The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of “mesoscopic” blocks alternating between an elastic behavior and plastic relaxation, when they are loaded above a threshold. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. A review is given of not only the physical insight provided by these models into practical issues such as strain localization, creep, and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, connections are discussed with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line.

• Received 6 September 2017

DOI:https://doi.org/10.1103/RevModPhys.90.045006