A two-dimensional unit cell structure and material with negative Poisson's ratio

Abstract

This invention relates to a two-dimensional unit cell structure and a negative Poisson's ratio material, belonging to the field of mechanical metamaterials technology. It includes a quadrangular star unit and a double-arrow unit. The quadrangular star unit is formed by four first V-shaped rods connected sequentially through their open ends, forming a first concave portion at the connection point. A first connecting rod is connected to the outside of the first concave portion. The double-arrow unit is formed by a double-arrow body composed of second V-shaped rods mirrored once around the line connecting the two endpoints of the open ends. One end of the double-arrow body is the arrowhead, and the other end is a second concave portion. A second connecting rod is connected to the outside of the second concave portion. Depending on the number of double-arrow units, the negative Poisson's ratio two-dimensional unit cell structure includes a single-arrow configuration and a double-arrow configuration. The negative Poisson's ratio two-dimensional unit cell structure obtains the negative Poisson's ratio material through periodic arrangement in a plane. This invention achieves negative Poisson's ratio properties with a simple structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical metamaterials, and particularly relates to a negative Poisson's ratio two-dimensional unit cell structure and a negative Poisson's ratio material. BACKGROUND

[0002] Metamaterials are composite materials artificially designed to possess extraordinary physical properties that natural materials do not have, without violating the basic laws of physics. They have great advantages in energy absorption and dissipation, acoustics, optics, and mechanical properties. The performance of metamaterials is not only determined by the performance of the basic materials they are composed of, but also related to the structure they are designed into. Mechanical metamaterials are a major category of metamaterials, which are artificially designed materials with counterintuitive mechanical properties, such as negative Poisson's ratio materials, negative compressibility materials, negative thermal expansion materials, and negative stiffness materials.

[0003] Negative Poisson's ratio materials, also known as auxetic materials, have a negative Poisson's ratio. In conventional materials, when subjected to external tensile force, the material usually shrinks in the direction perpendicular to the stretching direction, which is known as the positive Poisson's ratio effect. However, negative Poisson's ratio materials exhibit a completely different behavior, which expands in the direction perpendicular to the stretching direction when they are stretched. This unique property makes negative Poisson's ratio materials have potential application value in many engineering fields.

[0004] Taking the aerospace field as an example, traditional positive Poisson's ratio materials often produce unnecessary stress concentration in certain directions when subjected to external force, which may lead to material damage or performance degradation. Negative Poisson's ratio materials can more effectively disperse these stresses, thereby improving the overall strength and durability of the material. In addition to traditional structural components, negative Poisson's ratio materials can also be used for other innovative applications such as vibration and noise reduction, thermal protection, etc. in aircraft. In addition, negative Poisson's ratio materials also have excellent energy absorption capacity, which can significantly improve the impact resistance and fatigue resistance of structures, making them have broad application prospects in protective equipment, shock-absorbing materials, etc.

[0005] Although there are some natural materials with negative Poisson's ratio effect in nature, the performance of these materials is often difficult to meet the needs of engineering applications. Therefore, it is more important to use advanced material science and engineering technology to artificially synthesize negative Poisson's ratio materials with excellent performance. SUMMARY

[0006] The purpose of the present application is to provide a negative Poisson's ratio two-dimensional unit cell structure and a negative Poisson's ratio material, which has a simple structure and is easy to adjust, helping to solve the problem of material damage or performance degradation caused by stress concentration in the engineering field, and expanding the types of metamaterials.

[0007] In order to achieve the above object, the technical scheme adopted by the present application is: a negative Poisson's ratio two-dimensional cell structure comprising connected four-star type units and double-arrow type units;

[0008] The four-star type unit comprises a four-star type body formed by sequentially connecting and surrounding four identical first V-shaped rod bodies through open ends, the connection part of adjacent two first V-shaped rod bodies forming a first inner recess pointing to the center of the four-star type body, and each first inner recess further connected with a first connecting rod, and the extension line of each first connecting rod passing through the center of the four-star type body.

