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Spreading plastic failure as a mechanism for the shear modulus reduction in amorphous solids

We focus on the observed reduction in shear modulus when the stress on an amorphous solid is increased beyond the initial linear region. Careful numerical quasi-static simulations reveal an intimate relation between plastic failure and the reduction in shear modulus. The attainment of the smallest value of the shear modulus is identified with spreading of the regions that underwent a plastic event. We present an elementary “two-state” model that interpolates between failed and virgin regions and provides a simple and effective characterization of the phenomenon.