Systems far from equilibrium have numerous practical uses, but challenge our understanding of their underlying physics. Materials like foams, emulsions, suspensions and granular matter can show liquidlike properties or get trapped in a solidlike jammed state. The phase transition between the flowing and static state is often referred to as the ‘jamming transition‘. This work focuses on the mechanical behavior of amorphous viscoelastic materials, close to the jamming point. In many traditional solids, the relation between stress and strain is well described by a linear proportionality, known as Hooke’s law. In jammed solids, by contrast, the stressstrain relation quickly becomes nonlinear, making them much harder to model. Here we ask how and why the linear response breaks. To answer the questions, we investigate the breakdown of linear response as a function of deformation rate and amplitude. @en

We investigate irreversibility in soft frictionless disk packings on approach to the unjamming transition. Using simulations of shear reversal tests, we study the relationship between plastic work and irreversible rearrangements of the contact network. Infinitesimal strains are reversible, while any finite strain generates plastic work and contact changes in a sufficiently large packing. The number of irreversible contact changes grows with strain, and the stress–strain curve displays a crossover from linear to increasingly nonlinear response when the fraction of irreversible contact changes approaches unity.

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We report the results of molecular dynamics simulations of stress relaxation tests in athermal viscous soft sphere packings close to their unjamming transition. By systematically and simultaneously varying both the amplitude of the applied strain step and the pressure of the initial condition, we access both linear and nonlinear response regimes and control the distance to jamming. Stress relaxation in viscoelastic solids is characterized by a relaxation time τ∗ that separates short time scales, where viscous loss is substantial, from long time scales, where elastic storage dominates and the response is essentially quasistatic. We identify two distinct plateaus in the strain dependence of the relaxation time, one each in the linear and nonlinear regimes. The height of both plateaus scales as an inverse power law with the distance to jamming. By probing the time evolution of particle velocities during relaxation, we further identify a correlation between mechanical relaxation in the bulk and the degree of non-affinity in the particle velocities on the micro scale.@en

Materials like foams and emulsions display complex rhelogical behavior close to their jamming transition. When driven too hard the initial linear stress-strain response breaks down and the material softens. Using simulations of soft repulsive spheres, we characterize the softening crossover by establishing the relevant strain scale below which linear response is valid. We further perform shear reversal tests to investigate the interplay between proximity to jamming and the onset of irreversibility.@en

The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point-suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear start-up tests in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network.@en