[0009] The double-arrow type unit comprises a double-arrow type body formed by once mirroring a second V-shaped rod body with the line connecting the two end points of the open end as the symmetry axis, the two rod bodies of the second V-shaped rod body being different in length, one end of the symmetry axis of the double-arrow type body being an outer convex arrowhead, and the other end being a second inner recess, the second inner recess connected with a second connecting rod, and the extension line of the second connecting rod passing through the arrowhead.

[0010] The negative Poisson's ratio two-dimensional cell structure comprises a single-side arrow configuration and a double-side arrow configuration, in the single-side arrow configuration, one double-arrow type unit is arranged on one side of the four-star type unit, and the arrowhead of the double-arrow type body in the double-arrow type unit is connected with the first connecting rod, and in the double-side arrow configuration, two double-arrow type units are arranged on opposite sides of the four-star type unit, and the arrowheads of the two double-arrow type units are connected with the corresponding first connecting rods.

[0011] Further, a Cartesian coordinate system is established with the center of the four-star type body as the coordinate origin, the horizontal direction as the X axis, and the vertical direction as the Y axis, the arrowhead and the second inner recess of the double-arrow type unit are both located on the Y axis, and the top points of the two second V-shaped rod bodies forming the double-arrow type body have the same horizontal coordinates as the end parts of the first connecting rods on the same side.

[0012] Further, the top angle of the first V-shaped rod body is θ, and the included angle between the first V-shaped rod body and the adjacent first connecting rod is γ, and θ+90°=2γ.

[0013] The present application further provides another embodiment: a negative Poisson's ratio material comprising a plurality of the above-mentioned negative Poisson's ratio two-dimensional cell structures, and the negative Poisson's ratio two-dimensional cell structures are arranged periodically in the plane to form a two-dimensional cell structure.

[0014] As a specific embodiment, when the negative Poisson's ratio two-dimensional cell structure is in the single-side arrow configuration, the plurality of negative Poisson's ratio two-dimensional cell structures are arranged periodically along the Y axis, the end parts of the first connecting rods and the second connecting rods on the Y axis in adjacent two negative Poisson's ratio two-dimensional cell structures are connected, and then the two-dimensional cell structure is obtained by repeatedly mirroring along the X axis.

[0015] As a specific embodiment, when the negative Poisson's ratio two-dimensional cellular structure is a double-sided arrow configuration, a plurality of negative Poisson's ratio two-dimensional cellular structures are arranged periodically along the X-axis direction to form a transverse unit, the two first connecting rod ends on the X-axis in two adjacent negative Poisson's ratio two-dimensional cellular structures are connected, and the apexes of the second V-shaped rod bodies of the double arrow units are connected; then a plurality of rows of transverse units are arranged along the Y-axis, and adjacent rows of transverse units are staggered by a certain distance along the X-axis, to obtain a two-dimensional cellular structure, and the staggered distance is the length from the center of the star-shaped body to the first connecting rod end on the X-axis.

[0016] Further, the transverse units in the same odd row or the same even row are mirror images of each other on the Y-axis.

[0017] The beneficial effects of the present application are: the present application adopts a combination of a four-corner star-shaped unit and a double arrow unit to form a two-dimensional cellular structure, and designs a two-dimensional cellular structure with an adjustable Poisson's ratio according to different arrangement modes, so as to realize the negative Poisson's ratio characteristic with a simple structure. When the material is subjected to tensile or compressive change, each rod member constituting the material is subjected to axial elongation or shortening, and due to the adjustable geometric parameters of each rod member, the macroscopic Poisson's ratio of the material changes between positive, near zero and negative. The present application can be applied to the design of improving structural safety and light weight. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0019] Figure 1 It is a structural schematic diagram of the negative Poisson's ratio two-dimensional cellular structure in embodiment 1.

[0020] Figure 2 It is a size parameter schematic diagram of the negative Poisson's ratio two-dimensional cellular structure in embodiment 1.

[0021] Figure 3 It is a structural schematic diagram of the negative Poisson's ratio material in embodiment 2.

[0022] Figure 4 It is a diagram of the elongation of the negative Poisson's ratio material in the x direction with the change of the angle θ in embodiment 2.

[0023] Figure 5 It is a diagram of the Poisson's ratio υ of the negative Poisson's ratio material with the change of the angle θ in embodiment 2.

