Numerical simulation of inextensible elastic ribbons

TL;DR

This paper develops a finite element method for simulating narrow elastic bands using reduced models, providing convergence guarantees and practical algorithms, with numerical results confirming theoretical predictions and illustrating band behavior.

Contribution

It introduces a convergent finite element discretization and an energy-monotone iterative method for simulating inextensible elastic ribbons.

Findings

Numerical experiments confirm convergence and stability.

The method effectively captures the qualitative behavior of elastic bands.

The approach reduces computational complexity for thin elastic objects.

Abstract

Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element discretization for the one-dimensional energy functional together with a fully practical, energy-monotone iterative method for computing stationary configurations are devised. Numerical experiments confirm the theoretical findings and illustrate the qualitative behavior of elastic narrow bands.