Folded-shear paper three-dimensional periodic solid structures with negative poisson's ratio properties

Abstract

The application relates to the field of shock isolation and prevention by using a fold-cut paper mechanism, in particular to a fold-cut paper three-dimensional periodic solid structure with a negative Poisson's ratio characteristic. The fold-cut paper three-dimensional periodic solid structure comprises a plurality of fold-cut paper hollow double-layer units, the fold-cut paper hollow double-layer units are expanded along the vertical direction and the horizontal direction, adjacent fold-cut paper hollow double-layer units are fixedly connected through corresponding structure surfaces, and the fold-cut paper hollow double-layer units in the horizontal direction are fixedly connected through common edges; the fold-cut paper hollow double-layer unit comprises an upper layer and a lower layer, the upper layer and the lower layer each comprise four hollow inclined quadrangular prisms, and the hollow inclined quadrangular prisms of the upper layer and the corresponding hollow inclined quadrangular prisms of the lower layer are in a mirror image relationship. The research on the three-dimensional negative Poisson's ratio structure is realized, the periodic structure designed based on the negative Poisson's ratio characteristic of the fold-cut paper structure in the application can be used as a shock isolation and reduction device suitable for different load conditions and complex environments, and can be applied to the fields of buildings, machines, aerospace and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of shock isolation and prevention by using fold-cut paper mechanism, in particular to a fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio characteristics. BACKGROUND

[0002] The property that the structure shrinks (expands) in the transverse direction under the action of uniaxial compression (tension) is called negative Poisson's ratio. At present, the research on negative Poisson's ratio is mainly two-dimensional, and there are few structures with negative Poisson's ratio in two directions (plane / facade). Two-dimensional negative Poisson's ratio structure has certain limitations and cannot well participate in the research on mechanical properties, and it is more difficult to be applied to engineering. As a three-dimensional negative Poisson's ratio structure created by folding and cutting paper from two-dimensional deformation to three-dimensional space, the adjustable negative Poisson's ratio can be realized to meet various engineering application conditions. However, there is no fold-cut paper structure for studying three-dimensional negative Poisson's ratio. SUMMARY

[0003] The present application aims to overcome the above-mentioned defects in the prior art, and proposes a fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio characteristics, realizes the research on three-dimensional negative Poisson's ratio structure, and uses the negative Poisson's ratio characteristics of the fold-cut paper structure in the present application. The periodic structure designed based on this principle can be used as a shock isolation and reduction device suitable for different load conditions and complex environments, and can be applied to the fields of building, machinery, aerospace, etc.

[0004] The technical scheme of the present application is: a fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio characteristics, wherein a plurality of fold-cut paper hollow double-layer units are included, the fold-cut paper hollow double-layer units are expanded along the vertical direction and the horizontal direction, the adjacent fold-cut paper hollow double-layer units are fixedly connected through the corresponding structure surface, and the fold-cut paper hollow double-layer units in the horizontal direction are fixedly connected through the common edge.

[0005] The fold-cut paper hollow double-layer unit includes an upper layer and a lower layer, the upper layer and the lower layer each include four hollow inclined four-prism units, the hollow inclined four-prism units of the upper layer and the corresponding hollow inclined four-prism units of the lower layer have a mirror image relationship, the hollow inclined four-prism units of the upper layer and the corresponding hollow inclined four-prism units of the lower layer are connected through the adjacent structure surface, and the adjacent two hollow inclined four-prism units in the same layer are fixedly connected through the common edge.

[0006] The hollow inclined four-prism unit includes four small hollow inclined prism units, the adjacent two small hollow inclined prism units are fixedly connected through the common edge, and the common edges connecting the adjacent two small hollow inclined prism units in the same hollow inclined four-prism unit are arranged in a staggered manner.

[0007] In the present application, the hollow oblique quadrangular prism is unfolded into a basic fold-cut paper unit, which is formed by alternately connecting two rectangles and two parallelograms, the long side of the rectangle is connected with the bottom side of the parallelogram adjacent to it, the rectangle is sequentially connected by four small squares, and the parallelogram is sequentially connected by four small parallelograms, and the bottom side length of the small parallelogram is equal to the side length of the small square.

