Nonlinear Viscoelastic Elliptical Bar Under Combined Torsion with Tension
In  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 . 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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