Elastic constants of zero-temperature amorphous solids

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, nonaffine. 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.

Automated summary

This passage discusses the elastic constants of zero-temperature amorphous solids, which are calculated by subtracting a correction term from the Born term. The correction term represents the nonaffine deformation of the solid at the microscopic level. The derived alternative expressions for the elastic constants are non-negative and can be used in approximate theories for sound damping and elastic constants in zero-temperature amorphous solids.