Protocol-dependent shear modulus of amorphous solids

Abstract

We investigate the linear elastic response of amorphous solids to a shear strain at zero temperature. We find that the response is characterized by at least two distinct shear moduli. The first one, ${\mu }_{\mathrm{ZFC}}$, is associated with the linear response of a single energy minimum. The second, ${\mu }_{\mathrm{FC}}$, is related to sampling, through plastic events, an ensemble of distinct energy minima. We provide examples of protocols that allow one to measure both shear moduli. In agreement with a theoretical prediction based on the exact solution in infinite spatial dimensions, the ratio ${\mu }_{\mathrm{FC}}/{\mu }_{\mathrm{ZFC}}$ is found to vanish proportionally to the square root of pressure at the jamming transition. Our results establish that amorphous solids are characterized by a rugged energy landscape, on which the infinite-dimensional solution can give useful insight.

7 pages, 7 figures, to appear in JSTAT

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