Modelling nonlinear phenomena in thin rubber shells calls for stretch-based material models, such as the Ogden model which conveniently utilizes eigenvalues of the deformation tensor. Derivation and implementation of such models have been already made in Finite Element Methods. This is, however, still lacking in shell formulations based on Isogeometric Analysis, where higher-order continuity of the spline basis is employed for improved accuracy. This paper fills this gap by presenting formulations of stretch-based material models for isogeometric Kirchhoff–Love shells. We derive general formulations based on explicit treatment in terms of derivatives of the strain energy density functions with respect to principal stretches for (in)compressible material models where determination of eigenvalues as well as the spectral basis transformations is required. Using several numerical benchmarks, we verify our formulations on invariant-based Neo-Hookean and Mooney–Rivlin models and with a stretch-based Ogden model. In addition, the model is applied to simulate collapsing behaviour of a truncated cone and it is used to simulate tension wrinkling of a thin sheet.

模拟薄橡胶壳中的非线性现象需要基于拉伸的材料模型，例如 Ogden 模型，它可以方便地利用变形张量的特征值。此类模型的推导和实现已经在有限元方法中进行。然而，这在基于等几何分析的壳公式中仍然缺乏，其中使用样条基础的高阶连续性来提高精度。本文通过介绍等几何 Kirchhoff-Love 壳的基于拉伸的材料模型的公式来填补这一空白。对于需要确定特征值和谱基变换的（非）可压缩材料模型，我们根据应变能量密度函数的导数推导出基于显式处理的一般公式。使用几个数值基准，我们在基于不变性的 Neo-Hookean 和 Mooney-Rivlin 模型以及基于拉伸的 Ogden 模型上验证了我们的公式。此外，该模型还用于模拟截锥体的塌陷行为，并用于模拟薄片的张力起皱。