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.

This paper presents a multiscale fluid model based on mesoscale dynamics and viscous fluid equations as a generic tool for digital marbling purposes. The model uses an averaging technique on the adaptation of a stochastic mesoscale model to obtain the effect of fluctuations at different levels. It allows various user controls to simulate complex flow behaviors as in traditional marbling techniques, as well as laminar and turbulent flows. Material transport is based on an improved advection solution to be able to match the highly detailed, sharp fluid interfaces in marbling patterns. In the transport model, two reaction models are introduced to create different effects and to simulate density fluctuations.

The purpose of this paper is to present new special explicit inhomogeneous plane wave solutions of the linearized equations of motion for elastic cubic crystals. It is based upon the "directional-ellipse" method which leads to an eigenvalue problem for the complex symmetric acoustical tensor. The solutions are obtained by considering a special case for which the determination of the three complex eigenvalues of this tensor reduces to finding the three complex cubic roots of a real positive number. Explicit simple expressions are presented for the slowness and amplitude bivectors.

In this paper, special Blatz—Ko nonlinear elastic materials are considered, which are characterized by a constitutive constant and a constitutive function. We here deal with the propagation of finite-amplitude waves in such materials subjected to an arbitrary static homogeneous deformation. In a previous paper, it was shown that linearly polarized transverse damped inhomogeneous plane waves may propagate. The orthogonal propagation and polarization directions are arbitrary. The special Blatz—Ko materials are compressible so that homogeneous longitudinal waves may also propagate. Here it is shown that the superposition of a transverse damped inhomogeneous wave and of a longitudinal wave is also a solution, in the case when the propagation direction of the longitudinal wave is orthogonal to the polarization direction of the transverse wave. Also, results are obtained for the energy density and the energy flux of the superposition of these waves.

No abstract