We consider a recently introduced geometrically nonlinear elastic Cosserat shell model incorporating effects up to order \(O(h^{5})\) in the shell thickness \(h\). We develop the corresponding geometrically nonlinear constrained Cosserat shell model, we show the existence of minimizers for the \(O(h^{5})\) and \(O(h^{3})\) case and we draw some connections to existing models and classical shell strain measures. Notably, the role of the appearing new bending tensor is highlighted and investigated with respect to an invariance condition of Acharya (Int. J. Solids Struct. 37(39):5517–5528, 2000) which will be further strengthened.

我们考虑最近引入的几何非线性弹性 Cosserat 壳模型，在壳厚度\(h\) 中结合了高达\(O(h^{5}) \) 的影响。我们开发了相应的几何非线性约束 Cosserat 壳模型，我们展示了\(O(h^{5})\)和\(O(h^{3})\)情况下极小值的存在，并绘制了一些连接现有模型和经典壳应变测量。值得注意的是，针对 Acharya 的不变性条件（Int. J. Solids Struct. 37(39):5517–5528, 2000）强调和研究了出现的新弯曲张量的作用，这将得到进一步加强。