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：本文提出了一种新颖的变分一致膜褶皱模型，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与压缩项。应力与切线材料矩阵的拉伸部分与压缩部分，则通过对应变能进行一致变分得到。在变分公式中仅考虑应变能的正值部分，我们得到一种压缩刚度为零的薄膜。通过引入乘以折减系数的负应变能项，我们进一步获得残余压缩刚度，这提升了稳定性并使其能够处理松弛状态。通过与文献中膜褶皱问题的解析解、数值算例及实验结果进行比较，验证了所提方法具有优异的性能与处理能力，且该方法与商用有限元软件兼容。