The role of material and geometric nonlinearities in acoustoelasticity

Wave propagation in prestressed and prestrained continua can be modelled by the theory of acoustoelasticity, which typically includes dierent assumptions. These are third or fourth order expressions of hyperelastic strain energy, as well as nite initial strains and a formulation of balance equations in the current conguration. In this paper, we use a model describing wave propagation in a three dimensional elastically prestrained continuum to clarify the role of dierent mechanical aspects taken into account in the classical hypotheses of the theory. We consider dierent states of prestress: hydrostatic, biaxial and uniaxial. Changes in shear and longitudinal wave speeds and their polarization as a function of the initial prestress are described for all directions of propagation. The role of the strain energy power order in changes of speed is elucidated. Moreover, material and geometric nonlinearities are shown to aect changes with the opposite sign, depending also on the direction of propagation.