On elastic constants of zero-temperature amorphous solids

Abstract

Elastic constants of zero-temperature amorphous solids are given as the difference between the Born term, which results from a hypothetical affine deformation of an amorphous solid, and a correction term which originates from the fact that the deformation of an amorphous solid due to an applied stress is, at the microscopic level, non-affine. Both terms are non-negative and thus it is a priori not obvious that the resulting elastic constants are non-negative. In particular, theories that approximate the correction term may spuriously predict negative elastic constants and thus an instability of an amorphous solid. Here we derive alternative expressions for elastic constants of zero-temperature amorphous solids that are explicitly non-negative. These expressions provide a useful blueprint for approximate theories for elastic constants and sound damping in zero temperature amorphous solids.

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Cited by in corpus (2)

• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition