Abstract
Under shear, a system of particles changes its contact network and becomes unstable as it transitions between mechanically stable states. For hard spheres at zero pressure, contact breaking events necessarily generate an instability, but this is not the case at finite pressure, where we identify two types of contact changes: network events that do not correspond to instabilities and rearrangement events that do. The relative fraction of such events is constant as a function of system size, pressure and interaction potential, consistent with our observation that both nonlinearities obey the same finite-size scaling. Thus, the zero-pressure limit of the nonlinear response is highly singular.
Highlights
Disordered solids such as granular materials, metallic glasses, colloids, and foams undergo a sequence of transitions between mechanically stable states when slowly sheared
We find that at finite pressures, we can sharply distinguish two classes of contact changes: network events, which do not correspond to instabilities, and rearrangements, which correspond to saddles in the energy landscape
We have identified two types of contact changes that exist in finite pressure systems: network events and rearrangements
Summary
We observe events where the stresses exhibits a finite jump and the particles undergo discontinuous motion [Fig. 1(b)] We observe events where individual contacts are broken or created but the stress remains smooth [Fig. 1(c)] We refer to these as network events. To investigate the (ir)reversibility of each contact change, we study the change in the force contact network, defined using the quadrature sum of the differences in interparticle forces before and after an infinitesimal strain loop: F (γn) =. Our simulations are consistent with the latter scenario, and the existence of a finite minimum magnitude of stress drops associated with saddles (Supplemental Material Fig. S1) makes it possible to distinguish network events from rearrangements. For hard spheres at zero pressure, contact breaking events necessarily correspond to a saddle point or instability [5], which is clearly not the case at finite pressure
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