Finite elastic deformations of thin cylindrical tubes by mandrels with discontinuous curvature

Abstract

A thin cylindrical elastic tube, reinforced on the outer surface by a two parameter family of inextensible cords, is deformed in such a way that the inner surface assumes a given shape. A previous solution for this problem, valid only when the curvature of the deformed inner surface is continuous everywhere, is extended to the more general case where the curvature possesses discontinuities. The method of matched asymptotic expansions is used to construct the solution in the neighborhood of a discontinuity, and to join it smoothly with the earlier solution, which is shown to remain valid away from the discontinuity.The deformation described here occurs, for example, when a reinforced elastic tube is deformed due to an enclosed rigid mold or mandrel and an applied external pressure.