An analysis of the Propagation Condition for Small Displacement Waves in Prestressed Bodies

We analyze the local propagation condition for the small-displacement waves superimposed to an equilibrium configuration of a body with initial stress. The analysis is set up in terms of a certain acoustic tensor and shows the exact contributions of both the hydrostatic and deviatoric parts of the prestress. Some qualitative properties of wave propagation are deduced. For instance, we show that at any point of a body in any state of stress there exists at least one triad of orthogonal directions in which longitudinal waves may propagate. For any wave propagating at any given point an intrinsic reference triad is defined. By projection of the propagation condition on the axes of this triad we obtain the intrinsic equations of the wave; because of their simplicity, they are useful to study the possibility of local propagation of a given wave and to analyze the experimental information that this wave provides on the prestress and incremental elasticity tensor.