In the IoT era, the demand for wearable displays is rapidly growing, catalyzing the advancement of research into textile-based organic light-emitting diodes (OLEDs). This growing interest stems particularly from the inherent flexibility of textile-based OLEDs^1,2, allowing for seamless integration into the dynamic and interactive functionalities of cutting-edge wearable technology, alongside their superior electrical performance. The durability and mechanical robustness of these displays, especially under physical stress and deformation, are critical to their practical application and longevity. Thus, understanding and enhancing the mechanical properties of textile-based OLEDs is paramount for their successful integration into wearable technologies. However, many studies assessing the mechanical properties of OLEDs have predominantly relied on simplistic bending test outcomes determined by the radius, often neglecting or insufficiently analyzing the strain exerted on the OLEDs atop textile substrates in relation to curvature of these devices. Existing analyses typically presume pure bending, though such an assumption leads to considerable errors in strain estimations, making such approaches problematic if the goal is practical application in actual wearable display products. To address these limitations, an analytic model that includes a comprehensive energy equation is introduced, considering the stretching energy, bending energy, and shear energy of each layer composing the textile substrate. This holistic approach provides a novel formula specifically designed to calculate the top surface strain of textile substrates. Robust validation of this formula is conducted by comparing its results with strain measurements obtained from digital image correlation (DIC) and finite element analysis (FEA) outcomes from ANSYS across various bending radii (or equivalently, curvatures). The close alignment of the calculated strain values with those derived from DIC and FEA not only underscores the precision of this formula but also highlights its significant potential for enhancing the designs and functionalities of future wearable display technologies under real-world conditions.

在物联网时代，对可穿戴显示器的需求迅速增长，促进了对基于纺织的有机发光二极管 （OLED） 的研究进展。这种日益增长的兴趣尤其源于基于纺织品的 OLED^1,2 固有的灵活性，除了卓越的电气性能外，还可以无缝集成到尖端可穿戴技术的动态和交互功能中。这些显示器的耐用性和机械坚固性，尤其是在物理应力和变形下，对其实际应用和使用寿命至关重要。因此，了解和增强基于纺织品的 OLED 的机械性能对于它们成功集成到可穿戴技术中至关重要。然而，许多评估 OLED 机械性能的研究主要依赖于由半径确定的简单弯曲测试结果，往往忽略或未充分分析施加在纺织基材上的 OLED 上的应变与这些器件的曲率的关系。现有的分析通常假设纯弯曲，尽管这种假设会导致应变估计出现相当大的误差，如果目标是在实际可穿戴显示产品中实际应用，那么这种方法就会出现问题。为了解决这些限制，引入了一个包含综合能量方程的解析模型，考虑了构成纺织基材的每一层的拉伸能、弯曲能和剪切能。这种整体方法提供了一种新颖的公式，专门用于计算纺织基材的顶面应变。 通过将其结果与 ANSYS 在各种弯曲半径（或等效曲率）下的数字图像相关 （DIC） 和有限元分析 （FEA） 结果获得的应变测量值进行比较，可以对该公式进行稳健验证。计算出的应变值与 DIC 和 FEA 得出的应变值紧密一致，不仅强调了该公式的精确性，还突出了它在增强未来可穿戴显示技术在实际条件下的设计和功能方面的巨大潜力。