Non-equilibrium Strain and Elastic Hysteresis in Static and Dynamic Experiments in Sandstones

The physical origin of hysteretic elasticity in consolidated granular media is still debated. We show that hysteresis in quasi-static experiments (slow loading/unloading cycles) and dynamic acoustoelastic testing (fast perturbation of the sample obtained by a propagating or standing wave) can be seen as a consequence of slow dynamics, which also induces elastic anisotropy due to nonlinearity. Both conditioning (i.e. the evolution of the elastic properties towards a non-equilibrium steady state when a load is applied) and relaxation (i.e. the slow recovery of the original elastic properties when the strain is reduced) are described as the consequence of a non-equilibrium strain generated in the material by the applied load. Experiments performed span over five orders of magnitude in strain (from 10-7 to 10-2) and we demonstrate the proposed model captures well the observed phenomenology in the full strain range considered.