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Percolating Plastic Failure as a Mechanism for Shear Softening in Amorphous Solids

``Shear softening" refers to 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 shear softening. The attaintment of the steady-state value of the shear modulus associated with plastic flow is identified with a percolation 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 shear softening.