Two-stage fractal improved star-shaped negative Poisson's ratio honeycomb structure

Abstract

The utility model relates to the technical field of mechanical superstructures, in particular to a two-stage fractal improved star-shaped negative Poisson's ratio honeycomb structure which comprises a plurality of improved star-shaped negative Poisson's ratio honeycomb unit cells in a two-dimensional array. Each unit cell comprises a first-stage unit and a second-stage unit, and the first-stage unit is located outside the second-stage unit and serves as a basic framework of the unit cell; the second-stage unit is nested in the center position of the first-stage unit, and the shape of the second-stage unit is similar to that of the first-stage unit; the second-stage unit is installed at the central position of the first-stage unit after rotating by 45 degrees relative to the first-stage unit, and the outer wall of the second-stage unit is connected with the inner wall of the first-stage unit to form a central symmetry structure. According to the utility model, through the unique two-stage fractal design and the concave bending structure, the interaction between cell walls is more reasonable; according to the super structure, integration of the negative Poisson's ratio, the band gap characteristic, energy absorption and bearing capacity is achieved, the shock resistance of the metamaterial can be improved, and the good negative Poisson's ratio characteristic can be maintained.

Description

Technical Field

[0001] This utility model relates to the field of mechanical superstructure technology, specifically a two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure. Background Technology

[0002] Superstructures are a class of advanced composite structural systems that achieve properties absent in nature through artificial topological design. Their anomalous physical properties stem from the precise control of microscopic configuration rather than the intrinsic properties of the constituent materials. As an important branch of metamaterials, negative Poisson's ratio superstructures break through the limitations of the Poisson effect in the transverse expansion of traditional materials under compressive loads, exhibiting a reverse mechanical response of transverse contraction under axial compression. This characteristic brings innovative applications to numerous fields.

[0003] Negative Poisson's ratio structures demonstrate multi-dimensional application value in aerospace, biomedicine, intelligent sensing, and defense and transportation fields. Currently, common negative Poisson's ratio structures include concave polygonal negative Poisson's ratio structures, star-shaped negative Poisson's ratio structures, hand-shaped negative Poisson's ratio structures, rotated polygonal negative Poisson's ratio structures, and double-arrow structures. Among these, the star-shaped negative Poisson's ratio structure is the most widely studied due to its adaptability to parameter adjustments and its broad application range. However, traditional single star-shaped structures have a short stress plateau region, prematurely entering the densification stage, and poor deformation stability, resulting in unsatisfactory performance in compressive strength and energy absorption efficiency.

[0004] In recent years, the rapid development of 3D printing and additive manufacturing technologies has enabled the creation of various structures with more complex topological configurations. This has further promoted in-depth research by scholars on the deformation mechanisms of various negative Poisson's ratio materials.

[0005] The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure disclosed in this utility model has advantages such as negative Poisson's ratio, adjustable design, energy absorption and load-bearing capacity, which makes up for the lack of basic research on traditional star-shaped honeycomb and research on changing structural parameters in most studies. Utility Model Content

[0006] This invention aims to propose a two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure, which is an innovative design based on the classic star-shaped negative Poisson's ratio honeycomb. By breaking off the traditional protruding sharp corners and folding them inward to form concave corners, the structure retains the negative Poisson's ratio characteristics while achieving superior mechanical properties, including enhanced overall load-bearing capacity and improved energy absorption capacity, thus overcoming the shortcomings of traditional star-shaped structures in the prior art.

[0007] To achieve the above objectives, this utility model provides the following technical solution: a two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure, comprising multiple improved star-shaped negative Poisson's ratio honeycomb unit cells arranged in a two-dimensional array;

[0008] A unit cell consists of primary units and secondary units. Primary units are located outside secondary units, forming the basic framework of the unit cell; secondary units are nested in the center of primary units, and the shape of the secondary units is similar to that of the primary units; secondary units are assembled into the center of primary units after scaling and angular adjustment, and the outer wall of the secondary units coincides with the boundary of the primary units, forming a composite structure with internal and external coordination.

[0009] Furthermore, the primary unit is composed of four quarter-cell circular arrays. A single quarter-cell contains: a horizontal cell wall, a vertical cell wall, and four inclined cell walls;

[0010] The horizontal cell wall is straight and arranged horizontally;

[0011] The vertical cell wall is perpendicular to the horizontal cell wall, forming a straight line, and is arranged vertically;

[0012] Four inclined cell walls connect the horizontal cell wall and the vertical cell wall, forming an inwardly concave bending structure; the inclined cell walls are set at an angle, and the inclined cell walls contract inward when subjected to force.

