Finite-Amplitude Damped Inhomogeneous Waves in a Deformed Blatz-Ko Material

Abstract

In this paper special Blatz-Ko nonlinear elastic materials are considered, which are characterized by a constitutive constant and a constitutive function. We deal with the propagation of finite-amplitude inhomogeneous plane waves in such materials subjected to an arbitrary static homogeneous deformation. Linearly polarized transverse “damped” inhomogeneous plane wave solutions are explicitly obtained. Such waves are attenuated (or amplified) both in space and time (time-harmonic inhomogeneous plane waves obtained previously by Destrade appear as a special case). The properties of the energy flux vector and energy density associated with these wave solutions are investigated. With an appropriate concept of mean, it is seen that the “mean” energy-flux vector and the “mean” energy density satisfy two relations which are independent of the constitutive constant and constitutive function of the model, and of the homogeneous static deformation of the material. These relations are the same as those obtained by Hayes in the general context of time-harmonic inhomogeneous plane waves in linear systems. However, here, the theory is nonlinear, and the finite-amplitude waves are not time-harmonic.

Finite-amplitude Love waves in a pre-stressed compressible elastic half-space with a double surface layer

“…in accordance with the previous results about finite-amplitude inhomogeneous plane waves in unbounded pre-stressed special Blatz-Ko materials obtained in Destrade [22] and Rodrigues Ferreira and Boulanger [23]. These relations are the same as those derived by Hayes [28] in the context of linear theories.…”

“…The dispersive behavior of time-harmonic finite-amplitude shear horizontal waves propagating in a prestressed compressible elastic layer embedded between two identical compressible elastic half-spaces, has been investigated recently by Kayestha et al [18]. Earlier studies in the area of time-harmonic finite-amplitude homogeneous waves [19][20][21] and inhomogeneous waves [22][23][24] are already discussed in the introduction Section of [18], and will not be further elaborated on in the present paper.…”

“…Note that when the condition given in Eq. (20) is not satisfied, other solutions may be obtained (see Rodrigues Ferreira and Boulanger [23]) but they are not time-harmonic. In this paper, the interest is in time-harmonic Love waves.…”

“…(23) and (24), respectively. In the pre-stressed half-space, since the waves decay in the direction of the unit vector m, the displacement field given in Eq.…”

Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

“…Deschamps & Huet [9] consider complex surface waves associated with inhomogeneous skimming and Rayleigh waves in linear elastodynamics. Rodrigues Ferreira & Boulanger [10] extend the theory of damped inhomogeneous waves to the finite-amplitude case in a deformed Blatz-Ko material. Vashishth & Sukhija [11] extend the theory of inhomogeneous waves to the case of porous piezo-thermoelastic solids.…”