Chiral negative poisson's ratio cellular structure with variable ligament thickness

Abstract

The application discloses a chiral negative Poisson's ratio single cell structure with variable ligament thickness and a honeycomb structure, and belongs to the technical field of structural mechanics. The single cell structure comprises a central body and N ligaments distributed in a circumferential array around the central body, wherein N is greater than or equal to 3. Each ligament has a first side surface and a second side surface parallel to the central axis of the central body, and the profile lines of the first side surface and the second side surface are constructed by NURBS curves. The application uses NURBS curves to construct the boundary, so that the ligament has the characteristics of curved configuration and variable thickness, the structure form of the ligament can be flexibly regulated, the structure layout of the chiral negative Poisson's ratio structure is more flexible, the mechanical properties such as the structure strength can be flexibly adjusted according to different application scenarios, and the demand for the complexity and customization of the mechanical properties of the chiral negative Poisson's ratio structure in actual engineering can be met.

Description

TECHNICAL FIELD

[0001] The application relates to a chiral negative Poisson's ratio single-cell structure with variable ligament thickness and a honeycomb structure, and belongs to the technical field of structural mechanics. BACKGROUND

[0002] Metamaterials with both negative Poisson's ratio effect and chirality have attracted extensive attention in mechanical bearing and multifunctional design and application. The negative Poisson's ratio effect refers to the mechanical property that a material expands in the transverse direction within the elastic range when being stretched, and the transverse direction of the material shrinks when being compressed. Chirality refers to the structural property that a material has mirror symmetry and its mirror image cannot coincide with the original object. The honeycomb structure has very strong bearing capacity due to its special geometric configuration.

[0003] The chiral honeycomb structure is a kind of artificial material composed of periodic optimized microstructures, and has the properties of negative Poisson's ratio and high compressibility due to the coupling between local rotation, bending and volume deformation. The negative Poisson's ratio structure has the characteristics of light weight, high strength weight ratio, high energy absorption and high flexibility, and has wide application value in the field of aerospace, especially in the aircraft with variable structure. The variable structure can expand the flight envelope of the aircraft, eliminate the structure of the flap, reduce air resistance and help control vibration. In order to achieve the above-mentioned goals, the variable wing aircraft requires the wings to change the wingspan, the sweepback angle and the wingtip angle to achieve the optimal aerodynamic configuration at different flight speeds, and the property of the chiral negative Poisson's ratio honeycomb structure deforming in a specific direction under load can be fully utilized. The customizable deformation property makes the chiral negative Poisson's ratio honeycomb structure well adapt to the optimal aerodynamic configuration of the wings corresponding to different flight conditions, and can further improve the flight speed.

[0004] The microstructure of the cell, such as the length and thickness of the ligament in the cell structure, has an important influence on the macroscopic and microscopic mechanical properties of the chiral negative Poisson's ratio honeycomb structure. The traditional design method of the chiral negative Poisson's ratio honeycomb structure has limited degrees of freedom, usually only pays attention to the overall control of the center structure and the ligament size of the cell, and ignores the design of the change of the ligament thickness. This design method makes the controllable mechanical property range of the chiral negative Poisson's ratio honeycomb structure limited, and when a specific mechanical property is required in engineering, it may be difficult to design the required structure.

[0005] For example, the patent application with publication number CN 116447258 A provides a four-ligament reverse-handed Poisson's ratio cell and structure with energy absorption characteristics. Its unit cell is composed of a central structure connected to four ligaments. During the stress process, the coupling effect between the ligaments and the central structure makes the whole structure exhibit negative Poisson's ratio characteristics. However, the ligament thickness of this structure is a fixed value, and all the ligaments are straight beams. The lack of variation in the thickness and form of the ligaments limits the mechanical properties of the structure, resulting in a limitation on the energy absorption capacity of the entire structure.

