We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral decomposition of the strain tensor. Tensile and compressive parts of the stress and tangent material matrices are then obtained via consistent variation from the respective strain energies. Considering only the positive part of the strain energy in the variational formulation, we obtain a membrane with zero compressive stiffness. By adding the negative strain energy multiplied with a reduction factor, we further obtain a residual compressive stiffness, which improves stability and allows handling also states of slackening. Comparison with results from analytical, numerical and experimental examples from the literature on membrane wrinkling problems demonstrate the great performance and capability of the proposed approach, which is also compatible with commercial finite element software.

翻译：我们提出了一种新颖的变分一致薄膜褶皱模型，用于分析褶皱薄膜的力学响应。通过应变张量的谱分解，将弹性应变能密度分解为拉伸项和压缩项。基于变分一致性原理，分别从各自应变能中导出应力和切线材料矩阵的拉伸和压缩分量。在变分公式中仅考虑应变能的正部，得到零压缩刚度的薄膜；通过添加经折减系数乘处理的负应变能，进一步获得残余压缩刚度，这既增强了模型稳定性，又能处理松弛状态。与文献中关于薄膜褶皱问题的解析解、数值解和实验结果的对比表明，所提方法具有优异的性能与能力，且与商用有限元软件兼容。