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arXiv · 1512.06544

Protocol-dependent shear modulus of amorphous solids

Daiju Nakayama·Hajime Yoshino·Francesco Zamponi
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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, $μ_{\rm ZFC}$, is associated with the linear response of a single energy minimum. The second, $μ_{\rm FC}$, 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 $μ_{\rm FC}/μ_{\rm ZFC}$ 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.

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Daiju Nakayama, Hajime Yoshino, Francesco Zamponi. 2016-08-19. Protocol-dependent shear modulus of amorphous solids. https://doi.org/10.1088/1742-5468%2F2016%2F10%2F104001

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