基于应力张量谱分解的变分一致褶皱模型
A variationally consistent membrane wrinkling model based on spectral decomposition of the stress tensor
AI总结：
提出基于应力张量谱分解的变分一致薄膜褶皱模型，统一三种状态并融合多种准则，在提升精度与通用性的同时保持优异收敛性，经多类基准测试验证了其准确性与稳健性。
摘要：
我们提出了一种基于应力张量谱分解的变分一致褶皱模型，提供了一种能够捕捉三种不同薄膜状态的统一公式。与先前基于应变的谱分解方法相比，该模型通过满足张力场理论中的单轴拉伸条件并与混合褶皱准则保持一致，提高了准确性。它在各种载荷条件下表现出优异的性能，并通过在单一框架内统一基于应变、基于应力和混合准则，展现出更强的通用性。除上述改进外，该模型保留了先前方法的优越收敛特性，包括灵活包含或省略残余压缩刚度的框架。这缓解了松弛状态下的不收敛或奇异性问题。通过这些调整，一致地推导出了应力和本构张量的新表达式。最后，通过分析、数值和实验基准测试进行的广泛验证突显了该模型的稳健性。结果证实了其在捕捉褶皱薄膜力学响应方面的准确性、强收敛特性，以及对高级薄膜褶皱分析的价值。
英文摘要：
We present a variationally consistent wrinkling model based on spectral decomposition of the stress tensor, providing a unified formulation that captures the three distinct membrane states. Compared to the previous strain-based spectral decomposition approach, the proposed model improves accuracy by satisfying the uniaxial tension condition from tension field theory and aligning with the mixed wrinkling criterion. It also demonstrates excellent performance under various loading conditions and offers enhanced generality by unifying strain-based, stress-based, and mixed criteria within a single framework. Beyond these improvements, the model retains the superior convergence properties of the previous approach, including the framework for the flexible inclusion or omission of residual compressive stiffness. This mitigates nonconvergence or singularities in slackening states. With these adjustments, new expressions for stress and constitutive tensors are consistently derived. Finally, extensive validation through analytical, numerical, and experimental benchmark tests highlights the robustness of the model. The results confirm its accuracy in capturing the mechanical response of wrinkled thin membranes, strong convergence properties, and value for advanced membrane wrinkling analysis.
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