In this paper, we examine the response of an incompressible elastomer when it is subjected to small, steady-state oscillations superposed on a large steady deformation. The material is assumed to be isotropic in its undeformed state, and its viscoelastic behavior is characterized by means of two different approximate theories: (a) Lianis’ approximation of the theory of finite linear viscoelasticity, and (b) Bernstein, Kearsley, Zapas’ elastic fluid theory, Signorini approximation. Theoretical expressions are developed for the uniaxial stress in a body subjected to steady-state sinusoidal oscillations superposed on a state of steady, finite, uniaxial extension, using both theories. A complex modulus is defined, which reduces to the complex modulus of infinitesimal viscoelasticity when the finite strain is zero. Experiments were performed on three different polymers and the observed response is compared with that predicted by both theories.

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