[0013] Four quarter-cell circular arrays form a symmetrical four-cornered star structure, and the star structure has four concave bending structures.

[0014] Furthermore, the secondary unit is rotated 45° and merged into the primary unit, and the horizontal and vertical cell walls of the secondary unit are connected to the four concave bending structures of the primary unit.

[0015] Furthermore, the four inclined cell walls are respectively the first inclined supporting cell wall, the second inclined supporting cell wall, the third inclined supporting cell wall, and the fourth inclined supporting cell wall;

[0016] The horizontal cell wall, the first inclined supporting cell wall, the third inclined supporting cell wall, the fourth inclined supporting cell wall, the second inclined supporting cell wall, and the vertical cell wall are connected in sequence;

[0017] The lengths of the horizontal and vertical cell walls are L, the lengths of the first and second inclined supporting cell walls are L1, the lengths of the third and fourth inclined supporting cell walls are L2, the angle between the third and fourth inclined supporting cell walls is θ1, the angle between the horizontal cell wall and the first inclined supporting cell wall is θ2, and the angle between the first and third inclined supporting cell walls is θ3; θ2+θ3=2π−θ1.

[0018] Furthermore, the wall thickness of the first-order unit of the improved star-shaped negative Poisson's ratio honeycomb cell is t, the wall thickness of the second-order unit is t', and t'=βt, where 0<β<1.

[0019] Furthermore, the cross-section of the cell wall of all individual cells in the improved star-shaped negative Poisson's ratio honeycomb structure is rectangular.

[0020] Furthermore, the height and width of the first-level unit are both A, and the height and width of the second-level unit are both A'; where A = αA', and 0.37 < α < 0.77.

[0021] Furthermore, the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure is manufactured by 3D printing.

[0022] Beneficial effects

[0023] This novel two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure, through its unique two-level fractal design and concave bending structure, makes the interaction between cell walls more rational. This enhances the overall load-bearing capacity and energy absorption capacity of the structure. Under load, the interaction between the cell walls of the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure causes the vertical cell walls on both sides to bend and bear the main pressure, while the inclined supporting cell walls contract inwards, adhering to each other and sharing some of the energy. The overall structure contracts inwards, thus achieving the negative Poisson's ratio effect. Changes in the geometric parameters of this structure have a significant impact on its overall mechanical properties.

[0024] During quasi-static compression, the structure exhibits a relatively long stress plateau period. During this phase, the structure can continuously absorb energy, effectively increasing energy absorption efficiency. Compared to traditional star-shaped structures, the structure of this invention demonstrates superior energy absorption performance and can better meet application requirements in fields such as impact protection.

[0025] The mechanical properties of a structure can be achieved by adjusting its geometric parameters. By changing parameters such as the angle between cell walls, cell wall length, and wall thickness, the performance of the structure can be flexibly adjusted to suit different engineering applications, thus improving the structure's versatility and adaptability. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this utility model. For those skilled in the art, other drawings can be obtained based on these drawings.

[0027] Figure 1 This is a schematic diagram of the overall structure of the honeycomb structure disclosed in this utility model;

[0028] Figure 2 This is a plan view of a single cell of the honeycomb structure disclosed in this utility model;

[0029] Figure 3 This is a schematic diagram of the single cell structure of the honeycomb structure disclosed in this utility model;

[0030] Figure 4 This is a cloud diagram of the deformation process of the honeycomb structure disclosed in this utility model under the action of a gradually increasing quasi-static compressive load;

[0031] Figure 5 This is a stress-strain curve diagram of the honeycomb structure disclosed in this utility model;

[0032] Figure 6 This is the Poisson's ratio strain curve of the honeycomb structure disclosed in this utility model.

[0033] In the picture:

[0034] 1. Horizontal cell wall; 2. Vertical cell wall; 3. First inclined supporting cell wall; 4. Second inclined supporting cell wall; 5. Third inclined supporting cell wall; 6. Fourth inclined supporting cell wall. Detailed Implementation

[0035] The technical solutions of the present utility model will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present utility model, and not all embodiments. Based on the embodiments of the present utility model, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present utility model.

