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The Quarterly Journal of Mechanics and Applied Mathematics 1977 30(2):223-234; doi:10.1093/qjmam/30.2.223
© 1977 by Oxford University Press
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PLANE CIRCULAR SHEARING OF INCOMPRESSIBLE FLUIDS AND SOLIDS

M. M. CARROLL

( Department of Mechanical Engineering, University of California Berkeley )

It is shown that a certain type of motion, which is sinusoidal in time, can be sustained in every member of a general class of homogeneous isotropic incompressi ble viscoelastic materials in the absence of body force. The class of materials includes simple fluids and solids and Rivlin-Ericksen fluids. The motions represent generalizations, to materials with general nonlinear response, of the exponentially dampled plane circularly polarized progressive waves and standing waves to which they reduce when the shear response is linear.


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