How periodic surfaces bend without stretching

TL;DR

This paper characterizes how periodic surfaces deform without stretching, establishing a constraint that links inextensional bending and twisting, with various examples illustrating the concept.

Contribution

It introduces a new theoretical framework for understanding inextensional deformations of periodic surfaces, akin to a Gauss-like theorem.

Findings

Deformation modes are constrained by a Gauss-like relation.

Periodic surfaces can bend and twist without stretching.

Examples demonstrate practical applications of the theory.

Abstract

Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic surfaces. In a way reminiscent of Gauss theorem, the result builds a constraint that relates the ways in which the periodic surface stretches, effectively but isometrically, to the ways in which it bends and twists. Several examples and use cases are presented.