[0036] To achieve the above objectives, this utility model provides the following technical solution, such as... Figure 1-6 As shown,

[0037] Example 1;

[0038] A two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure includes multiple improved star-shaped negative Poisson's ratio honeycomb unit cells arranged in a two-dimensional array;

[0039] The unit cell consists of primary and secondary units. Primary units are located outside the secondary units, forming the basic framework of the unit cell; secondary units are nested at the center of the primary units, with their outer walls connected to the inner walls of the primary units. The shapes of the secondary units are similar to those of the primary units; the outer walls of the secondary units connect to the inner walls of the primary units, forming a centrally symmetrical structure. The internal secondary unit structure is assembled at the center of the primary unit by scaling down and rotating the outer structure of the primary unit by 45°. The outer walls of the secondary units coincide with the boundaries of the primary units, forming a composite structure with internal and external coordination. The hierarchical fractal improved star-shaped negative Poisson's ratio honeycomb structure unit cell has a height of LY, a width of LX, and a thickness of b.

[0040] Furthermore, the primary unit is composed of four quarter-cell circular arrays. A single quarter-cell contains: a horizontal cell wall 1, a vertical cell wall 2, and four inclined cell walls;

[0041] Horizontal cell wall 1: It is straight and horizontally distributed. It is the basic component for the transverse support of the structure and bears the vertical pressure component.

[0042] Vertical cell wall 2: perpendicular to horizontal cell wall 1, straight, vertically distributed, and bends under pressure to resist load.

[0043] Inclined cell walls: Four inclined cell walls connect 1 to the vertical cell wall 2, forming an inwardly concave bending structure. The inclined cell walls are set at an angle, and when subjected to force, these inclined cell walls contract inward and fit together in pairs, which not only achieves the negative Poisson's ratio effect (lateral contraction), but also distributes energy, enhancing the structure's load-bearing and energy absorption capacity.

[0044] Four quarter-cell circular arrays form a symmetrical four-cornered star structure, and the star structure has four concave bending structures.

[0045] Furthermore, the secondary unit is merged into the primary unit by scaling and rotating the primary unit by a certain coefficient and then rotating it by 45°. The horizontal cell wall 1 and vertical cell wall 2 of the secondary unit are connected to the four concave bending structures of the primary unit. The secondary unit works in concert with the primary unit to improve the load-bearing capacity and energy absorption capacity of the structure while ensuring the negative Poisson's ratio characteristics.

[0046] Furthermore, the four inclined cell walls are the first inclined supporting cell wall 3, the second inclined supporting cell wall 4, the third inclined supporting cell wall 5, and the fourth inclined supporting cell wall 6, respectively.

[0047] The lengths of the horizontal cell wall 1 and the vertical cell wall 2 are L, the lengths of the first inclined support cell wall 3 and the second inclined support cell wall 4 are L1, the lengths of the third inclined support cell wall 5 and the inclined support cell wall 6 are L2, the angle between the third inclined support cell wall 5 and the fourth inclined support cell wall 6 is θ1, the angle between the horizontal cell wall 1 and the first inclined support cell wall 3 is θ2, and the angle between the first inclined support cell wall 3 and the third inclined support cell wall 5 is θ3; θ2+θ3=2π−θ1; the cell walls of the second-level units are all represented by the superscript '. These dimensions and angle parameters together determine the shape and mechanical properties of the structure.

[0048] Furthermore, the wall thickness of the first-order unit of the improved star-shaped negative Poisson's ratio honeycomb is t, and the wall thickness of the second-order unit is t', and t'=βt, where β is the wall thickness scaling factor, 0<β<1; by adjusting the wall thickness and the wall thickness scaling factor β, the mechanical properties of the structure can be optimized.

[0049] Furthermore, in the improved star-shaped negative Poisson's ratio honeycomb structure, the cross-section of the cell wall of all units is rectangular; the rectangular cross-section helps to ensure structural strength and is convenient for manufacturing and calculation.

[0050] Furthermore, the height of the first-level element is A, and the width is A', where A = αA', and α is the scaling factor for the second-level element; 0.37 < α < 0.77; this proportional relationship further defines the dimensional characteristics of the structure and affects its overall performance. A' represents the height and width of the second-level element.

[0051] Furthermore, the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure was fabricated using 3D printing.

[0052] Furthermore, the material used to prepare the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure is PLA. PLA is a renewable biodegradable material with advantages such as thermal stability, air permeability, biocompatibility and degradability.

[0053] Example 2;

[0054] To further illustrate the above structure, this embodiment provides a modeling process for the structure, as detailed below:

[0055] The unit cell is derived from the traditional four-pointed star-shaped negative Poisson's ratio honeycomb unit cell by breaking its original four sharp-cornered inclined cell walls to generate four inclined supporting cell walls.

