Plane waves in microstretch elastic solid with voids

Abstract

A linear theory of microstretch elastic solid containing uniform distribution of uniform voids has been formulated. Constitutive relations are developed by constructing suitable strain energy density function from the basic state variables. Then using the principles of mechanics, the field equations are derived for isotropic homogeneous microstretch elastic medium containing voids. The possibility of propagation of plane waves is explored and found that there may exist four sets of coupled dilatational waves and two sets of coupled transverse waves traveling with distinct speeds. The coupled longitudinal waves are found to be attenuating and dispersive, while the coupled transverse waves are dispersive but non-attenuating in nature. The coupled transverse waves are found to be independent of the presence of stretch and voids in the medium. The attenuation of coupled longitudinal waves arises due to the presence of dissipation coefficient of void volume fraction. In case of Voigt model, only the coupled transverse waves arising due to the microrotation disappear below their respective critical frequency, while in case of non-Voigt model, three sets of coupled longitudinal waves and one set of coupled transverse waves corresponding to predominantly due to the microrotation are non-progressive waves below their respective critical frequencies. Some limiting cases have been discussed and explained. Numerical computations have been carried out for Gauthier composite plate material and the results are displayed graphically.