The Effect of Elastic Surface Coating on the Finite Deformation and Bifurcation of a Pressurized Circular Annulus

Abstract

A plane-strain theory of an elastic solid coated with a thin elastic film on part or all of its boundary was developed recently by Steigmann and Ogden (1997a). In this paper the theory is applied to the (plane-strain) problem of a thick-walled circular cylindrical tube which is subject to both internal and external pressure and which has an elastic coating on one or both of its circular cylindrical boundaries. The effect of the coating on the symmetrical response of the annular cross-section of the tube is determined first. It is noted, in particular, that while the pressure may exhibit a maximum followed by a minimum during inflation for an uncoated tube it may be a monotonic increasing function of the radius for a coated tube with coating elastic modulus sufficiently large. Next, the possibility of bifurcation from a symmetrical configuration is examined and again the influence of the coating is analysed. The effect of a coating on the outer boundary is compared with that on the inner boundary. Specifically, during compression, coating on the outer boundary delays bifurcation compared with the uncoated case. On the other hand, when the coating is on the inner boundary, bifurcation is either delayed or advanced relative to the uncoated situation depending on the values of the bending stiffness and tube thickness parameters. Generally, bifurcation is delayed by an increase in the magnitude of the bending stiffness of the coating at fixed values of the other parameters.