[0008] In the basic fold-cut paper unit, the vertices of the small square and the small parallelogram are all control angle points, wherein the straight lines AQ, BR, CS and DT are mountain fold marks, the straight lines HE, EF, FG, JK, LI, IJ, PM, MN and NO are cut marks, the straight lines GH, OP and KL are valley fold marks, and the basic fold-cut paper unit is folded and cut according to the above-mentioned fold marks, so that a hollow oblique prism formed by connecting four small hollow oblique prism units is obtained, two adjacent small hollow oblique prism units are connected at the valley fold marks, and the corresponding side edges of two adjacent hollow oblique prisms are connected through the cut marks.

[0009] The hollow oblique quadrangular prism is mirrored along the upper surface ADTQ thereof, and then mirrored along the side surface ABRQ-A'B'R'Q', so that a fold-cut paper hollow double-layer unit is obtained.

[0010] When the fold-cut paper hollow double-layer unit is in an initial state, the adjacent small hollow oblique prism units are in a close state, the upper surface and the lower surface of the hollow oblique quadrangular prism are closed rectangular, the front side surface and the rear side surface of the hollow oblique quadrangular prism are closed parallelogram, the side length of the four small squares forming the rectangle is a, the diagonal length of the four small parallelograms forming the parallelogram is b, the internal angle of the small parallelogram is γ, and γ<90°, so that the length of the hollow oblique quadrangular prism is 4a, the width is a, and the height is h.

[0011] h=bsinγ.

[0012] When the fold-cut paper hollow double-layer unit is compressed, the adjacent small hollow oblique prism units are separated from the close state, the control angle points in the same plane of the small hollow oblique prism unit are always in a plane, and the adjacent two small hollow oblique prism units are respectively rotated in opposite directions at the cut marks and generate linear displacement in the plane, at this time,

[0013] AB=AB′=HG=HG′=IJ=IJ′=b

[0014] ∠ABG=∠AB'G′=∠AHG=∠AHG′=∠IJG=∠IHG=∠IHG′=IJ′G′=γ

[0015] ∠GBJ=∠G′B′J′=∠GJB=∠G′J′B′=∠HAI=∠HIA=ψ

[0016] ∠ABJ = ∠AB'J' = ξ

[0017] Let the plane of face ABRQ be the main plane in the initial state, the angle between the compressed face ABHG and the main plane be θ, and the angle between the bottom face of the compressed hollow oblique quadrangular prism and face HIJG be Then the height S of the hollow oblique prism at this time is:

[0018]

[0019] The straight-line distance L of AI, HP, and IQ changes from 2a to:

[0020]

[0021] The distance C of point G to straight line BJ is:

[0022] C = asin θ sin γ

[0023] The distance V of point I to straight line JJ' is:

[0024]

[0025] Let the length of the folded-paper hollow double-layer unit after compression and deformation be R,

[0026]

[0027] The width of the folded-paper hollow double-layer unit after compression and deformation is B,

[0028]

[0029] The height of the folded-paper hollow double-layer unit after compression and deformation is H,

[0030]

[0031] Take the derivatives of the length R, width B, and height H with respect to angle ξ, respectively:

[0032]

[0033]

[0034]

[0035] The longitudinal Poisson's ratio v1 of the folded-paper hollow double-layer unit in the transverse stretching process and the transverse Poisson's ratio v2 in the vertical compression process are:

[0036]

[0037]

[0038] The eight small hollow inclined prismatic units at the eight corner points have two common edges, respectively, and the sixteen small hollow inclined prismatic units located on the horizontal and vertical longitudinal edges of the double-layer unit and excluding the corner points have three common edges, respectively, and the other eight small hollow inclined prismatic units have four common edges, respectively, and the common edges are provided with connecting pieces. The connecting pieces include but are not limited to: wheel shaft connection, roller connection, guide running wheel, steel hinge hinge, flexible material bonding.

[0039] Adjacent fold-paper cutting hollow double-layer units are fixedly connected through adjacent structure surfaces; in each fold-paper cutting hollow double-layer unit, adjacent small hollow inclined prismatic units are fixedly connected through adjacent structure surfaces. The fixed connection mode includes but is not limited to: welding, bonding, high-temperature melting, 3D printing, bolt connection.

