Abstract
A finite deformation solution has been developed for the radial, circumferential and axial stress distributions in an axially stretched hollow cylindrical tube in equilibrium under constant internal and external pressure. These results for longitudinal tethering (i.e. axial stretch) of the tube have been compared with the case of plane strain finite deformation and it has been shown that the plane strain results reduce to the values given in the classical theory of elasticity when the deformations become infinitesimal. It has also been shown that the resultant hoop tension in the vessel wall may take either positive or negative values, depending upon the pressure and the radius of the tube, and furthermore that the resultant hoop tension is less for the axially stretched tube than for the un stretched tube in the intermediate to large range of circumferential wall stretch.
A salient feature of the finite deformation solution is its treatment of strain induced anisotropy of the cylindrical wall. An initially isotropic material exhibits elastic moduli that are equal in all directions but when the material of a cylindrical tube undergoes finite deformation the elastic moduli are no longer equal in all directions if calculated as incremental moduli. The distinction between such strain induced anisotropy of an initially isotropic material and true material anisotropy needs to be incorporated in future studies of vessel walls.
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