[0006] The patent application CN 116947420 A discloses a cross-chiral negative Poisson's ratio structure made of high-ductility cement-based composite material. Its unit cell consists of four L-shaped rods connected to the four sides of a central prism, forming a swastika-shaped cross-chiral structure. This structure exhibits high compressive strength, flexural strength, and good dynamic mechanical properties and energy absorption characteristics. Although this structure uses L-shaped beams, the ligament shape is fixed, and the ligament thickness is not considered for adjustment. Therefore, the mechanical properties of the structure cannot be adjusted, limiting its application in various complex situations.

[0007] The patent with publication number CN209654492U provides a performance-adjustable negative Poisson's ratio structure, which is inspired by the double-arrow type negative Poisson's ratio structure. It uses NURBS curves to generate a compliant curved beam with uniform thickness.

[0008] It should be noted that the above content falls within the inventor's technical knowledge and does not necessarily constitute prior art. Summary of the Invention

[0009] To address the problems existing in the prior art, this invention provides a chiral negative Poisson's ratio unit cell structure and a honeycomb structure with variable ligament thickness. By using NURBS curves to construct the boundary, the ligament has the characteristics of bending configuration and variable thickness, which can flexibly control the structural form of the ligament.

[0010] The present invention achieves the above objectives by adopting the following technical solutions:

[0011] On one hand, the present invention provides a chiral negative Poisson's ratio unit cell structure with variable ligament thickness, comprising a central body and N ligaments distributed in a circular array around the central body, where N≥3 and N is an integer;

[0012] Each ligament has a first side and a second side parallel to the central axis of the centrosome. The outlines of the first side and the second side are constructed by NURBS curves. The distance between the first side and the second side is defined as the ligament thickness, and the length of the first side and the second side extending away from the centrosome is defined as the ligament length.

[0013] The single-cell structure exhibits chiral characteristics.

[0014] Generally, 3≤N≤6.

[0015] In another aspect, the present application also provides a method for constructing the ligament, comprising the following steps:

[0016] C1 and C2 are respectively the profile lines of the first side and the second side of the ligament, the expressions of the two NURBS curves C1 and C2 are

[0017] C1(t) = R p (t)B1

[0018] C2(t) = R p (t)B2

[0019] wherein B1 = [X Y1] and B2 = [X Y2] are respectively the control point coordinates of the two NURBS curves C1 and C2, wherein,

[0020]

[0021] N i,p (t) is the base function of the NURBS curve, controlled by the node vector Ξ, p is the order of the curve, and {ω i} is the control point weight sequence.

[0022] The two profile line coordinates are calculated according to the control point coordinates, the order p, the node vector Ξ, and the control point weight sequence {ω i}, and the construction of the ligament is completed.

[0023] Further, in one specific embodiment, the specific construction method of the ligament is as follows:

[0024] C0 is set as the center line of the ligament, the size of the unit cell structure is L0, and the size of the central body is 2x1;

[0025] An xoy rectangular coordinate system is established with the center of the central body as the origin, the length direction of the ligament as the x-axis, and the thickness direction of the ligament as the y-axis;

[0026] The control points of the three NURBS curves C0, C1, and C2 are m groups, and the m groups of control points are uniformly distributed along the length direction of the ligament from x1 to L0 / 2, each group of control points having three control points, which are respectively the control points of the center line and the two profile lines;

[0027] The shape of the ligament is controlled by determining the control point coordinates (X, Y0, Y1, Y2) of the three curves C0, C1, and C2;

[0028] X is the x-coordinate of each group of control points, and Y0, Y1, and Y2 are respectively the y-coordinates of the control points of the center line and the two profile lines, X = [x1, …, x i ,…,x m ]i =(m-i)x1 / (m-1)+(i-1)L0 / 2(m-1), Y0 is the distance of the middle line control point from the x axis, Y1 and Y2 are the distances of the two profile line control points from the x axis respectively;

[0029] The upper index represents the curve controlled by the control point, and the lower index represents the control point grouping;

[0030] In order to ensure the connection between the whole chiral unit structures, let

[0031] The distance of the control points of the two profile lines along the y axis is Y0, and according to the geometric relationship, The relationship between the two profile line control points Y1 and Y2 and the middle line Y0 can be obtained as:

[0032]

[0033] That is, the shape of the ligament can be controlled by changing the values of Y0 and The control parameters Y1 and Y2 of the two profile lines of the ligament are given.

