Slow dynamics experiments in solids with nonlinear mesoscopic elasticity

Abstract

As revealed by longitudinal bar resonance experiments, materials such as rocks and concrete show show a rich diversity of nonlinear elastic behavior. As a function of increasing drive level, resonance frequencies shift downward by several percent, the resonant line shape changes, and harmonics and slow dynamics appear. Slow dynamics [1] refers to the time-dependent recovery of an elastic modulus to its initial value after being softened by large strain. In order to explore the mechanisms of nonlinear response including slow dynamics, we performed experiments on concrete and several different earth materials. The softening (conditioning) and recovery processes appear to be asymmetric. Conditioning takes place quickly; full recovery of the elastic modulus (as measured by drift of the resonance peak) takes minutes to hours, depending on the length of time the conditioning strain was applied. We find that for a wide variety of rocks and concretes, the recovery of the resonant frequency goes as log(time). Logarithmic time-dependence is a phenomenon associated with static friction and restoration of surface contacts, which in rocks probably takes place at touching crack surfaces.