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Elasticity and anelasticity; Friction; Wave propagation; Acoustic properties;
Rheology and friction of fault zones; Plasticity, diffusion, and creep
Abstract:
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
