标题： 刚性和非刚性可折叠折纸超材料的均质化框架 显示英文标题

标题： Homogenization framework for rigid and non-rigid foldable origami metamaterials

摘要： 折纸超材料通常由具有周期性图案的折叠片材组成，赋予它们卓越的机械性能。 在连续力学的背景下，现有的大多数预测方法都是机制类比，倾向于刚性折叠和板弯曲。 虽然在预测主要变形模式方面有效，但现有方法在捕捉非刚性可折叠折纸的完整变形谱方面存在不足，例如沿直线折痕出现的曲率、顶点处的局部应变以及板面的翘曲。 为了全面捕捉整个变形谱并提高现有方法的准确性，本文引入了一个用于折纸超材料的均质化框架，其中面被建模为板单元。 制定了并实现了渐近和基于能量的均质化方法。 作为代表性折痕图案，我们研究了作为等效基尔霍夫-洛夫板均质化的Miura折纸片。 结果表明，某些有效弹性属性与初始折叠角度和折痕刚度呈非线性关系。 与完全解析的模拟结果进行基准测试时，我们的框架产生的误差高达12.9%，而现有的模型，包括杆-铰链模型和刚性板模型，误差高达161%。 误差差异与非刚性折纸中折痕和板面的复杂变形模式有关，这些模式尚未被现有模型探索。 这项工作展示了用于折纸超材料的精确且高效的连续介质框架，作为一种有效预测其弹性性能、理解其力学行为和设计其功能性的策略。 显示英文摘要

摘要： Origami metamaterials typically consist of folded sheets with periodic patterns, conferring them with remarkable mechanical properties. In the context of Continuum Mechanics, the majority of existing predictive methods are mechanism analogs which favor rigid folding and panel bending. While effective in predicting primary deformation modes, existing methods fall short in capturing the full spectrum of deformation of non-rigid foldable origami, such as the emergence of curvature along straight creases, local strain at vertices and warpage in panels. To fully capture the entire deformation spectrum and enhance the accuracy of existing methods, this paper introduces a homogenization framework for origami metamaterials where the faces are modeled as plate elements. Both asymptotic and energy-based homogenization methods are formulated and implemented. As a representative crease pattern, we examine the Miura origami sheet homogenized as an equivalent Kirchhoff-Love plate. The results reveal that certain effective elastic properties are nonlinearly related to both the initial fold angle and the crease stiffness. When benchmarked with results from fully resolved simulations, our framework yields errors up to 12.9\%, while existing models, including the bar-and-hinge model and the rigid-panel model, show up to 161\% error. The differences in errors are associated with the complex modes of crease and panel deformation in non-rigid origami, unexplored by the existing models. This work demonstrates a precise and efficient continuum framework for origami metamaterials as an effective strategy for predicting their elastic properties, understanding their mechanics, and designing their functionalities.