Inflation and eversion of functionally graded non-linear elastic incompressible circular cylinders

Abstract

We study axisymmetric radial deformations of a circular cylinder composed of an inhomogeneous Mooney–Rivlin material with the two material parameters varying continuously through the cylinder thickness either by a power law or an affine relation. It is found that for the exponent of the power law function equal to 1, the hoop stress for an internally pressurized cylinder is uniform in the cylinder. One can tailor the gradation of these two material parameters to make the maximum tensile hoop stress occur either on the inner surface or on the outer surface. Also, the stress concentration in a pressurized thick cylinder strongly depends upon the value of the exponent of the power law variation of the two material parameters. For an affine through-the-thickness variation of the two elastic moduli the hoop stress at the point R = R in R ou is nearly the same as that in a cylinder composed of a homogeneous material. Here R in and R ou equal, respectively, the inner and the outer radii of the cylinder in the unstressed reference configuration, and R is the radial coordinate of a point in the reference configuration. The stress distribution in an everted cylinder strongly depends upon its thickness in the reference configuration.