Study on an incompressible nonlinear hyperelastic thin-walled toroidal mem- brane of circular cross-section subjected to inflation due to a uniform pressure is conducted in this work. Comparisons are made for three elastic constitutive mod- els (neo-Hookean, Mooney–Rivlin, and Ogden) and for different geometric aspect ratios (ratio of the radius of cross-section to the radius of revolution). A variational approach is used to derive the equations of equilibrium and bifurcation. An analysis of the pressure–deformation plots shows occurrence of the well-known limit point (snap through) instabilities in membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of solution corresponding to loss of symmetry. Tension field theory is employed to study the wrinkling instability that, in this case, typically occurs near the inner regions of tori with large aspect ratios.

中文翻译：

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非线性超弹性环形膜自由膨胀的不稳定性

在这项工作中，对圆形截面的不可压缩非线性超弹性薄壁环形膜由于均匀压力而受到膨胀的研究进行了研究。对三种弹性本构模型（neo-Hookean、Mooney-Rivlin 和 Ogden）和不同的几何纵横比（横截面半径与旋转半径之比）进行了比较。使用变分方法推导出平衡方程和分岔方程。压力-变形图的分析表明膜中发生了众所周知的极限点（快速通过）不稳定性。执行计算以研究弹性屈曲点以预测对应于对称性损失的解的分叉。张力场理论被用来研究起皱的不稳定性，在这种情况下，