Abstract
We consider the propagation of finite amplitude plane transverse waves in a class of homogeneous isotropic incompressible viscoelastic solids. It is assumed that the Cauchy stress may be written as the sum of an elastic part and a dissipative viscoelastic part. The elastic part is of the form of the stress corresponding to a Mooney-Rivlin material, whereas the dissipative part is a linear combination of A 1, A 21 and A 2, where A 1, A 2 are the first and second Rivlin-Ericksen tensors. The body is first subject to a homogeneous static deformation. It is seen that two finite amplitude transverse plane waves may propagate in every direction in the deformed body. It is also seen that a finite amplitude circularly polarized wave may propagate along either n + or n −, where n +, n − are the normals to the planes of the central circular section of the ellipsoid x · B −1x =1. Here B is the left Cauchy-Green stra in tensor corresponding to the finite static homogeneous deformation.
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Dedicated with esteem to Professor Roger Fosdick.
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Hayes, M.A., Saccomandi, G. (2000). Finite Amplitude Transverse Waves in Special Incompressible Viscoelastic Solids. In: Carlson, D.E., Chen, YC. (eds) Advances in Continuum Mechanics and Thermodynamics of Material Behavior. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0728-3_14
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DOI: https://doi.org/10.1007/978-94-010-0728-3_14
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