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.

翻译：本文提出了一种直接以曲面形式建立的非线性超弹性壳体弯曲模型，并将其与四种主流弯曲模型进行了比较。通过一系列基础非线性弯曲测试案例，解析分析了各模型的应力与弯矩。唯有所提出的弯曲模型通过所有测试案例，而其他弯曲模型要么失效，要么仅能通过小变形测试案例。该新模型可处理大变形及初始曲面工况，它基于初始构型的主曲率及其方向，因此能沿不同方向设置不同的弯曲模量。这些特性使得该模型在模拟给定材料时具有灵活性，且避免了现有弯曲模型的病态问题。进一步，通过四个经典基准算例及一个接触算例对弯曲模型进行了数值比较。由于底层壳体理论基于Kirchhoff-Love运动学，因此采用等几何NURBS形函数对壳体曲面进行离散化。本文还给出了该新模型的线性化处理及高效有限元实现方法。