[0024] Figure 6 It is a structural schematic diagram of the negative Poisson's ratio two-dimensional cellular structure in embodiment 3.

[0025] Figure 7 Structure diagram of the negative Poisson's ratio material in Example 4;

[0026] Figure 8 Graph of the elongation of the negative Poisson's ratio material in Example 4 in x direction versus angle θ;

[0027] Figure 9 Graph of the Poisson's ratio υ of the negative Poisson's ratio material in Example 4 versus angle θ;

[0028] Marked in the figure: 100, four-star type unit, 101, four-star type body, 102, first V-shaped rod body, 103, first inner recess, 104, first connecting rod;

[0029] 200, double arrowhead unit, 201, double arrowhead body, 202, second V-shaped rod body, 203, arrowhead tip, 204, second inner recess, 205, second connecting rod;

[0030] 300, transverse unit. DETAILED DESCRIPTION

[0031] The application will be further described in detail below in combination with the drawings and examples, but it is not as the basis for any limitation on the application.

[0032] Example 1: As shown in Figure 1 、 2 A negative Poisson's ratio two-dimensional cell structure, which belongs to a single-sided arrowhead configuration, includes a four-star type unit 100 and a double arrowhead unit 200. The four-star type unit 100 includes a four-star type body 101 and four first connecting rods 104 connected to the four-star type body 101. The four-star type body 101 is composed of four first V-shaped rod bodies 102 of the same size. The first V-shaped rod body 102 is a V-shaped structure formed by connecting two straight rods of the same length. The four first V-shaped rod bodies 102 are circumferentially connected by their open ends to form the four-star type body 101. The tips of the first V-shaped rod bodies 102 serve as the four corners of the four-star type body 101. The connection between adjacent two first V-shaped rod bodies 102 forms an inner recessed first inner recess 103. Therefore, the four-star type body 101 has four first inner recesses 103. The inner side of the first inner recess 103 points to the center of the four-star type body 101. The outer side of the first inner recess 103 is further connected to the first connecting rod 104. The opposite two first connecting rods 104 in the four-star type unit 100 are on the same straight line passing through the center of the four-star type body 101. The adjacent two first connecting rods 104 are perpendicular to each other.

[0033] The double-arrow unit 200 includes a double-arrow body 201 and a second connecting rod 205. The double-arrow body 201 is composed of two second V-shaped rods 202 of the same size connected together. The second V-shaped rod 202 is composed of two straight rods of different lengths connected together. One of the second V-shaped rods 202 forms the double-arrow body 201 by mirroring the line connecting the two ends of the open end as the axis of symmetry. One end of the double-arrow body 201 on the axis of symmetry is an outwardly convex arrow tip 203, and the other end is an inwardly concave second concave part 204. The second connecting rod 205 is connected to the outside of the second concave part 204, and the extension line of the second connecting rod 205 passes through the arrow tip 203.

[0034] When the quadrangular star unit 100 and the double-arrow unit 200 form the negative Poisson's ratio two-dimensional unit cell structure, the double-arrow unit 200 is disposed on one side of the quadrangular star unit 100, and the arrow tip 203 of the double-arrow body 201 in the double-arrow unit 200 is connected to the first connecting rod 104.

[0035] like Figure 2 As shown, a Cartesian coordinate system is established with the centroid of the four-pointed star-shaped main body 101 as the origin, with the horizontal axis as the X-axis and the vertical axis as the Y-axis. The arrow tip 203 and the second concave part 204 of the double arrow unit 200 are both located on the Y-axis. The vertices of the two second V-shaped rods 202 that make up the double arrow main body 201 have the same horizontal coordinate as the end of the first connecting rod 104 on the same side.

[0036] The specific size requirements of the negative Poisson's ratio two-dimensional unit cell structure described in this embodiment are as follows: Figure 2 As shown, in the double-arrow unit 200, its overall structure is symmetrical about the Y-axis. The two second V-shaped rods 202 that make up the double-arrow body 201 are composed of straight rods CA and AD, and straight rods CA′ and A′D, respectively. Points C and D are both located on the Y-axis. The lengths of straight rods AC and A′C are L1, and the lengths of straight rods AD and A′D are L2. The included angle between the vertices of the second V-shaped rods 202 is ∠CAD, where ∠CAD=α, and the arrowhead tip is ∠ADA′, where ∠ADA′=β. The second connecting rod 205 is BC, and the length of BC is L4.