[0034] In another aspect, the application also provides a honeycomb structure composed of the chiral negative Poisson's ratio unit structure with variable ligament thickness, wherein each unit structure is connected with N surrounding unit structures, and the outer end surface of the i-th ligament of the unit structure is connected with the outer end surface of one ligament of the i-th unit structure, i=1, 2, …, N.

[0035] The beneficial effects of the present application include but are not limited to:

[0036] The chiral negative Poisson's ratio unit structure with variable ligament thickness and the honeycomb structure provided by the application are composed of a central body and N ligaments arranged in a circumferential array around the central body, the profile line of the ligament is a NURBS curve, the use of the curve to construct the boundary makes the ligament have the characteristics of curved configuration and variable thickness, the structure form of the ligament can be flexibly regulated, the structure layout of the chiral negative Poisson's ratio structure is more flexible, the mechanical properties such as structural strength can be flexibly adjusted according to different application scenarios, and the demand for complexification and customization of the mechanical properties of the chiral negative Poisson's ratio structure in actual engineering can be met. BRIEF DESCRIPTION OF DRAWINGS

[0037] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application, the illustrative embodiments of the present application and the description thereof are used to explain the present application, and do not constitute improper limitation on the present application. In the drawings:

[0038] Figure 1 ​A schematic view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application;

[0039] Figure 2 A perspective view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application; Figure 1

[0040] A perspective view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application; Figure 3

[0041] A perspective view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application; Figure 4

[0042] A schematic view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application; Figure 5

[0043] A schematic view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application; Figure 6 A schematic view of the chiral negative Poisson's ratio cellular structure with variable ligament thickness provided by the present application;

[0044] In the figure, 100, the center body; 200, the ligament. DETAILED DESCRIPTION

[0045] To make the technical features of the present application clear, the present application will be described in detail below with specific embodiments and in conjunction with the accompanying drawings.

[0046] It should be noted that in the following description, many specific details are set forth in order to provide a thorough understanding of the present application, however, the present application can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present application is not limited by the specific embodiments disclosed below.

[0047] Figure 1 As shown in the present application, the chiral negative Poisson's ratio cellular structure with variable ligament thickness, including a center body 100 and N ligaments 200 distributed in a circumferential array around the center body, N≥3. Figure 2 Each ligament has a first side and a second side parallel to the central axis of the center body, the profile lines of the first side and the second side are constructed by NURBS curves, the distance between the first side and the second side is set as the ligament thickness d, and the extension length of the first side and the second side is the ligament length.

[0048] The cellular structure has a chiral feature.

[0049] Further, the present application provides a cellular structure composed of the cellular structure, each cellular structure is connected with the surrounding N cellular structures, the outer end surface of the i-th ligament of the cellular structure is connected with the outer end surface of one ligament of the i-th cellular structure, i=1, 2, …, N.

[0050]

[0051] ​​Wherein, the NURBS curve is the abbreviation of Non-Uniform Rational B-Spline Curve, used for describing and generating smooth curve or surface, and the method makes the shape of the curve can be freely changed by adjusting the position and weight of the control vertex.

[0052] The traditional structure is mainly subjected to pressure in the deformation process, and the chiral feature of the honeycomb structure provided by the application makes the core rotate in the deformation process, converts the pressure into the bending moment at the ligament, and simultaneously, the whole structure appears the negative Poisson's ratio phenomenon due to the rotation of the structure.

[0053] As shown in Figure 3 The shape of the NURBS curve is controlled by 1. order p, 2. control point sequence {B i}, 3. node vector Ξ = {ξ1, ξ2, ξ3, ξ4, ξ5, ξ6, ξ7, ξ8}, 4. control point weight sequence {ω i}. The curve is composed of B-spline curve as the base function, when the order p = 0, the base function of the B-spline function is represented as:

[0054]

[0055] The high-order base function can be represented by the low-order base function (1), and the representation method is:

[0056]

[0057] Wherein p = 1, 2, 3, …. The weight sequence {ω i} is introduced into the B-spline function,

[0058]

[0059] At this time, the base function of the NURBS curve is obtained as:

[0060]

[0061] The expression of the NURBS curve is:

[0062]

[0063] In the application, the order p of the NURBS curve selected is 2, the node vector is Ξ = {0 0 0 0.3 0.6 1 1 1}, and the control point weight sequence is ω = {1 1 1 1 1}.

