
A Wrinkling Model Based on the Spectral Decomposition of the Stress Tensor and the Mixed Wrinkling Criterion
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We present a novel variationally consistent wrinkling model based on spectral decomposition of the stress tensor that captures three distinct membrane states in a unified formulation, demonstrating strong performance in wrinkled membrane analysis. Compared with the strain-based spectral decomposition approach presented in [1], it improves predictive accuracy in stress analysis by satisfying the uniaxial tension condition from tension field theory [2] and aligning with the widely accepted mixed wrinkling criterion [3], while also achieving superior convergence performance. These enhancements stem from refinements that prevent overestimation of in-plane compressive behaviour, thereby improving accuracy. In addition, the model retains a residual compressive stress framework with a degradation factor to robustly handle slackening states, resulting in new stress and constitutive tensor expressions. Extensive validation through analytical, numerical, and experimental benchmarks demonstrates the model’s versatility and robustness in both standard finite element and isogeometric analysis frameworks. Results confirm accurate wrinkling behaviour, strong convergence, and solidify its value for advanced membrane wrinkling analysis. REFERENCES [1] D. Zhang, J. Kiendl, A variationally consistent membrane wrinkling model based on spectral decomposition of the strain tensor, Computer Methods in Applied Mechanics and Engineering 432 (2024) 117386. [2] D. Steigmann. Tension-field theory. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 429, 1876:141-173, 1990. [3] K. Nakashino, and M. Natori. Efficient modification scheme of stress-strain tensor for wrinkled membranes. AIAA journal, 43.1:206-215, 2005.