[0037] In the four-star unit 100, the structure is symmetrical about the X axis and the Y axis as a whole. The four first V-shaped rods 102 are rods FEG, GIJ, JI'G' and G'E'F, which are sequentially connected end to end around the origin O of the coordinate system to form a four-star main body. The straight rods constituting the four first V-shaped rods have a length L3, i.e. EF=EG=IG=IJ=I'J=I'G'=G'E'=E'F=L3, and the four corners of the four-star main body 101, i.e. the top corners of the four first V-shaped rods 102, are all equal, i.e. ∠FEG=∠GIJ=∠JI'G'=∠G'E'F=θ. The four first connecting rods 104 are straight rods HG, DF, JK and H'G', and the straight rods HG and H'G' are located on the X axis and have a length L4, and the straight rods DF and JK are located on the Y axis and have a length L5. In this way, the vertices E and E', the vertices G and G', the vertices H and H', and the vertices I and I' are symmetrical about the Y axis, and the vertices E and I, the vertices F and J, and the vertices E' and I' are symmetrical about the X axis. The first connecting rod and the adjacent first V-shaped rod 102 have an equal angle, such as ∠DFE=γ. Therefore, θ+90°=2γ.

[0038] The vertex A has the same X axis coordinate as the vertex H, and the vertex A' has the same X axis coordinate as the vertex H', so as to realize the arrangement and connection of the negative Poisson's ratio two-dimensional unit cell structures along the X axis direction.

[0039] According to the symmetry relationship of the unit cell, the above-mentioned negative Poisson's ratio two-dimensional unit cell structure is symmetrical about the Y axis as a whole.

[0040] Embodiment 2

[0041] The negative Poisson's ratio material involved in this embodiment is a two-dimensional unit cell structure obtained by periodic arrangement in the plane by using the negative Poisson's ratio two-dimensional unit cell structure described in embodiment 1.

[0042] Specifically, a plurality of negative Poisson's ratio two-dimensional unit cell structures are periodically arranged along the Y axis direction, the end portions of the first connecting rods and the second connecting rods located on the Y axis in two adjacent negative Poisson's ratio two-dimensional unit cell structures are connected, and then a two-dimensional unit cell structure is obtained by repeatedly mirroring along the X axis direction.

[0043] The following uses numerical simulation by using ANSYS software to verify the negative Poisson's ratio characteristics of the metamaterial. The model size used in the X axis and Y axis directions has 6 unit cells, i.e. there are 6 negative Poisson's ratio two-dimensional unit cell structures in the X axis and Y axis directions, and the structure is as shown in Figure 3 The unit type used is BEAM3. The model overall rod uses Q235 alloy steel, i.e. the Young's modulus E 1= E 2= 203Gpa, Poisson's ratio υ=0.3, and the cross-sectional area of the rod constituting the unit cell is uniformly taken as 0.1×0.1mm 2rectangular cross section, wherein L 1= 15mm, L 2=17.3mm, L 3= 12mm, L 4= 8mm, L 5= 6.7mm, the top angle θ of the four-star-shaped body is respectively 32°, 34°, 36°, 38°, 40°. When the Poisson's ratio of the super material is solved by numerical simulation, the longitudinal (Y direction) elongation of the structure is set to 12mm, and the Poisson's ratio υ of the model is measured. The numerical simulation analysis results are shown in Figure 4 、 5 , Figure 4 is a graph of the transverse (X direction) elongation Δx of the material with respect to the angle θ, Figure 5 is a graph of the Poisson's ratio υ with respect to the angle θ. From Figure 4 and Figure 5 , it can be seen that within the adjustable range of the angle θ, the overall transverse elongation of the structure decreases with the increase of the angle θ, the negative Poisson's ratio property of the material weakens with the increase of the angle θ, and both are approximately linearly changed.

