Acoustoelasticity of solid/fluid composite systems

A heterogeneous medium composed of inviscid fluid and solid constituents is pre-stressed, resulting in relative slip of material particles at the interfaces between the solid and the fluid. The standard theory of acoustoelasticity, which is concerned with small deformation superimposed upon large initial strain, is generalized here to include the effects of the interfacial slip. Difficulties arise from the possibility that the traction, viewed as a function of either the undeformed material (Lagrangian) coordinates or of the intermediate coordinates, is not necessarily continuous across the interface. It is shown that the problem is most easily considered in the intermediate coordinates, leading to a divergence formulation of the equations of small motion from which the interface conditions arise naturally. The theory is demonstrated for the problem of a fluid-filled borehole with a pressurized fluid and pre-strained solid. An explicit expression is found for the change in the speed of the tube wave, which is the quasi-static limit of the Stoneley wave mode.