Abstract
We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency ``pump'' wave induces a strain field in the sample and modulates the propagation of a high-frequency ``probe'' wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.
Highlights
Nonlinear mesoscopic elastic materials (NMEMs) refer to a class of materials that can be mechanically described as an assembly of mesoscopic-sized “hard” elements embedded in a “soft” bond system [1]
The the relative velocity modulation (RVM) of the P wave in the “e2” direction is symmetric with respect to the zero-strain axis, which agrees with the theoretical prediction on the absence of coupling between the propagation speed of the P wave in the “e2” direction and the third-order elastic constants
The original formulation of Hughes and Kelly [29] was extended to introduce conditioning effects, through a scalar parameter α that is projected onto the principal strain axes. This model was derived in a very general form and can be applied to arbitrary wave polarizations and strain fields. It captures many features observed in experiments of dynamic acoustoelasticity including
Summary
Nonlinear mesoscopic elastic materials (NMEMs) refer to a class of materials that can be mechanically described as an assembly of mesoscopic-sized “hard” elements (e.g., grains with characteristic lengths ranging from tens to hundreds of microns) embedded in a “soft” bond system (e.g., cement between grains, pore space, fluid) [1]. Depending on the strain amplitude, there exist different regimes in which the variation of the resonance frequency with strain is dominated by classical nonlinearity, slow dynamics, or both [21,22] These observations have been described theoretically through a number of models derived from 1D theory of elasticity [13,15,23,24,25]. Measurement of these constants in solids has been made possible via the simplification of Murnaghan’s theory by Hughes and Kelly [29] They consider the particular case of a high-frequency (HF) pulse of relatively small amplitude (probe) used to probe the local change of elastic wave speed induced by a large deformation (pump). The experimental findings are compared to theoretical predictions from the approach proposed by Lott et al [40]
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