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From a theoretical study of the mechanical response of jammed materialscomprising frictionless and overdamped particles under oscillatory shear, wefind that the material becomes soft, and the loss modulus remains finite evenin an absorbing state where any irreversible plastic deformation does notexist. The trajectories of the particles in this region exhibit hysteresisloops. We succeed in clarifying the origin of the softening of the material andthe residual loss modulus with the aid of Fourier analysis. We also clarify theroles of the yielding point in the softening to distinguish the plasticdeformation from reversible deformation in the absorbing state.

Softening and residual loss modulus of jammed grains under oscillatory shear in an absorbing state