Finite-Amplitude Waves in Deformed Mooney-Rivlin Materials

Professor Michael A. Hayes
Department of Mathematical Physics
University College Dublin
Dublin, Ireland

Sponsored by the Engineering Mechanics Department

Date:  Tuesday, August 12, 1997
Time:  3:30 p.m.
Place:  306 Bancroft Hall


Two linearly polarized finite-amplitude plane shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.  Explicit expressions are given for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'.  These are the only directions such that the two wave speeds are equal.  They are determined only by the basic static deformation of the material.  There are two such directions, if this deformation is triaxial; and one, if it is biaxial.  Although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution.  In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.  An energy-flux velocity vector is introduced and a duality between slowness and energy-flux velocity is exhibited.  The slowness and ray surfaces are obtained.  As in crystal optics and crystal acoustics, cones of internal and external conical refraction may be introduced.