Acceleration Waves in Isotropic Constrained Thermoelastic Materials

Abstract

Publisher Summary This chapter discusses acceleration waves in isotropic constrained thermoelastic materials. The chapter discusses the cases of homothermal and homentropic waves; for both the propagation conditions are analogs of the classical Fresnel–Hadamard condition. Growth equations have also been derived for plane waves propagating into homogeneously deformed material which is at rest ahead of the wave front. The conditions for propagation of acceleration waves in the light of the isotropy of the material are reexamined. Restrictions imposed by the constraint equations on the propagation of acceleration waves are examined. The three special cases for which the constraint equations take simple forms, and for which the acceleration wave is a principal wave is discussed in the chapter. It is shown that for these three cases that the constraints are linearly dependent, and furthermore, that acceleration waves are always transverse. These observations also hold for acceleration waves propagating in material that is in a state of uniform dilatation.