标题： 基于应力张量谱分解的变分一致膜起皱模型 显示英文标题

标题： A variationally consistent membrane wrinkling model based on spectral decomposition of the stress tensor

摘要： 我们提出了一种基于应力张量谱分解的变分一致皱纹模型，提供了一种统一的公式，能够捕捉三种不同的膜态。 与之前的基于应变的谱分解方法相比，所提出的模型通过满足张力场理论中的单轴拉伸条件并与混合皱纹准则对齐来提高精度。 它还在各种加载条件下表现出色，并通过在一个单一框架内统一基于应变、基于应力和混合准则提供了增强的通用性。 除了这些改进之外，该模型保留了先前方法的优异收敛特性，包括灵活包含或省略残余压缩刚度的框架。 这减轻了松弛状态下的非收敛或奇异性。 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的广泛验证突显了该模型的稳健性。 结果证实了其准确捕捉皱纹薄膜机械响应的能力、强大的收敛特性和用于先进薄膜皱纹分析的价值。 显示英文摘要

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.