Spacetime interpretation of Torsion in Prismatic Bodies

Abstract

A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl's linear soap-film approximation and N\'adai's sand-pile model . Geometrically Prandtl's soap film and N\'adai's wavefront are unified into a single smooth surface of constant mean curvature in three-dimensional Minkowski spacetime. Although the theory is non-linear, a general solution may be given in terms of a freely specifiable holomorphic function of a single complex variable.