Geometry And Mechanics Of Origami And Kirigami Inspired Metamaterials

In recent years,ancient origami and kirigami techniques have been applied into different research fields,including math,physics and engineering.Folding and unfolding property of origami and kirigami structures enable them a great variety of potential shapes and tunabilities and thus quite advantageous and superior in many directions.In this research,inspired by origami and kirigami geometries,we developed a few novel mechanical metamaterials analytically,numerically and experimentally.Based on previous studies,we believe that our fruitful results will be a valuable addition to this field in terms of geometry design,theoretical supplements and fabrication methods.The main contributions of this research are:(1)Therotically,numerically and experimentally,we study two kinds of foldable cylinders.In the rigid foldable design,we propose a pattern with negative Possion' s ratio and self-locking property.For non-rigid foldable pattern,we add one more crease on the six-crease origami pattern to minimize structural stress.(2)A novel pattern with both cuts and folds is developed.Free flaps will overlap once fully folded.This novel pattern can not only change surface Gaussian curvature much easier,but also perform self-interlocking through its geometry.Flaps can be fit neatly between neighboring units and therefore provide perfect locking mechanism without any external help.From loading experiments,we observe unusual high strength in this pattern: neighboring discrete units are turn into a whole structure and provide additional supporting to each other.Since folded structure has high nonlinearity,small perturbation can change its buckling mode.Inward buckled walls can turn simply supported plates into four-edge supported plates and force individual units to form spherical walls.Paper is a complicated material with nonhomogeneous layers and anisotropic fire alignments.The interleaved kirigami pattern has high symmetry and enables neutralized geometry,which can wash out the anisotropy.With loading experiments of paper with different thickness,we find a good agreement between material bending tests and pattern strength tests.Therefore,we can ignore the differences between different kinds of paper.Self-locking,high strength and the ability to tune material anisotropy are all from pure pattern geometry rather than different surface roughness.We also manage to forward the pattern to copper sheeting and transparent photo films,which shows the material generalizability of our pattern.(3)Introduce different cutting patterns in bilayer expandable strips to tune deformed geometry.When rigid material is on the flat side of the strip,its deformation mode is a combination of bending and twisting;when rigid material is on the flat side of the strip,the deformation mode is pure bending.Using local theory of curve,we firstly decoupled bending and twisting geometrically.With modified Timoshenko bilayer beam theory,we obtain bending strain and twisting strain in bilayer strips respectively.Put geometry and mechanics together,we build a closedform solution for to predict and characterize deformed helical geometries.(4)Boundary conditions can exert great influence on deformation modes of bilayer strips with cuts.Firstly,we experimentally and numerically study deformation modes of four different boundary conditions: free strip,two fixed ends,one fixed end-one moveable end and one fixed end-one constraint movable end.Once actuated,due to the incompatibility between boundaries and strip geometry,the same strip with small cuts at two ends have helical shapes and a perversion in the middle when both ends are totally fixed or one of them have constraint movement.Notably,one fixed end-one constraint movable end strip have multiple stable points.We extract force-displacement curve and calculate system energy versus time to understand the snap-through effect.(5)After understanding how to make a rough prediction on deformed bilayer strips,we study the design of bilayer plates with cuts.To simplify the problem,we start with stress analysis in ridges to get a reasonable design range.Then,we are able to consider it as a pure geometry problem using local surface theory in differential geometry.To connect cutting pattern with objective shapes,first and second form of surfaces are used and we verify the whole formula by two simply examples.Besides,we did two intuitive designs on zero Gaussian curvature rings.