**44**, 1, pp. 31-53, 1996

### Nonlinear Viscoelastic Elliptical Bar Under Combined Torsion with Tension

In [1] DARWISH and CANNON considered the problem of twisting of a cylindrical bar of elliptic cross-section. The bar was assumed to consist of a viscoelastic material. The principal cubic theory of nonlinear viscoelasticity was used to obtain a nonlinear Volterra integral equation of the second kind for the angle of twist *θ*(*t*) as a function of time *t*. In this work we consider a cylindrical bar of elliptic cross-section which consists of a viscoelastic material. At first, we subject the bar to torsion around the axis of the bar as we did in the previous work [1]. After an interval of time, we subject the bar to a longitudinal axial tensile force, in addition to torsion, for an additional period of time. We derive a system of two nonlinear Volterra integral equations of the second kind for the angle of twist *θ*(*t*) and the relative extension function *γ*(*t*). We prove the existence and uniqueness of the solution pair (*θ*(*t*), *γ*(*t*)) and analyze a numerical procedure for the approximate solution of the pair (*θ*(*t*), *γ*(*t*)). Results of a numerical study of (*θ*(*t*), *γ*(*t*)) are presented for both the linear and nonlinear theory. The behaviour of the normal axial stress and the shearing stresses are also investigated for each pair (*θ*(*t*), *γ*(*t*)), and the results for both the linear and nonlinear theory are presented.

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