[0040] The beneficial effects of the present application are:

[0041] (1) Special mechanical properties: the present application provides the negative Poisson's ratio structure characteristics based on the fold-paper cutting principle, which not only exists in two dimensions, but also exists in three dimensions, and has wider application space and prospect in fields such as building, machinery, aerospace and the like;

[0042] (2) Adjustable negative Poisson's ratio: in the obtained calculation results, adjusting gamma can make the Poisson's ratio change from negative to positive or from positive to negative, so that the engineering application can be better adapted;

[0043] (3) Special Poisson's ratio value: under certain parameters, the Poisson's ratio of the structure is always 0 or -1 when the structure is stressed; the zero Poisson's ratio structure has the characteristics of high out-of-plane stiffness, strong deformation ability, light weight, small density and the like, is a very good anti-seismic and disaster reduction isolation device, and can greatly reduce the transportation space when applied to other fields; when the Poisson's ratio is -1, the structure has significant shear resistance.

[0044] (4) In the compression process, each small unit is in a two-dimensional rotation state; the horizontal force makes it rotate uniaxially while having in-plane displacement, and the vertical force makes it rotate uniaxially. This performance can be used in mechanical devices and the like. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1-1 is the unfolded view of the basic fold-paper cutting unit provided by the present application;

[0046] Figure 1-2 is the deformation view of the basic fold-paper cutting unit provided by the present application;

[0047] Fig. 1-3(a) is a mirror image replication display of the fold-paper cutting unit deformation of the present application;

[0048] Figure 1-3(b) is a mirror image of Figure 1-3(a);

[0049] Figure 1-3(c) is a mirror image of Figure 1-3(b);

[0050] Figure 1-4 is a definition and calculation of the parameters of the fold-cut paper hollow double-layer unit structure;

[0051] Figure 1-5(a) is a top view of the structure in the initial state in Example 1;

[0052] Figure 1-5(b) is a front view of the structure in the initial state in Example 1;

[0053] Figure 1-5(c) is a side view of the structure in the initial state in Example 1;

[0054] Figure 1-6 is a Poisson's ratio diagram ξ-ν1 of the structure in Example 1 under lateral force, only changing the value of γ;

[0055] Figure 1-7(a) is a Poisson's ratio diagram ξ-ν1 of the structure in Example 1 under lateral force, only changing the value of a / b when γ=60°;

[0056] Figure 1-7(b) is a Poisson's ratio diagram ξ-ν1 of the structure in Example 1 under lateral force, only changing the value of a / b when γ=45°;

[0057] Figure 1-8 is a Poisson's ratio diagram ξ-ν2 of the structure in Example 1 under vertical force, only changing the value of γ;

[0058] Figure 1-9 is a structure diagram of the structure in Example 1 in the compression state;

[0059] Figure 1-10 is a structure diagram of the structure in Example 1 in the fully compressed state;

[0060] Figure 2-1 is a structure diagram of the structure in Example 2 in the initial state;

[0061] Figure 2-2 is a structure diagram of the structure in Example 2 in the compression state;

[0062] Figure 3-1 is a structure diagram of the structure in Example 3 in the initial state;

[0063] Figure 3-2 is a structure diagram of the structure in Example 3 in the compression state. DETAILED DESCRIPTION

[0064] In order to make the above objectives, features and advantages of the present application more clear and comprehensible, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0065] In the following description, specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced without the specific details, which are presented in the following description. Therefore, the present application is not limited to the details described hereinafter.

[0066] Embodiment 1

[0067] The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio characteristics described in the present application comprises a plurality of fold-cut paper hollow double-layer units, and the fold-cut paper hollow double-layer units are expanded in the horizontal direction and the vertical direction to obtain the fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio characteristics of the present application. The fold-cut paper three-dimensional periodic solid structure in the embodiment comprises one fold-cut paper hollow double-layer unit.

[0068] The fold-cut paper hollow double-layer unit is divided into an upper layer and a lower layer, wherein the upper layer and the lower layer each comprise four hollow oblique quadrangular prisms, and the hollow oblique quadrangular prisms of the upper layer and the hollow oblique quadrangular prisms of the lower layer are mirror image arranged. Figure 1-2 As shown in FIG. 1, each hollow oblique quadrangular prism comprises four small hollow oblique prismatic units, and adjacent two small hollow oblique prismatic units are fixedly connected through common edges, and the common edges connecting adjacent two small hollow oblique prismatic units in the same hollow oblique quadrangular prism are staggered arranged.

