A theory of locally impenetrable elastic tubes

Abstract

We present a reduced-order theory for locally impenetrable elastic tubes with uniform circular cross-section. The constraint of local impenetrability is incorporated into a variational scheme to derive a complete set of governing equations, jump conditions, and boundary conditions. We show that when local impenetrability is actively enforced, the configurations of the tube comprise segments of standard Kirchhoff rod solutions appropriately connected to segments of constant Frenet curvature. The theory is illustrated via three examples: a fully flexible tube and an elastic tube, both hanging under self-weight, and a highly twisted elastic tube.