Rheology of Jammed Solids as a function of Stability

When an external deformation is applied to an amorphous solids, its mechanical response is dictated by the degree of stability in terms of its energy landscape. If the system is in a marginal state, tiny perturbations can lead the system to change its state and end up in a different energy minimum, whereas if the system finds itself in a configurations which corresponds to a very deep minimum in the landscape, a much stronger perturbation is required to drive the system away from its state. Amorphous solids show exotic behaviors under mechanical deformations such as memory effects, periodic orbit under oscillatory shear and ductile to brittle yielding transition. All these problems can be investigated by shearing the system in a particular direction and measuring the stress as a reaction to the applied strain. Thanks to a novel algorithm based on integrating radial degrees of freedom in the energy minimization of randomly distributed soft particles, it is now possible to tune the stability of amorphous packings producing from marginal to highly stable jammed configurations. This allowed for different findings which we summarize here:

• Highly stable packings keep a finite stress drop down to the jamming point;
• Marginal systems can encode a memory of a strain amplitude performing cyclic shear until the systems finds a limit cycle;
• The strain amplitudes that can be encoded have a higher bound which depends on the polydispersity of the system;
• After “breaking” highly stable systems by shearing them until a strain bigger than the yielding strain in a particular shear direction, they still show a major stress drop in the shear directions perpendicular to the previous one.