[0069] The basic origami unit after unfolding of the hollow oblique quadrangular prism is shown in FIG. 2. Figure 1-1 As shown in FIG. 2, the basic origami unit has 20 control corner points, which are sequentially labeled by letters in order from A to T. The basic origami unit is alternately spliced by two rectangles BCSR, ADTQ and two parallelograms CDTS, ABRQ, wherein one side long edge of the rectangle ADTQ and one side bottom edge of the parallelogram CDTS adjacent thereto are common edges. The other side long edge of the rectangle ADTQ and one side bottom edge of the parallelogram ABRQ adjacent thereto are common edges. One side long edge of the rectangle BCSR and the other side bottom edge of the parallelogram CDTS adjacent thereto are common edges. The rectangle BCSR and the rectangle ADTQ are respectively connected by four small squares in order. The parallelogram CDTS and the parallelogram ABRQ are respectively connected by four small parallelograms in order. The bottom edge length of the small parallelogram is equal to the edge length of the small square.

[0070] In the basic origami unit, straight lines AQ, BR, CS, DT are mountain creases, straight lines GH, OP, KL are valley creases, and straight lines HE, EF, FG, JK, LI, IJ, PM, MN, NO are cutting lines. The hollow oblique quadrangular prism can be obtained by folding, cutting and deforming the basic origami unit according to the mountain creases, valley creases and cutting lines AB, BG, GH, HE, EF, FG, GB, BC, CD, DA, AH, DE, CF. The hollow oblique quadrangular prism obtained after deformation includes eight corner points: A, B, C, D, Q, R, S, T, and twelve boundary points: H, I, P, G, J, O, F, K, N, E, L, M.

[0071] As shown in Figure 1-2 , each hollow oblique quadrangular prism is connected by four small hollow oblique prism units in turn. In the small hollow oblique prism unit AHGB-DEFC, the upper surface and the lower surface are both squares, the front side and the back side are both parallelograms, and the left side and the right side are both rectangles. The upper surface and the lower surface of the hollow oblique quadrangular prism are rectangles composed of four small squares, and the front side and the back side of the hollow oblique quadrangular prism are parallelograms composed of four small parallelograms. The left side and the right side of the hollow oblique quadrangular prism are rectangles.

[0072] Let the side length of the small square be a, the diagonal length of the small parallelogram be b, and the internal angle of the small parallelogram be γ, where γ < 90. At this time, the length of the hollow oblique quadrangular prism, i.e. the length of BR, is 4a, the width of the hollow oblique quadrangular prism, i.e. the length of BC, is a, and the height h of the hollow oblique quadrangular prism is:

[0073] h = bsinγ.

[0074] As shown in Figure 1-2 , the hollow oblique quadrangular prism shown in FIG. 1-3(a) can be mirrored along the upper surface ADTQ to obtain the structure shown in FIG. 1-3(b), and the structure shown in FIG. 1-3(b) can be mirrored again along its side ABRQ-A’B’R’Q’ to obtain the structure shown in FIG. 1-3(c). The structure is a fold-cut paper hollow double-layer unit, and the fold-cut paper hollow double-layer unit includes thirty-two small hollow oblique prism units. In the fold-cut paper hollow double-layer unit, the mirror planes are fixedly connected, i.e. the adjacent surfaces of adjacent small hollow oblique prism units are fixedly connected, and the fixed connection modes include but are not limited to welding, bonding, high-temperature melting, 3D printing, bolt connection, etc.

[0075] In addition, in the fold-cut paper hollow double-layer unit, eight small hollow inclined prismatic units at eight corner points have two common edges respectively, sixteen small hollow inclined prismatic units except the corner points have three common edges respectively, and other eight small hollow inclined prismatic units have four common edges respectively, and connecting members are arranged at the common edges.

[0076] As shown in FIGS. 1-5(a), 1-5(b) and 1-5(c), the structure schematic diagram of the fold-cut paper hollow double-layer unit in the initial state is shown. At this time, the upper surface and the lower surface of the fold-cut paper hollow double-layer unit are a square composed of sixteen small squares. By applying a horizontal pulling force in the x direction to the fold-cut paper hollow double-layer unit, the fold-cut paper hollow double-layer unit expands obviously in the y direction, i.e. the horizontal direction perpendicular to the x direction, at this time the fold-cut paper hollow double-layer unit shows auxeticity, i.e. negative Poisson's ratio characteristic. While by applying a compression force perpendicular to the upper surface direction to the fold-cut paper hollow double-layer unit, the negative Poisson's ratio characteristic is not obvious, and the accurate Poisson's ratio value needs to be calculated. During the pulling process, the adjacent small hollow inclined prismatic units are from the close state to the separation, and during the separation process, the control corner points in the same plane of the small hollow inclined prismatic units are always in a plane, and the adjacent two small hollow inclined prismatic units rotate in opposite directions at the shear mark and generate linear displacement in the plane.

