Mesoscale models of amorphous solids under cyclic shear: emergence and character of limit cycles.

Amorphous solids (amorphous metallic alloys, glassy polymers, foams, emulsions, pastes, compressed granular packings, etc.) respond in complex ways to imposed shear. In steady shear, the response depends on preparation and shear may or may not localize upon yielding. In cyclic shear, if the amplitude of cycling remains below the yielding threshold, the system may either exhaust all plastic behavior and become purely elastic, or lock into a periodic orbit where plasticity is reversed after one or many cycles and the system returns to its previous configuration. These complex limit cycles have been observed in experiments and particle-based simulations. Here, we show that a simple mesoscale model which treats the material as a mosaic of yielding plaquettes is able to capture the complex limit cycles with orders of magnitude less computational time than particle-scale models. We use the mesoscale model to study the limit cycles at various strain amplitude.