[0044] Example 3

[0045] This embodiment is based on example 1, and adjusts the negative Poisson's ratio two-dimensional unit cell structure to obtain a negative Poisson's ratio two-dimensional unit cell structure with a double-sided arrow configuration different from that of example 1.

[0046] As shown in Figure 6 , in the negative Poisson's ratio two-dimensional unit cell structure with a double-sided arrow configuration, two double-arrow units 200 are arranged on opposite sides of the four-star-shaped unit 100, the arrow tips 203 of the two double-arrow units 200 are connected with the corresponding first connecting rods 104, and the two first connecting rods in the four-star-shaped unit 100 in another direction are used to connect with other four-star-shaped units 100. In this embodiment, the double-arrow unit 200 no longer has a second connecting rod, and the remaining structures and size parameters are the same as those of example 1.

[0047] The negative Poisson's ratio two-dimensional unit cell structure with a double-sided arrow configuration is symmetrical about the X axis and the Y axis. In this embodiment, the two double-arrow units 200 are located in the Y axis direction of the four-star-shaped unit 100 and are connected with the first connecting rods 104 in the Y axis direction, and the two first connecting rods 104 in the X axis direction are used to expand the negative Poisson's ratio two-dimensional unit cell structure in the X axis direction.

[0048] Example 4

[0049] The negative Poisson's ratio material involved in this embodiment is a two-dimensional unit cell structure obtained by periodic arrangement in the plane using the negative Poisson's ratio two-dimensional unit cell structure described in example 3.

[0050] Specifically, such as Figure 7 As shown, multiple negative Poisson's ratio two-dimensional unit cell structures are periodically arranged along the X-axis to form transverse units 300. In the transverse units 300, the ends of the two first links 104 on the X-axis in two adjacent negative Poisson's ratio two-dimensional unit cell structures are connected, and the vertices of the second V-shaped rods 202 of the double-arrow units are connected. Then, multiple rows of transverse units 300 are arranged along the Y-axis, and adjacent rows of transverse units 300 are staggered by a certain distance along the X-axis to obtain a two-dimensional multi-cell structure. The staggered distance is the length from the centroid of the star-shaped main body to the end of the first link 104 on the X-axis. In two staggered rows of adjacent transverse units 300, the vertices of the second V-shaped rods 202 on the double-arrow units 200 in one row of transverse units 300 are connected to the second concave portion 204 of the adjacent double-arrow unit 200 in the other row of transverse units 300. Therefore, transverse units 300 that are both odd-numbered rows or both even-numbered rows are mirror images of each other on the Y-axis.

[0051] The simulation test method described in Example 2 was used to verify the negative Poisson's ratio characteristics of the metamaterial through numerical simulation using ANSYS software. The model used was a 4×3 structure, meaning that the transverse elements in the X-axis direction had four two-dimensional unit cells with negative Poisson's ratios, and there were three rows of transverse elements in the Y-axis direction. The overall rods of the model were made of Q235 alloy steel, i.e., Young's modulus... E 1= E 2 = 203 GPa, Poisson's ratio υ = 0.3, and the cross-sectional area of ​​the rods constituting the cell is uniformly taken as 0.1 × 0.1 mm. 2 A rectangular cross-section, in which L 1 = 15mm L 2 = 17.3 mm L 3 = 12mm L 4 = 8mm, L 5 = 6.7 mm, and the apex angles θ of the four-pointed star-shaped main body are taken as 32°, 34°, 36°, 38°, and 40° respectively. When performing numerical simulation to solve for the Poisson's ratio of the shown metamaterial, the longitudinal (Y-direction) elongation of the structure is set to 12 mm, and the Poisson's ratio υ of the model is measured. The numerical simulation analysis results are as follows... Figure 8 , 9 As shown, Figure 8 This is a graph showing the variation of the material's transverse (X-direction) elongation Δx with angle θ. Figure 9 This is a graph showing the variation of Poisson's ratio υ with angle θ. From... Figure 8 and Figure 9 It can be seen that within the adjustable range of angle θ, the overall lateral elongation of the structure decreases as angle θ increases, the negative Poisson's ratio property of the material weakens as angle θ increases, and both are approximately linear changes.

