Acoustoelastic equations and Lamb waves dispersion characteristics of finitely deformed biological soft tissues with the growth-mechanical coupling

Abstract

Acoustoelastic equations, especially the incremental constitutive law and the constitutive parameters associated with the growth increment, were presented for biological soft tissues coupling the growth and the mechanical effects. Both the initial growth deformation and the growth increment make biological tissues different from the general soft materials in acoustoelastic equations. Lamb waves dispersion in two finitely deformed biological soft layers was then investigated to explore the wave dispersion in biological tissues. The frequency dispersion equations were derived from which characteristics of wave dispersion of the first two modes were discussed. The influence of the predeformation and the external load on Lamb waves dispersion was quantitatively examined. It is found that some special dispersion phenomena such as the mode vanishment, frequency cut-off, frequency block, frequency pass and frequency gap may come up in Lamb waves dispersion. These dispersion features are dependent on the existence of phase velocity limits, the two-layer structure and the type of predeformation. Moreover, phase velocity limits were analytically deduced from the dispersion equations for the pre-stretched biological soft tissues. The elastic predeformation and the mechanical properties of biological tissues can then be determined from phase velocity limits, which provides a potential method to distinguish the growth deformation.