Szamel Grzegorz
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA.
Phys Rev E. 2023 Jun;107(6-1):064608. doi: 10.1103/PhysRevE.107.064608.
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.
零温度非晶态固体的弹性常数表示为玻恩项（由非晶态固体的假设仿射变形产生）与修正项（源于施加应力导致的非晶态固体变形在微观层面是非仿射的这一事实）之间的差值。这两项均为非负，因此所得弹性常数为非负这一点并非显而易见。特别是，对修正项进行近似的理论可能会错误地预测出负的弹性常数，进而导致非晶态固体的不稳定性。在此，我们推导了零温度非晶态固体弹性常数的替代表达式，这些表达式明确为非负。这些表达式为零温度非晶态固体弹性常数及声衰减的近似理论提供了有用的蓝本。