[0052] The negative Poisson's ratio two-dimensional cell structure of the present application can adjust the macro negative Poisson's ratio coefficient of the super material by adjusting the length and angle of each straight rod of the base structure, and the negative Poisson's ratio characteristic is realized by a simple structure, so the present application effectively solves the material damage or performance decline problem caused by stress concentration in many engineering fields, and expands the types of super materials.

[0053] The above examples are only used to illustrate the technical solutions of the present application but not to limit it, and those skilled in the art should understand that the specific embodiments of the present application can be modified or replaced by equivalents according to the above examples, and any modification or equivalent replacement without departing from the spirit and scope of the present application is within the protection scope of the claims.

Claims

1. A negative Poisson's ratio two-dimensional cellular structure, characterized by: The negative Poisson's ratio two-dimensional cellular structure comprises a four-star-shaped unit and a double-arrow-shaped unit. The four-star-shaped unit comprises a four-star-shaped body, which is formed by sequentially connecting four identical first V-shaped rods through open ends. The double-arrow-shaped unit comprises a double-arrow-shaped body, which is formed by once mirroring a second V-shaped rod with the line connecting the two end points of the open ends as the axis of symmetry. The negative Poisson's ratio two-dimensional cellular structure comprises a one-side arrow-shaped configuration and a double-side arrow-shaped configuration.

2. The negative Poisson’s ratio two-dimensional unit cell structure of claim 1, wherein: In the one-side arrow-shaped configuration, one double-arrow-shaped unit is arranged on one side of the four-star-shaped unit, and the arrow tip of the double-arrow-shaped unit is connected to the first connecting rod.

3. The negative Poisson’s ratio two-dimensional unit cell structure of claim 2, wherein: In the double-side arrow-shaped configuration, two double-arrow-shaped units are arranged on opposite sides of the four-star-shaped unit, and the arrow tips of the two double-arrow-shaped units are connected to the corresponding first connecting rods.

4. A negative Poisson's ratio material comprising a plurality of negative Poisson's ratio two-dimensional unit cells as claimed in claim 2 or 3, characterised in that: A Cartesian coordinate system is established with the center of the four-star-shaped body as the origin, the horizontal direction as the X axis, and the vertical direction as the Y axis.

5. A negative Poisson's ratio material according to claim 4, wherein: The arrow tip and the second concave part of the double-arrow-shaped unit are located on the Y axis, and the vertices of the two second V-shaped rods forming the double-arrow-shaped body have the same horizontal coordinate as the end of the first connecting rod on the same side.

6. A negative Poisson's ratio material according to claim 4, wherein: The top angle of the first V-shaped rod is θ, and the angle between the first V-shaped rod and the adjacent first connecting rod is γ, and θ + 90° = 2γ.

7. A negative Poisson's ratio material according to claim 6, wherein: The negative Poisson's ratio two-dimensional cellular structure is obtained by periodic arrangement in the plane. When the negative Poisson's ratio two-dimensional cellular structure is in the one-side arrow-shaped configuration, multiple negative Poisson's ratio two-dimensional cellular structures are periodically arranged along the Y axis, the end of the first connecting rod and the end of the second connecting rod on the Y axis of adjacent two negative Poisson's ratio two-dimensional cellular structures are connected, and then the two-dimensional cellular structure is obtained by repeatedly mirroring along the X axis. When the negative Poisson's ratio two-dimensional cellular structure is in the double-side arrow-shaped configuration, multiple negative Poisson's ratio two-dimensional cellular structures are periodically arranged along the X axis to form a horizontal unit, the ends of the two first connecting rods on the X axis of adjacent two negative Poisson's ratio two-dimensional cellular structures are connected, and the vertices of the second V-shaped rods of the double-arrow-shaped units are connected. Then, multiple horizontal units are arranged along the Y axis, and adjacent horizontal units are staggered along the X axis by a certain distance to obtain the two-dimensional cellular structure. The staggered distance is the length from the center of the star-shaped body to the end of the first connecting rod on the X axis. Horizontal units in the same odd row or the same even row are mirror images of each other along the Y axis.

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