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Disorder and fluctuations in the yielding transition of amorphous solids under strain
When slowly deformed at low temperature from an initial quiescent state, amorphous solids yield beyond some finite level of applied strain and reach a steady state characterized by plastic flow. The way yielding takes place is classified in two main categories : the “brittle” extreme where the sample catastrophically breaks into pieces and show macroscopic shear bands, as often observed in molecular and metallic glasses, and “ductile” behavior in which plastic deformation increases progressively, commonly found in soft-matter glassy systems. We argue on the basis of analytically solvable mean-field elasto-plastic models and extensive computer simulations of generic atomic glasses that the variety of behavior can be understood within a unique theoretical framework. The nature of yielding is shown to depend on the degree of effective disorder which is controlled by the preparation of the amorphous solid. Yielding evolves from a mere crossover for poorly annealed samples to a nonequilibrium discontinuous transition for well-annealed, very stable samples. The transition between these two regimes is marked by a random critical point.