高度柔性细长结构弯曲弹性的数值与实验框架
Numerical and experimental framework for bending elasticity of highly flexible slender structures
AI总结：
研究针对高度柔性细长结构弯曲弹性，开发混合材料点法计算框架模拟三点弯曲试验，应用于弹性管和带状弹簧，数值模拟与实验及理论相符，为预测复杂接触结构大变形提供可靠框架。
AI中文摘要：
细长结构高度灵活，长度尺度跨越几个数量级。其变形取决于横截面的细长程度，表明结构的弹性和几何形状内在耦合。横截面变形很显著，如管道弯曲时的布拉齐尔不稳定性。虽通过标准三点弯曲试验对细长结构弯曲性能进行实验量化，但数值模拟因需考虑复杂接触力学而研究不足。本研究用混合材料点法开发计算框架模拟实验三点弯曲试验，该方法整合了拉格朗日有限元和欧拉有限差分框架。将框架应用于弹性管和带状弹簧，数值模拟预测与桌面实验和经典理论验证相符。这表明混合材料点法框架能为预测涉及复杂接触的结构大变形提供可靠计算框架，如软机器人和可展开结构。
英文摘要：
Slender structures are highly flexible, spanning several orders of magnitude in length scale. Their deformation depends on the slenderness of their cross sections, highlighting that the elasticity and geometry of structures are intrinsically coupled. The deformation of the cross-section becomes significant, particularly when tubes and pipes are subjected to bending, known as the Brazier instability. Although the bending performance of slender structures is quantified experimentally using a canonical three-point bending test, their numerical counterparts remain under-explored because complex contact mechanics must be implemented in simulations. In this study, we develop a computational framework to simulate experimental three-point bending tests using a hybrid material point method (hybrid-MPM) approach, which integrates Lagrangian finite element and Eulerian finite difference frameworks. We adapt our framework to elastic tubes and tape springs as canonical examples that exhibit characteristic bending deformation in which the cross-sectional and lengthwise bending are coupled. The predictions of numerical simulations are validated against desktop experiments and classical theory. The excellent agreement between the simulation and the experiments implies that the hybrid-MPM framework provides a robust computational framework for predicting the large deformation of structures involving complex contact, such as soft robots and deployable structures.
