Stress formulation of acoustoelasticity

Acoustoelasticity describes the relationship between elastic wave velocities and the initial stress present in a material. Traditional theories consider successive deformations involving small amplitude wave motion superimposed on an initially deformed material. Then, a constitutive relationship must be applied to relate the initial static deformation to the desired relationships involving initial stress, resulting in expressions of wave velocities involving a mix of elastic stiffness and compliance constants. In this article, a pure stress formulation is developed for acoustoelasticity. In this setting, the problem involves the superposition of a dynamic stress wave on an initially stressed material configuration, rather than the superposition of kinematic variables. The phase velocity of the stress wave is naturally related to the initial stress through only the compliance constants. Thus, compliances are the fundamental constants of acoustoelasticity.