Anomalous Softness in Amorphous Matter in the Reversible Plastic Regime

We study an elastoplastic model of an amorphous solid subject to athermal quasistatic cyclic shear strain. We focus on cycling amplitudes in the so-called reversible-plastic regime where, after a transient, the system locks into a hysteretic limit cycle and returns to the same microscopic configuration after one or more strain cycles. We show that the ground state energy of the terminal limit cycle decreases with increasing cycling amplitude. In analogy to an annealed alloy or an aged colloidal glass, one would expect the states with lower energy to be mechanically harder and to require larger stresses and strains to trigger microscopic rearrangements. However, we show the opposite result: the systems with lower energy cycled at higher strain amplitude are mechanically softer and begin to exhibit plastic rearrangements at smaller stresses and strains within the cycle. We explain this anomaly quantitatively in terms of Eshelby inclusion theory where an inclusion is subjected to a particular negative stress value after it undergoes a yielding event. These results point the way toward measurements to be conducted in experiments and particle-based computer simulations on cyclically sheared amorphous solids.