Viscoelastic Solids

  • Alan WinemanEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 262)


Elastomers and soft biological tissues can undergo large deformations and exhibit time-dependent behavior that is characteristic of nonlinear viscoelastic solids. An overview of this subject is contained herein, beginning with a review of pertinent topics from linear viscoelasticity. After stating the general constitutive assumption for nonlinear viscoelastic solids, and then imposing restrictions imposed by consideration of superposed rotations and material symmetry, a number of specific forms that have been proposed in the literature are discussed. The emphasis is then confined to nonlinear single integral constitutive equations, specific cases being finite linear viscoelasticity and the Pipkin–Rogers constitutive equations. The latter contains, as a special case, the quasi-linear viscoelastic model used in the biomechanics of soft tissue. Representations for the Pipkin–Rogers model are provided for isotropy, transverse isotropy, and orthotropy. Uniaxial stretch histories for isotropic materials are used to show the deviation from linear behavior as nonlinear effects become important. A number of examples involving non-homogeneous deformations that have appeared in the literature are summarized.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

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