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Mathematics and Mechanics of Solids
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Superposition of transverse and longitudinal finite-amplitude waves in a deformed Blatz—Ko Material

E. Rodrigues Ferreira

Département de Mathématique, Université Libre de Bruxelles, Campus Plaine C.P.218/1, 1050 Bruxelles, Belgium

PH Boulanger

Département de Mathématique, Université Libre de Bruxelles, Campus Plaine C.P.218/1, 1050 Bruxelles, Belgium

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.

Key Words: finite elasticity • exact wave solutions • rubberlike materials • homogeneous and inhomogeneous plane waves

This version was published on October 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 5, 543-558 (2007)
DOI: 10.1177/1081286506064720
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