Amorphous matter at the mesoscale: Avalanches and reversible hysteresis.

Abstract: Many solids and solid-like materials lack any underlying crystalline order.  Examples include amorphous alloys; glassy polymers; soft glassy materials (e.g. emulsions, foams, pastes, and dense suspensions); densely confined granular matter; confluent biological tissues, etc.  The mechanical response of crystalline and polycrystalline solids — elasticity, plastic yielding, and fracture — is generally understood in terms of microstructural defects (such as voids, dislocations, grain boundaries, etc.), but in a highly disordered amorphous material, the notion of structural defects becomes tenuous.  Over the last several decades, it has become increasingly clear that the mechanical behavior of these amorphous materials is governed by so-called shear transformations: small clusters of particles which yield and rearrange collectively to accommodate the imposed loading.  We will discuss a class of models which operate at the meso-scale — coarser than the constituent particle scale but below the scale at which a continuum description would apply — based on these localized yielding events.  We show how these models recover the basic phenomenology observed in particle-based simulation and experiments and predict new phenomena not yet observed in experiments.  In particular, we will look at i) the bursty, intermittent response — resulting from so-called avalanches — during steadily imposed shear strain and its relationship with shear induced diffusion and ii) the response to cyclicly imposed shear and, in particular, the existence of a reversible-hysteric regime.