[0064] The construction method of the single cell structure, the honeycomb structure and the ligament provided by the present application will be described in detail below through specific examples.

[0065] Example 1

[0066] As shown in Figure 1 , Figure 2 and Figure 4 , the single cell structure provided by the present embodiment is composed of a middle body with a square cross section and four ligaments arranged in a circumferential array around the middle body, the profile lines of the two sides of the ligament are NURBS curves, and the thickness of the ligament is variable.

[0067] Specifically, the construction method of the single cell structure provided by the present embodiment is as follows:

[0068] The size of the single cell structure is L0, the size of the middle body is 2x1, and the control point coordinates (X, Y0, Y1, Y2) of the three NURBS curves C0, C1 and C2 are the design points.

[0069] The control points of the three NURBS curves C0, C1 and C2 are divided into five groups, which are evenly distributed along the length of the ligament from x1 to L0 / 2, and the x-direction coordinates of the five groups of control points are X = [x1, L0 / 8+3x1 / 4, L0 / 4+x1 / 2, 3L0 / 8+x1 / 4, L0 / 2]. Each group of control points has three, which are the control points of the center line and the two profile lines.

[0070] is the distance of the center line control point from the x-axis, the upper subscript represents the curve controlled by the control point, and the lower subscript represents the grouping of the control point. In order to ensure the connection between the whole chiral structure, let

[0071] is the distance between the left and right control points, and from the geometric relationship the relationship between the profile line control point and the center line Y0 can be obtained as:

[0072]

[0073] That is, by Y0 and the control parameters Y1 and Y2 of the profile line of the ligament of the chiral structure can be given. Thus, by changing the value of , the shape of the ligament can be controlled.

[0074] The expressions of the three curves are

[0075] C0(t) = R p (t)B0

[0076] C1(t) = R p(t)B1

[0077] C2(t)=R p (t)B2

[0078] in, B0 = [X Y0], B1 = [X Y1], and B2 = [X Y2] are the coordinates of the control points of the three curves.

[0079] In summary, given the order p = 2, the coordinates of the control points B0 = [X Y0], B1 = [X Y1], B2 = [X Y2], the node vector Ξ = {0 0 0 0.3 0.6 1 1 1}, and the control point weight sequence ω = {1 1 1 1 1}, the coordinates of the centerline and the contour line can be written.

[0080] Example 2:

[0081] like Figure 5 As shown, the honeycomb structure provided by the present invention is obtained by arranging the illustrated four-ligament unit cell structure in a 6×8 array.

[0082] Furthermore, this invention employs a computational averaging method to obtain the mechanical properties of the structure. Specifically, it introduces the micro-polar elasticity theory of independent rotational motion, where the generalized strain on the two-dimensional plane can be expressed by the displacement gradient, micro-rotational gradient, and micro-rotational gradient as follows:

[0083]

[0084] In the formula ε ij For the asymmetric strain tensor, κ i Let φ be the curvature tensor, φ be the infinitesimal rotation, and e be the constant. 3ij Let be the Levi-Civita arrangement symbol constrained on a two-dimensional plane. Using the Voigt form, the above equation can be expressed as:

[0085]

[0086] The corresponding generalized stress is

[0087] σ={σ 11 ,σ 22 ,σ 12 ,σ 21 ,m1,m2} T (8)

[0088] Where σ ij and m i These are the stress tensor and the couple stress tensor, respectively.

[0089] The strain energy density can be expressed as:

[0090]

[0091] In the formula For the fourth-order elastic tensor related to the axial loading method, For the third-order semi-polar tensor related to axial bending coupling, K is the second-order elastic tensor related to the bending mode. g and d g These are the stiffness matrix and the displacement vector, respectively.