[0056] The first step is to draw a sketch of the first-level unit 1 / 4 cell of the improved star-shaped negative Poisson's ratio honeycomb. In the sketch in CATIA software, take the origin of the coordinate system as the starting point and draw a straight line connecting the two points on the left and right to determine the horizontal cell wall 1.

[0057] The second step is to draw the first inclined side L1 with an included angle of θ2, starting from the right endpoint.

[0058] The third step is to draw another inclined side L2 with an included angle of θ3, starting from the second point of the inclined side L1, to obtain the 1 / 8 unit cell model.

[0059] The fourth step is to draw an angle bisector at 45° in the first quadrant of the coordinate system, starting from the origin. Then, mirror the edges drawn in the first three steps around the 45° bisector to obtain a 1 / 4 unit cell model.

[0060] The fifth step is to rotate the obtained 1 / 4 unit cell model 90° clockwise three times to obtain the improved star-shaped negative Poisson's ratio honeycomb unit cell sketch.

[0061] Step 6: Thin-wall stretching to thickness b yields an improved star-shaped negative Poisson's ratio honeycomb unit cell.

[0062] Example 3;

[0063] In the preprocessing module of the ABAQUS finite element software, the material parameters of the structure are first set, the S4R shell element mesh is used to divide the finite element mesh of the structure, the analysis step, boundary conditions and load conditions are set, and the contact properties are set, so as to perform out-of-plane quasi-static compression simulation of the structure.

[0064] Material parameters were set in the ABAQUS finite element simulation software. PLA was selected as the research object, with an elastic modulus E = 2800 MPa, a Poisson's ratio μ = 0.35, and a yield stress σ = 41 MPa.

[0065] according to Figure 4 As shown, this embodiment provides a deformation contour map of a two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure under quasi-static compressive load. From Figure 4 As can be seen, with the continuous increase of load (the amount of downward compression from 0 mm to 8.2 mm to 20 mm to 47 mm to 80 mm to 110 mm and finally to 160 mm), at a strain ε = 3.5%, the structure compresses downwards, and the two side vertical cell walls 2 and the middle improved star structure contract inwards, exhibiting negative Poisson's ratio performance. With the increase of strain, both the outer vertical cell walls 2 and the middle star structure contract. When the strain ε = 5%, the structure further compresses and reaches the stress plateau. When the strain reaches ε = 73%, the structure further contracts and contacts, exhibiting a more obvious densification.

[0066] according to Figure 5-6 As shown in the figure, this embodiment provides the stress-strain curves and Poisson's ratio-strain curves of a two-stage fractal improved star-shaped negative Poisson's ratio honeycomb structure under quasi-static compressive loading. As can be seen from the figure, the stress-strain curves of the two-stage fractal improved star-shaped negative Poisson's ratio honeycomb structure exhibit a typical three-stage evolution. First, at relatively small strains, the stress increases linearly with strain; this region is called the linear elastic region, during which the structure does not undergo plastic deformation until the peak stress is reached. Subsequently, it enters a relatively long plateau region. When the strain is approximately ε = 73%, the stress rises rapidly, reaching the densification region. The two-stage fractal improved star-shaped negative Poisson's ratio honeycomb structure has a long stress plateau period, which can effectively increase the energy absorption of the structure.

[0067] Two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure: The mechanical properties of the improved star-shaped negative Poisson's ratio honeycomb structure under quasi-static compressive load can be determined by adjusting the geometric parameters of the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure, such as the included angles θ1, θ2, and θ3 between each cell wall.

[0068] The working principle and process are as follows:

[0069] The principle of negative Poisson's ratio effect: The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure of this invention exhibits a lateral contraction negative Poisson's ratio effect when subjected to axial compressive load. This principle is based on the structure's unique geometric configuration. When the structure is under pressure, the inclined support cell walls in the quarter-cell will contract inward. Since the inclined support cell walls are connected to the horizontal cell wall 1 and the vertical cell wall 2, this contraction will cause corresponding deformation of the horizontal cell wall 1 and the vertical cell wall 2, resulting in a reduction in the lateral dimension of the entire structure. For example, in the simulation of Example 3, when the strain reaches 3.5%, the structure compresses downward, and the vertical cell walls 2 on both sides and the improved star-shaped structure in the middle contract inward, visually demonstrating the negative Poisson's ratio effect. This effect stems from the design of the structure, which breaks off the sharp corners of the traditional star-shaped structure and folds them inward to form concave corners, changing the deformation mode of the structure under stress, allowing the structure to produce lateral deformation opposite to that of traditional materials under pressure.

