A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation

TL;DR

This paper introduces a novel nonlinear hyperelastic bending model for shells that accurately handles large deformations and curved surfaces, outperforming existing models in analytical tests and computational benchmarks.

Contribution

The paper presents a new surface-based bending model based on principal curvatures, capable of modeling large deformations and initially curved shells, with an efficient isogeometric finite element implementation.

Findings

The new model passes all elementary nonlinear bending tests.

It handles large deformations and curved initial geometries effectively.

Computational benchmarks show improved accuracy over existing models.

Abstract

A new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four prominently used bending models. Through an essential set of elementary nonlinear bending test cases, the stresses and moments of each model are examined analytically. Only the proposed bending model passes all the test cases while the other bending models either fail or only pass the test cases for small deformations. The proposed new bending model can handle large deformations and initially curved surfaces. It is based on the principal curvatures and their directions in the initial configuration, and it thus can have different bending moduli along those directions. These characteristics make it flexible in modeling a given material, while it does not suffer from the pathologies of existing bending models. Further, the bending models are compared computationally through four classical benchmark examples and one contact example. As the underlying shell theory is based on Kirchhoff-Love kinematics, isogeometric NURBS shape functions are used to discretize the shell surface. The linearization and efficient finite element implementation of the proposed new model are also provided.