The small bending behavior of linear elastic materials has been widespread in engineering in the history of mechanics. With the occurrence of soft materials, finite deformation bending is of great interest due to the high nonlinearity in large bending deformation. Previous theories primarily focus on the pure bending assumption, which is hard to achieve in practical bending experiments of soft materials because compressive forces cannot be neglected. In this paper, we propose a continuum mechanics-based nonlinear bending theory that incorporates an initial compression process to align with real-world experiments. We compare experimental data and simulation to our theoretical prediction to verify the accuracy of our theoretical model. The results demonstrated good agreement between our theory, experimental data, and finite element simulation. Furthermore, we compare our nonlinear bending theory with the classical Euler–Bernoulli theory to understand their respective behaviors better. This paper advances our understanding of bending phenomena by considering the effects of initial compression and incorporating a nonlinear approach. It provides valuable insights for practical applications of soft materials subjected to large bending deformation.

中文翻译：

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受到垂直压缩的软板的非线性弯曲：连续介质力学模型

线弹性材料的小弯曲行为在力学史上已广泛应用于工程领域。随着软材料的出现，有限变形弯曲由于大弯曲变形的高非线性而引起人们极大的兴趣。以往的理论主要集中于纯弯曲假设，在软材料的实际弯曲实验中很难实现，因为压缩力不能忽略。在本文中，我们提出了一种基于连续介质力学的非线性弯曲理论，该理论结合了初始压缩过程以与现实世界的实验保持一致。我们将实验数据和模拟与我们的理论预测进行比较，以验证我们的理论模型的准确性。结果表明我们的理论、实验数据和有限元模拟之间具有良好的一致性。此外，我们将非线性弯曲理论与经典的欧拉-伯努利理论进行比较，以更好地理解它们各自的行为。本文通过考虑初始压缩的影响并结合非线性方法，增进了我们对弯曲现象的理解。它为承受大弯曲变形的软材料的实际应用提供了宝贵的见解。