[0092] Constitutive relations can be expressed by C. ijkl B ijk and D ij The 6×6 stiffness matrix Q represents:

[0093]

[0094] For K g and d g We can obtain the components of Q by correlating Eq.(9), and the effective Young's modulus E and Poisson's ratio v of the chiral structure are expressed by the following formula:

[0095] E = 1 / Q -1 (1,1),v=-Q -1 (1,2) / Q -1 (1,1) (11)

[0096] like Figure 6 As shown in (a)-(f), 2×2 honeycomb structures composed of different forms of unit cell structures are presented. The dimensional parameters of each structure are labeled above the schematic diagram, and the mechanical properties [E,v] (Young's modulus (MPa), Poisson's ratio) are labeled below the schematic diagram. It can be seen that the honeycomb structure provided by this invention has a negative Poisson's ratio characteristic, and the ligament configuration with curved shape is varied, allowing for a wide range of designs.

[0097] The above specific embodiments should not be construed as limiting the scope of protection of this invention. For those skilled in the art, any alternative improvements or modifications made to the embodiments of this invention shall fall within the scope of protection of this invention.

[0098] Any aspects of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A chiral negative Poisson's ratio unit cell structure with variable ligament thickness, characterized in that, It includes a central body and N ligaments distributed in a circular array around the central body, where N≥3 and N is an integer; Each ligament has a first side and a second side parallel to the central axis of the centrosome. The outlines of the first side and the second side are constructed by NURBS curves. The distance between the first side and the second side is defined as the ligament thickness, and the length of the first side and the second side extending away from the centrosome is defined as the ligament length. The single-cell structure exhibits chiral characteristics; The method for constructing ligaments includes the following steps: Let C1 and C2 be the contour lines of the first and second lateral sides of the ligament, respectively. The expressions for the two NURBS curves, C1 and C2, are as follows: in , These are the coordinates of the control points for NURBS curves C1 and C2, respectively. ,in, in, N i,p ( t ) represents the basis functions of the NURBS curve, derived from the node vectors. control, p Let { be the order of the curve, { } represents the sequence of control point weights; Based on the control point coordinates, order p, and node vectors Control point weight sequence { The coordinates of the two contour lines are calculated, thus completing the ligament construction. The method for constructing ligaments also includes the following specific steps: Let C0 be the midline of the ligament, the size of the unit cell be L0, the size of the centrosome be 2x1, and the centrosome be a regular polygon; Establish an xoy rectangular coordinate system with the center of the centrosome as the origin, the length direction of the ligament as the x-axis, and the thickness direction of the ligament as the y-axis; There are m sets of control points for the three NURBS curves C0, C1, and C2. The m sets of control points are evenly distributed along the ligament length from x1 to L0 / 2. Each set of control points has 3 points, namely the control points for the midline and the two contour lines. The shape of the ligament is controlled by determining the coordinates (X, Y0, Y1, Y2) of the control points of three curves C0, C1, and C2. X represents the x-coordinate of each group of control points. ,in x i =( m - i ) x 1 / ( m -1)+( i -1) L 0 / 2( m -1), Y0 is the distance from the centerline control point to the x-axis, and Y1 and Y2 are the distances from the control points of the two contour lines to the x-axis, respectively; , , Superscripts represent curves controlled by control points, and subscripts represent control point groups; To ensure the overall connectivity between chiral unit cell structures, ; Let be the distance between the control points of the two contour lines along the y-axis, which can be known from geometric relationships. This allows us to obtain two contour control points Y1 and Y2 and the centerline. The relationship between them is as follows: That is, through and The control parameters for the two contour lines of the ligament are given. and ,Change The value can control the shape of the ligament.

2. The chiral negative Poisson's ratio unit cell structure with variable ligament thickness according to claim 1, characterized in that, 3≤N≤6。 3. A honeycomb structure, characterized in that, It is composed of multiple unit cell structures as described in any one of claims 1-2, each unit cell structure being connected to N surrounding unit cell structures, and the outer end face of the i-th ligament of the unit cell structure being connected to the outer end face of one of the ligaments of the adjacent i-th unit cell structure, i=1,2,…,N.

Images