A model for nonlinear elasticity in rocks based on friction of internal interfaces and contact aging

Non-classical nonlinear elasticity in micro-inhomogeneous materials such as rocks and cracked or granular materials leads to a number of phenomena ranging from hysteresis and memory to a transient response of elastic properties to perturbations in dynamic or quasi-static experiments. Dynamic acousto-elastic testing (DAET) provides very detailed observations of some of these phenomena that are still not fully understood in terms of their physical origin. We suggest that the observations of non-classical nonlinear elasticity can be related to the physics of friction. We propose a conceptual model for the nonlinear elasticity based on friction of internal interfaces and the process of contact aging that leads to an increase of friction with increasing contact time. The central element of the model is the continuous interplay between (1) softening that occurs as small-scale damage due to shear motion of internal contacts and (2) stiffening (healing) as a thermally activated process of establishing connections across the contact at the current strain state. Chemical bonds, mineral fibres or capillary bridges are the most likely candidates for the physical nature of these connections. Our model qualitatively describes dynamic softening, hysteresis, slow dynamics and the shape of DAET loops including the absence of cusps and the loop orientation that leads to a stiffening at both maxima and minima of the dynamic strain.