[0077] In the following, the structure of the face ABGH-HGJI and its mirror image after being stressed and deformed will be taken as an example to define the simple parameters, as shown in FIGS. 1-6(a), 1-6(b) and 1-6(c). Figure 1-4

[0078] AH=BG=B′G′=HI=GJ=G′J′=a

[0079] AB=AB′=HG=HG′=IJ=IJ′=b

[0080] ∠ABG=∠AB'G′=∠AHG=∠AHG′=∠IJG=∠IHG=∠IHG′=IJ′G′=γ

[0081] ∠GBJ=∠G′B′J′=∠GJB=∠G′J′B′=∠HAI=∠HIA=ψ

[0082] ∠ABJ=∠AB′J′=ξ

[0083] Suppose that the plane of the face ABRQ in the initial state is the main plane, the included angle between the compressed face ABHG and the main plane is θ, and the included angle between the bottom surface of the compressed hollow inclined prismatic and the face HIJG is Then the height S of the hollow inclined prismatic at this time is:

[0084] ​

[0085] The straight-line distance L of AI, HP, IQ is:

[0086]

[0087] The distance C of point G to straight line BJ is:

[0088] C = asin θ sin γ

[0089] The distance V of point I to straight line JJ' is:

[0090]

[0091] The four parameters C, S, L, V control the deformation degree of the structure, and there are angle relationships:

[0092] tan ξ = cos θ tan γ sin Ψ = sin θ sin γ

[0093] cos γ = cos ξ cos ψ

[0094] Wherein, γ ∈ (0, 90°], θ ∈ [0, 90°], ξ ∈ [0, γ], Ψ ∈ [0, γ];

[0095] Let the length of the fold-cut paper hollow double-layer unit after compression deformation be R,

[0096]

[0097] The width of the fold-cut paper hollow double-layer unit after compression deformation is B,

[0098]

[0099] The height of the fold-cut paper hollow double-layer unit after compression deformation is H,

[0100]

[0101] The length R, width B and height H are respectively differentiated with respect to angle ξ:

[0102]

[0103]

[0104]

[0105] The longitudinal Poisson's ratio v1 of the structure in the transverse stretching process and the transverse Poisson's ratio v2 in the vertical compression process are:

[0106]

[0107]

[0108] like Figure 1-6 As shown in Figures 1-7(a) and 1-7(b), the ξ-ν1 graph reveals that under lateral force, the value of Poisson's ratio ν1 is related to parameters a, b, and the angle γ between them. When γ decreases, the Poisson's ratio tends towards -1; when γ increases, there exists a γ that allows the Poisson's ratio to transition from negative to positive, exhibiting adjustability. Specifically, when γ = 90°, the Poisson's ratio is always equal to 0, meaning there is no longitudinal strain when the structure is subjected to lateral force; when a << b, the Poisson's ratio changes from negative to positive; when a >> b, the Poisson's ratio is always -1, at which point the shear modulus of the structure is much smaller than the elastic modulus, making the structure highly compressible; furthermore, when γ = 45°, the Poisson's ratio can always be negative.

[0109] like Figure 1-8 As shown in the ξ-ν² graph, under vertical force, the Poisson's ratio v² is only related to the angle γ between a and b. The existence of γ ≤ 60° allows the Poisson's ratio to change from positive to negative, significantly improving shear resistance and making the Poisson's ratio adjustable.

[0110] Specifically, the structure is unlikely to compress if and only if a compressive force perpendicular to the upper surface is present, because each small hollow oblique prism element rotates about the axial direction while undergoing vertical displacement. When the frictional force between the surface of the small hollow oblique prism element and the adjacent plane is greater than the vertical force component that counteracts the frictional force, the structure will not undergo compressive deformation; when the component of the bearing force exceeds the frictional force, the structure begins to undergo compressive deformation.

