, the nonlinear quantities associated with either contact changes or irreversible events exhibit the same finite-size scaling with pressure and system size as linear response quantities such as the shear modulus, suggesting an unexpected connection between curvature and saddle points in the potential energy landscape. Together our results indicate that soft spheres at finite pressure are not a smooth perturbation away from hard spheres, and that the nonlinear response of soft spheres is singular at zero pressure.