Programmed buckling by controlled lateral swelling in a thin elastic sheet

TL;DR

This paper develops a theoretical framework for designing three-dimensional shapes in thin elastic sheets through controlled lateral swelling patterns, identifying feasible shapes and obstructions based on growth patterns and sheet thickness.

Contribution

It introduces an analytical solution for shape design via isotropic growth patterns in thin elastic sheets, highlighting limitations and obstructions.

Findings

Not all 3D shapes are achievable through controlled swelling.

Sheet thickness influences the feasibility of certain shapes.

Analytical solutions are provided for axisymmetric growth patterns.

Abstract

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.