Subdivision Shell Elements with Anisotropic Growth

TL;DR

This paper introduces a subdivision shell element method based on Loop's surfaces, capable of modeling large deformations and anisotropic growth in thin shells, with applications demonstrated through various growth scenarios.

Contribution

It extends Kirchhoff-Love shell theory to include arbitrary in-plane growth within a computationally efficient subdivision shell element framework.

Findings

The method handles large deformations and anisotropic growth effectively.

Demonstrated applications include growth of spheres and boundary instabilities.

The approach is computationally efficient and suitable for complex growth scenarios.

Abstract

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.