Elastic building blocks for confined sheets

TL;DR

This paper investigates how thin elastic sheets deform under weak confinement, revealing the coexistence of distinct stress domains with different constraints and energy characteristics, which enhances understanding of their complex shape behavior.

Contribution

It introduces a novel analysis of elastic sheets showing the coexistence of geometric and mechanical stress domains under confinement, highlighting different constraints and energy distributions.

Findings

Identification of two stress domains: focused-stress patches and diffuse-stress regions.

Distinct constraints govern each stress domain: geometric inextensibility vs. stress tensor dominance.

Implications for analyzing elastic sheet behavior under various forcing conditions.

Abstract

We study the behavior of thin elastic sheets that are bent and strained under the influence of weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains that differ in their characteristic stress distributions and energies, and reflect different constraints. A focused-stress patch is subject to a geometric, piecewise-inextensibility constraint, whereas a diffuse-stress region is characterized by a mechanical constraint - the dominance of a single component of the stress tensor. We discuss the implications of our findings for the analysis of elastic sheets that are subject to various types of forcing.