The stress and deformation analysis of an anisotropic linear viscoelastic hollow sphere under a symmetrical loading on the boundaries is considered. In order to reduce some of the mathematical difficulties, assumptions of small strain with quasistatic stress-strain conditions are consistently made. The solution is found for a system of non-homogeneous anisotropic viscoelastic media, and subsequently reduced to that for a homogeneous medium. Numerical results for both short-time and long-time behavior are presented for a number of simple model media in the anisotropic viscoelastic case and compared with the result for the elastic or viscoelastic medium in the isotropic case.

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