Abstract
We demonstrate theoretically that an ultrasonic wave propagating in a hyperelastic medium can self-control its phase velocities. This phenomenon occurs because the propagation of the ultrasonic wave generates acoustic radiation stresses in the medium, which can induce large deformation of the medium with significant stiffening effect. In turn, such deformation reshapes the wave propagation while the deformation stiffening changes significantly the phase velocities of the wave till the acoustic radiation stresses are balanced by elastic stresses in the current configuration of the hyperelastic medium. As a result of deformation stiffening, an initially isotropic medium becomes anisotropic, thus enabling self-control or self-bending of the wave propagation. We further reveal that, due to snap-through instability of acoustomechanical deformation in the hyperelastic medium, the ultrasonic wave can discontinuously switch its phase velocities from one state to another by jumping over a large unstable regime. This self-control and switchable mechanism of ultrasonic wave propagation in homogenous hyperelastic media offers innovative design opportunities for phononic, thermal and acoustic materials and devices.
Highlights
We demonstrate theoretically that an ultrasonic wave propagating in a hyperelastic medium can selfcontrol its phase velocities
Upon harnessing acoustic radiation stresses induced by both wave propagation and material deformation stiffening, we demonstrate that the phase velocity of the wave can be controlled by its own magnitude
As the acoustomechanical deformation of a hyperelastic medium is inevitably associated with snap-through instability, the stable profiles in Fig. 2 are plotted using solid lines while the unstable profiles are plotted with dashed lines
Summary
Propagation of the two ultrasonic waves generates acoustic radiation stress, which are capable of inducing large deformation in the layer with significant stiffening: as a result, the ultrasonic waves can self-change their phase velocities. From the viewpoint of a series of steady deformation states, changes in the amplitudes of input ultrasonic waves by acoustic sources can alter the acoustic radiation stresses, the deformation and the phase velocities of the waves. The hyperelastic medium deforms to current state with stiffened tangential stiffness, and the Christoffel equation determines the three polarized phase velocities along prescribed propagation direction. The phase velocity of quasi-longitudinal wave is adopted in the current study to demonstrate the speed of self-controlled waves in hyperelastic media. Because the compressible Gent model has accounted for the effect of deformation stiffening, the acoustomechanical deformation of the hyperelastic material can remarkably alter the three phase velocities, as elucidated below
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