The application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure (\(P\)) – inflation (\(\lambda \) or \(v\)) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

本文论证了一种新提出的广义新Hookean应变能函数在不可压缩橡胶状球壳和圆柱壳膨胀中的应用。推导并给出了四种壳的压力（\（P \））-膨胀（\（\ lambda \）或\（v \））关系：薄壁和厚壁球形气球，薄壁和厚壁球囊圆柱管。分析了模型针对四个已考虑的弹壳预测的充气曲线的特征，并显示了用于显示极限点不稳定性的模型参数的临界值被建立。将演示该模型在从19世纪到21世纪的研究中获得的现有实验数据集上的应用，表明该模型与实验数据之间具有良好的一致性。该模型从理论分析和曲线拟合方法中都可以清楚地看出模型在橡胶状材料的充气过程中捕获两个特征性不稳定性现象的能力，即极限点和充气-跳跃不稳定性。 。还证明了与考虑到的数据的Gent模型预测的比较，并表明我们提出的模型提供了改进的拟合度。鉴于该模型的简单性，它能够拟合各种实验数据并捕获两者极限点和充气跳跃的不稳定性，我们建议将模型应用到橡胶状材料的充气中。