Spacetime interpretation of Torsion in Prismatic Bodies

TL;DR

This paper develops a non-linear geometric theory for the plastic deformation of prismatic bodies, unifying classical models through a spacetime interpretation involving surfaces of constant mean curvature.

Contribution

It introduces a novel spacetime geometric framework that interpolates between existing linear and non-linear models of plastic deformation in prismatic bodies.

Findings

Unified geometric interpretation of deformation models

Explicit general solutions via holomorphic functions

Connection between classical models and spacetime geometry

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.