Equivalence theorems on the propagation of small amplitude waves in prestressed linearly elastic materials with internal constraints

By extending the procedure of linearization for constrained elastic materials in the papers by R. S. Marlow [J. Elasticity 27 (1992), no. 2, 97–131; MR1151543 (93c:73027)] and P. Chadwick, A. M. Whitworth and P. Borejko [Arch. Rational Mech. Anal. 87 (1985), no. 4, 339–354; MR0767505 (86b:73009)], we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory). The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell’s two equivalence theorems on wave propagation in finite elasticity hold for each type of wave.