[0111] Furthermore, the structure initially undergoes compressive deformation only when a horizontal force is present. However, as the force gradually increases and the compressive deformation reaches a certain level, it will cease to compress further, i.e., it will not compress into a two-dimensional plane, regardless of how much the force increases. This is because within the structure, all units are connected along a single axis with consistent angles and opposite directions. Under the action of a lateral force, the force is evenly distributed along the single axis. Initially, each small hollow oblique prism unit rotates around its axis while also undergoing in-plane displacement. When the in-plane displacement space is insufficient, it begins to rotate around its axis, but a lateral force alone is insufficient to initiate this rotation. At this point, if a small vertical perturbation is applied, the fold-and-cut three-dimensional periodic solid structure will rapidly continue to compress and deform.

[0112] Figure 1-9 This is a schematic diagram of the three-dimensional periodic solid structure with negative Poisson bit properties in the folding-cutting method in this embodiment under compression. Figure 1-10Structure schematic diagram of the fold-and-cut three-dimensional periodic solid structure with negative Poisson's ratio characteristics in the embodiment in a fully compressed state.

[0113] When the fold-and-cut hollow double-layer unit is fully compressed, one side of the fold-and-cut hollow double-layer unit will present a pattern of four squares, three triangles, one parallelogram, and three irregular quadrilaterals that are congruent. Among them, the edge length of the four squares is a. The triangle is an isosceles triangle with a bottom angle of γ, a waist length of a, and a bottom side of The parallelogram is a pair of parallelograms with a length of a, a length of b, and an internal angle of (90°-γ). The irregular quadrilateral is composed of two right-angled triangles: one of which has a hypotenuse of b and a right-angled side of a, and the included angle between the hypotenuse and the right-angled side is (90°-γ); the other of which has an angle of (2γ-90°) and a right-angled side of

[0114] Embodiment 2

[0115] As shown in Figure 2-1 , the fold-and-cut three-dimensional periodic solid structure with negative Poisson's ratio characteristics in the embodiment includes four fold-and-cut hollow double-layer units, and the four fold-and-cut hollow double-layer units are expanded in the vertical direction, and the adjacent fold-and-cut hollow double-layer units are fixedly connected through the adjacent structural surfaces, that is, the mirror surfaces.

[0116] The embodiment includes 128 small hollow oblique prismatic units, and the small hollow oblique prismatic units are in a mirror relationship with their adjacent small hollow oblique prismatic units in the vertical direction and the horizontal direction. The 32 small hollow oblique prismatic units located at the corner points are respectively connected to the adjacent small hollow oblique prismatic units through two common edges, the 64 small hollow oblique prismatic units located at the horizontal and vertical longitudinal edges and excluding the corner points are respectively connected to the adjacent small hollow oblique prismatic units through three common edges, and the other 32 small hollow oblique prismatic units are respectively connected to the adjacent small hollow oblique prismatic units through four common edges. Figure 2-2 Structure schematic diagram of the fold-and-cut three-dimensional periodic solid structure with negative Poisson's ratio characteristics in the embodiment in a compressed deformed state.

[0117] The others are the same as Embodiment 1.

[0118] Embodiment 3

[0119] As shown in Figure 3-1 , the fold-and-cut three-dimensional periodic solid structure with negative Poisson's ratio characteristics in the embodiment includes eight fold-and-cut hollow double-layer units, and the eight fold-and-cut hollow double-layer units are expanded in the vertical direction and the horizontal direction, and the adjacent fold-and-cut hollow double-layer units are fixedly connected through the adjacent structural surfaces, that is, the mirror surfaces.

[0120] The embodiment includes 512 small hollow rhombic prism units, which are mirror images with their adjacent small hollow rhombic prism units in the vertical direction and the horizontal direction. The 32 small hollow rhombic prism units at the corner points are connected with the adjacent small hollow rhombic prism units by two common edges, respectively; the 192 small hollow rhombic prism units at the horizontal and vertical edges except the corner points are connected with the adjacent small hollow rhombic prism units by three common edges, respectively; and the other 288 small hollow rhombic prism units are connected with the adjacent small hollow rhombic prism units by four common edges, respectively. Figure 3-2 A structure schematic diagram of the foldable-paper three-dimensional periodic solid structure with negative Poisson's ratio in a compression deformation state.

[0121] The other is the same as embodiment 1.

