The Critical Role of the Base Curve for the Qualitative Behavior of Shearable Rods

Abstract

In this paper, we treat several aspects of the induced geometrically exact theory of shearable rods, of central importance for contact problems, for which the regularity of solutions depends crucially on the presence of shearability. (An induced theory is one derived from three-dimensional theory by the imposition of constraints. Because the role of thickness enters into our theory in an essential way, it is an exact version of what has been called the theory of “moderately thick” rods.) In particular, we study how the theory and constitutive restrictions depend upon the choice of the base curve, and we show how this choice has major qualitative consequences, which are illustrated with several concrete examples.