Finite deformations of a hyperelastic, compressible and fibre reinforced tube

Finite torsion and axial stretch of a long, hyperelastic, compressible and circular tube is studied for the design of a prototype of small diameter vascular prosthesis. The analysis is carried out in the context of the finite elasticity theory by using a class of Ogden strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The highly non-linear differential equations with variable coefficients governing the problem are solved numerically using a Runge–Kutta method. For different prestresses supported by the tube, the effects of the combined deformation on the stress distributions are presented.