[0122] The foldable-paper three-dimensional periodic solid structure with negative Poisson's ratio is described in detail above. The principles and implementation manners of the present application are described by using specific examples in this paper, and the above embodiment is only used to help understand the method of the present application and its core idea. It should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, the present application can be improved and modified in several ways, and these improvements and modifications also fall within the protection scope of the claims of the present application. The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fold-cut paper three-dimensional periodic solid structure having a negative Poisson's ratio property, characterized in that, The paper folding and cutting hollow double-layer unit is expanded in the vertical and horizontal directions, and is fixedly connected between adjacent paper folding and cutting hollow double-layer units through corresponding structure surfaces. The paper folding and cutting hollow double-layer unit comprises upper and lower layers, and each of the upper and lower layers comprises four hollow inclined quadrangular prisms. The hollow inclined quadrangular prism comprises four small hollow inclined prism units, and each of the small hollow inclined prism units is fixedly connected with an adjacent small hollow inclined prism unit through a common side. The hollow inclined quadrangular prism is unfolded into a basic paper folding and cutting unit. The basic paper folding and cutting unit is formed by alternately connecting two rectangles and two parallelograms. The rectangle is formed by sequentially connecting four small squares, and the parallelogram is formed by sequentially connecting four small parallelograms.

2. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 1, wherein, The top points of the small squares and the small parallelograms in the basic paper folding and cutting unit are control points.

3. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 1, wherein, When the paper folding and cutting hollow double-layer unit is compressed, the adjacent small hollow inclined prism units are separated from each other. The paper folding and cutting hollow double-layer unit is obtained by mirroring the hollow inclined quadrangular prism along the upper surface ADTQ thereof and then mirroring the side surface ABRQ-A'B'R'Q' thereof.

4. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 1, wherein, The upper surface and the lower surface of the hollow inclined quadrangular prism are closed rectangles, the front side surface and the rear side surface of the hollow inclined quadrangular prism are closed parallelograms, the length of the closed rectangle is 4a, the width of the closed rectangle is a, the height of the closed rectangle is h, and h=bsinγ. When the paper folding and cutting hollow double-layer unit is compressed, the adjacent small hollow inclined prism units are separated from each other. AB=AB'=HG=HG'=IJ=IJ'=b ∠ABG = ∠AB'G' = ∠AHG = ∠AHG' = ∠IJG = ∠IHG = ∠IHG' = IJ'G' = γ ∠GBJ = ∠G' B'J' = ∠GJB = ∠G'J' B' = ∠HAI = ∠HIA = ψ ∠ABJ = ∠AB'J' = ξ Let the initial state plane ABRQ be the main plane, the angle between the compressed plane ABHG and the main plane be θ, and the angle between the bottom surface of the compressed hollow oblique quadrilateral prism and the plane HIJG be At this time, the height S of the hollow oblique prism is: The straight line distance L of AI, HP and IQ is: The distance C of point G to the straight line BJ is: C = asin θ sin γ The distance V of point I to the straight line JJ' is: Supposing the length of the fold-cut paper hollow double-layer unit after compression deformation is R, The width of the fold-cut paper hollow double-layer unit after compression deformation is B, The height of the fold-cut paper hollow double-layer unit after compression deformation is H, Deriving the length R, the width B and the height H with respect to the angle ξ respectively: The longitudinal Poisson's ratio v1 of the fold-cut paper hollow double-layer unit in the horizontal stretching process and the transverse Poisson's ratio v2 in the vertical compression process are:

5. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 1, wherein, In the fold-cut paper hollow double-layer unit, eight small hollow inclined prismatic units at eight corner points have two common edges, sixteen small hollow inclined prismatic units located in the horizontal longitudinal edge and the vertical longitudinal edge of the double-layer unit have three common edges, and other eight small hollow inclined prismatic units have four common edges, and the common edges are provided with connecting pieces.

6. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 5, wherein, The connecting pieces include but are not limited to: wheel shaft connection, roller connection, guide running wheel, steel hinge hinge, flexible material bonding.

7. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties of claim 1, wherein, Adjacent fold-cut paper hollow double-layer units are fixedly connected through adjacent structural surfaces. In each fold-cut paper hollow double-layer unit, adjacent small hollow inclined prismatic units are fixedly connected through adjacent structural surfaces.

8. The fold-cut paper three-dimensional periodic solid structure with negative Poisson's ratio properties according to claim 7, characterized in that, The fixed connection mode includes but is not limited to: welding, bonding, high-temperature melting, 3D printing, bolt connection.

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