[0070] Load-bearing and energy absorption principle: In terms of load-bearing, the structure mainly relies on the cell walls to withstand external loads. When subjected to pressure, the two sides will bend and deform, bearing the main pressure. This is because the vertical cell wall 2 is in a critical position for axial force in the structure, and its material properties and structural design enable it to withstand greater pressure without excessive deformation or failure. At the same time, the inclined supporting cell walls will contract inward when the structure is under stress, and the two sides will stick together to share some of the energy. During the deformation process of the structure, the contraction and interaction of the inclined supporting cell walls will consume energy, and the connection between them and the horizontal cell wall 1 and the vertical cell wall 2 allows energy to be transferred and dispersed throughout the structure. As can be seen from the stress-strain curve of Example 3, the structure has a long stress plateau period, which means that the structure can continuously absorb energy during this stage, effectively enhancing the load-bearing capacity and energy absorption capacity of the structure. This load-bearing and energy absorption mechanism is achieved through the synergistic effect of the cell walls in the structure. The two-level fractal design further optimizes this synergistic effect and improves the mechanical performance of the structure.

[0071] The embodiments of this utility model are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the utility model to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical applications of this utility model, and to enable those skilled in the art to understand this utility model and design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure, characterized in that, It includes multiple improved star-shaped negative Poisson's ratio honeycomb units arranged in a two-dimensional array; A unit cell consists of primary units and secondary units. Primary units are located outside secondary units and serve as the basic framework of the unit cell. Secondary units are nested in the center of primary units, and the shapes of secondary units are similar to those of primary units. The secondary unit is rotated 45° relative to the primary unit and then installed at the center of the primary unit. The outer wall of the secondary unit is connected to the inner wall of the primary unit, forming a centrally symmetrical structure.

2. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The primary unit is composed of four quarter-cell circular arrays; a single quarter-cell includes a horizontal cell wall (1), a vertical cell wall (2) and four inclined cell walls; Horizontal cell walls (1) are arranged horizontally; vertical cell walls (2) are arranged vertically. Four inclined cell walls connect the horizontal cell wall (1) and the vertical cell wall (2) to form an inwardly concave bending structure; the inclined cell walls are set at an incline, and the inclined cell walls contract inward when subjected to force; Four quarter-cell circular arrays form a symmetrical four-cornered star structure, and the star structure has four concave bending structures.

3. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 2, characterized in that, After rotating 45°, the secondary unit merges into the primary unit, and the horizontal cell wall (1) and vertical cell wall (2) of the secondary unit are connected to the four concave bending structures of the primary unit.

4. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 2, characterized in that, The four inclined cell walls are the first inclined supporting cell wall (3), the second inclined supporting cell wall (4), the third inclined supporting cell wall (5), and the fourth inclined supporting cell wall (6); The horizontal cell wall (1), the first inclined supporting cell wall (3), the third inclined supporting cell wall (5), the fourth inclined supporting cell wall (6), the second inclined supporting cell wall (4), and the vertical cell wall (2) are connected in sequence; The lengths of the horizontal cell wall (1) and the vertical cell wall (2) are L, the lengths of the first inclined support cell wall (3) and the second inclined support cell wall (4) are L1, the lengths of the third inclined support cell wall (5) and the inclined support cell wall (6) are L2, the angle between the third inclined support cell wall (5) and the fourth inclined support cell wall (6) is θ1, the angle between the horizontal cell wall (1) and the first inclined support cell wall (3) is θ2, and the angle between the first inclined support cell wall (3) and the third inclined support cell wall (5) is θ3; θ2+θ3=2π−θ1.

5. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The wall thickness of the first-level element is t, and the wall thickness of the second-level element is t', and t'=βt, where 0<β<1.

6. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The cross-section of the cell wall of all units in the improved star-shaped negative Poisson's ratio honeycomb structure is rectangular.

7. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The height and width of the first-level unit are both A, and the height and width of the second-level unit are both A'; where A = αA', and 0.37 < α < 0.

77.

8. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure is made by 3D printing.

9. The two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure according to claim 1, characterized in that, The material used to prepare the two-level fractal improved star-shaped negative Poisson's ratio honeycomb structure is PLA.

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