Modeling and simulation of thin sheet folding

TL;DR

This paper develops a rigorous mathematical model for the folding of thin elastic sheets along curved arcs, deriving a 2D Kirchhoff plate model and proposing numerical methods for large deformation simulations.

Contribution

It introduces a new reduced 2D model for thin sheet folding derived from hyperelasticity and develops numerical schemes for large deformation analysis.

Findings

Successful derivation of a 2D folding model from 3D hyperelasticity

Implementation of a discontinuous Galerkin method for numerical approximation

Effective simulation of large deformations in thin sheets

Abstract

The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling conditions on the energy and the geometric properties of the folding arc in dependence on the small sheet thickness. The resulting two-dimensional model is a piecewise nonlinear Kirchhoff plate bending model with a continuity condition at the folding arc. A discontinuous Galerkin method and an iterative scheme are devised for the accurate numerical approximation of large deformations.