DG Approach to Large Bending Plate Deformations with Isometry Constraint

TL;DR

This paper introduces a novel discontinuous Galerkin method for modeling large isometric bending deformations in Kirchhoff plates, addressing nonconvex minimization with a discrete gradient flow and proving convergence.

Contribution

It presents a new dG method with a practical gradient flow for nonlinear plate models, including convergence proofs and numerical validation.

Findings

The method effectively computes discrete minimizers satisfying isometry constraints.

The approach demonstrates high accuracy and flexibility in numerical experiments.

Gamma-convergence of the discrete energies is established.

Abstract

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove $\Gamma$-convergence of the discrete energies and discrete global minimizers. We document the flexibility and accuracy of the dG method with several numerical experiments.