Summary
The modelling of a pre-stressed anisotropic viscoelastic solid is briefly reviewed and a general thermodynamic restriction is derived for a linearized costitutive equation around the prestressed state. Next the thermodynamic restriction is shown to imply the negative definiteness of the divergence of the energy flux. Indeed, the divergence proves to be unaffected by the pre-stress. The pre-stress instead affects the wave modes as is shown explicitly in the particular case when the pre-stress and the incremental stress-strain relation are isotropic.
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References
Mandal, B.: Reflection and transmission properties of elastic waves on a plane interface for general anisotropic media. J. Acoust. Soc. Am.90, 1106–1118 (1991).
Lanceleur, P., Ribeiro, H., De Belleval, J. F.: The use of inhomogeneous waves in the reflection-transmission problem at a plane interface between two anisotropic media. J. Acoust. Soc. Am.93, 1882–1892 (1993).
Boulanger, Ph., Hayes, M.: Bivectors and waves in mechanics and optics. London: Chapman & Hall 1993.
Caviglia, G., Morro, A.: Inhomogeneous waves in solids and fluids. Singapore: World Scientific 1992.
Buchen, P. W.: Plane waves in linear viscoelastic media. Geophys. J. R. Astr. Soc.23, 531–542 (1971).
Boulanger, Ph., Hayes, M.: Waves in elastic media. In: Stability and wave propagation in fluids and solids (Galdi, G. P., ed.), pp. 1–38. Wien: Springer 1995.
Hayes, M.: Viscoelastic plane waves. In: Wave propagation in viscoelastic media (Mainardi, F., ed.), pp. 28–40. Boston: Pitman 1982.
Caviglia, G., Morro, A.: Inhomogeneous waves in anisotropic dissipative bodies. Continuum Mech. Thermodyn.7, 231–248 (1995).
Fabrizio, M., Morro, A.: Mathematical problems in linear viscoelasticity. Philadelphia: SIAM 1992.
Morro, A.: Rays in dissipative solids. In: Waves and stability in continuous media (Rionero, S., Ruggeri, T., eds.), pp. 277–288. Singapore: World Scientific 1994.
Haupt, P., Pao, Y. H., Hutter, K.: Theory of incremental motion in a body with initial elasto-plastic deformation. J. Elasticity28, 193–221 (1992).
Marsden, J. E., Hughes, T. J. R.: Mathematical foundations of elasticity. Englewood Cliffs: Prentice-Hall 1983.
Hoger, A.: The elasticity tensor of a transversely isotropic hyperelastic material with residual stress. J. Elasticity42, 115–132 (1996).
Synge, J. L.: Flux of energy for elastic waves in anisotropic media. Proc. R. Irish Acad. A58, 13–18 (1956).
Achenbach, J. D.: Wave propagation in elastic solids, § 1.7. Amsterdam: North-Holland 1975.
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Caviglia, G., Morro, A. Energy flux and dissipation in pre-stressed solids. Acta Mechanica 128, 209–216 (1998). https://doi.org/10.1007/BF01251891
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DOI: https://doi.org/10.1007/BF01251891