折纸超材料合规机制的设计

Design of compliant mechanisms for origami metamaterials

折纸作为一种折纸艺术,几个世纪以来一直被艺术家们广泛探索.直到最近几十年,它才因其复杂的几何形状和丰富的力学性能而受到数学家和工程师的关注.以折纸为灵感的超材料的激增为材料和结构的设计打开了一扇新的窗口.通常,会根据标有合规机制的折痕线折叠一张材料来构建折纸结构.尽管它们在折纸制造中很重要,但在折纸超材料的设置中,这种合规机制尚未得到探索.本研究探讨了合规机制设计参数与折纸力学性能之间的关系.尤其我们采用的是单铰链折痕和Kresling折纸,这是刚性和非刚性折纸单元的代表性示例,采用双针穿孔兼容机构设计制造.我们使用不同的折痕参数进行轴向压缩测试,并将结果拟合到由轴向和扭转弹簧组成的棒铰折纸模型中.使用高斯回归过程提取弹簧系数和折痕参数之间的关系.结果表明,折痕参数的变化以非常不同的方式对每个弹簧元件有显著贡献,这表明合规机制根据变形模式的微调性.特别是,刚性和非刚性折纸的弹簧刚度随折痕参数而变化不同,即使调整了相同的折痕参数也是如此.此外,我们报道了Kresling折纸的定性静态响应只需改变折痕参数,就可以在单稳态和双稳态之间,或者线性和非线性之间调节,同时可以保持相同的折叠图案几何形状.我们相信,我们的结果为折纸机械超材料的褶皱选择合规机制提供了一个库和指南.

As an art of paper folding,origami has been widely explored by artists for centuries.Only in recent decades has it gained attention from mathematicians and engineers for its complex geometry and rich mechanical properties.The surge of origami-inspired metamaterials has opened a new window for designing materials and structures.Typically,to build origami structures,a sheet of material is folded according to the creaselines that are marked with compliant mechanisms.However,despite their importance in origami fabrication,such compliant mechanisms have been relatively unexplored in the setting of origami metamaterials.In this study,we explore the relationship between the design parameters of compliant mechanisms and origami mechanical properties.In particular,we employ single hinge crease and Kresling origami,representative examples of rigid and non-rigid origami units,fabricated using a double-stitch perforation compliant mechanism design.We conduct axial compression tests using different crease parameters and fit the result into the bar-hinge origami model consisting of axial and torsional springs.We extract the relationship between the spring coefficients and crease parameters using Gaussian process regression.Our result shows that the change in the crease parameter contributes significantly to each spring element in a very different manner,which suggests the fine tunability of the compliant mechanisms depending on the mode of deformation.In particular,the spring stiffness varies with the crease parameter differently for rigid and non-rigid origami,even when the same crease parameter is tuned.Furthermore,we report that the qualitative static response of the Kresling origami can be tuned between monostable and bistable,or linear and nonlinear,by only changing the crease parameter while keeping the same fold pattern geometry.We believe that our compiled result proffers a library and guidelines for choosing compliant mechanisms for the creases of origami mechanical metamaterials.