A negative Poisson's ratio honeycomb structure based on Bezier curve with variable thickness

Abstract

The present invention relates to the technical field of mechanical metamaterials, and discloses a negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve. The structure is formed by a single cell of a concave triangular honeycomb structure through several horizontal and vertical arrays. The single cell is formed by two symmetrically arranged first straight wall beams and two second straight wall beams connected end to end. There is a first straight wall beam and a second straight wall beam on each side of the symmetry axis, and the first straight wall beam and the second straight wall beam are connected at an acute angle. The thickness of each straight wall beam varies along the length of the straight wall beam, and the thickness distribution trend is defined by a Bezier curve. The overall trend of the straight wall beam thickness is thicker in the middle and thinner on both sides compared to a uniform thickness distribution. The present invention can improve the design freedom and energy absorption capacity of the honeycomb structure.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical metamaterials, and in particular to a negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve. Background Art

[0002] Negative Poisson's ratio honeycomb structures are a key branch of mechanical metamaterials. Compared to positive Poisson's ratio materials, they exhibit the unique mechanical property of expanding (contracting) laterally under longitudinal tension (compression). Due to their excellent surface isotropic properties, shear resistance, and energy absorption and vibration isolation capabilities, they have long been a research focus and are widely used in aerospace, automotive, and other fields.

[0003] Regarding the design strategies for negative Poisson's ratio honeycomb structures, there are macroscopic hybrid design strategies, which combine different types of unit cells. At the microscopic scale, there are hierarchical and gradient designs. Hierarchical design strategies embed smaller unit cells within larger ones. Gradient design strategies link several unit cells with gradient geometric parameters. These strategies increase the design freedom of negative Poisson's ratio honeycomb structures and can achieve mechanical properties distinct from those of traditional honeycombs.

[0004] In the existing research on gradient design of negative Poisson's ratio structures, the external configuration of the three-dimensional gradient negative Poisson's ratio honeycomb skeleton structure in the published patent number CN117366451A is a truncated cone tube structure, and its preparation method and use. The truncated cone tube structure includes a number of curved concave hexagonal cells arranged with a gradient around the central axis of the truncated cone tube structure and along the direction of the truncated cone busbar. The gradient can first be achieved by relying on the inherent characteristics of the inclined wall of the truncated cone tube structure, and can be further controlled by adjusting the internal cell parameters. Compared with other three-dimensional circular tube negative Poisson's ratio structures with uniform and perfectly symmetrical structures, this design provides a linearly variable expansion deformation mode in the gradient negative Poisson's ratio circular tube, which can be used in non-uniform external environments or special locations, and has a wider range of application scenarios.

[0005] Previous designs of gradient honeycombs mainly used single cells or single-layer cells as the minimum design unit. In this case, due to the limitation of the design unit size, the energy absorption potential of the negative Poisson's ratio honeycomb structure cannot be fully utilized. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the present invention provides a negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve, which improves the design freedom and energy absorption capacity of the honeycomb structure.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve includes cells, each of which is a concave triangular structure. The cells are arranged in a horizontal and vertical array to form a honeycomb structure. The cells are symmetrical and include straight-wall beams, which include a first straight-wall beam and a second straight-wall beam. The first straight-wall beam and the second straight-wall beam are respectively provided on both sides of the symmetry axis of the cell, and the first straight-wall beam and the second straight-wall beam are connected at an acute angle. The thickness of the straight-wall beam varies along the length of the straight-wall beam, and the thickness distribution is defined by the Bezier curve. The overall trend of the thickness of the straight-wall beam is thicker in the middle and thinner on both sides compared with a more uniform thickness distribution.

[0009] Furthermore, the length of the first straight wall beam is greater than the length of the second straight wall beam.

[0010] Furthermore, the first straight wall beam on one side of the symmetry axis forms an acute angle with the symmetry axis. The angle between the second straight wall beam and the symmetry axis is an acute angle Preferably, .

[0011] Furthermore, the Bezier curve is a fourth-order Bezier curve, which is a fourth-order polynomial controlled by five control points.

[0012] Furthermore, the expression of the quartic polynomial is: ;

[0013] in, is the function expression of the Bezier curve, is the first control point, is the second control point, is the third control point, is the fourth control point, is the fifth control point, is the control parameter of the Bezier curve.

[0014] Furthermore, the thickness of the straight-walled beam has a one-to-one correspondence with the function value of the Bezier curve, that is, the thickness of the straight-walled beam is equal to the function value of the Bezier curve at the same position plus the initial thickness value, which can be expressed as: ;in, is the thickness distribution expression of the straight beam, is the initial thickness value, is the function expression of the Bezier curve, is the control parameter of the Bezier curve.

[0015] Furthermore, the coordinates of the first control point are , the coordinates of the second control are , the coordinates of the third control point are , the coordinates of the fourth control point are , the coordinates of the fifth control point are ;in, is the length of the straight wall beam, is the ordinate of the second control point, is the ordinate of the third control point, is the vertical coordinate of the fourth control point.

[0016] Furthermore, in order to ensure the stability of the connection between the first straight wall beam and the second straight wall beam, the line connecting the first control point and the fifth control point is a horizontal line.

[0017] Furthermore, The value of is positively correlated with the thickness of the straight-wall beam at the second control point. The smaller the value, the thinner the thickness of the straight-wall beam at the corresponding part. The value of is positively correlated with the thickness of the straight wall beam at the third control point. The larger the value, the thicker the straight wall beam thickness of the corresponding part. The value of is positively correlated with the thickness of the straight-wall beam at the fourth control point. The smaller the value, the thinner the thickness of the straight-wall beam in the corresponding part.

[0018] Furthermore, the initial thickness value , .

[0019] Furthermore, for the first straight wall beam, ; For the second straight wall beam, ; , , .

[0020] The negative Poisson's ratio honeycomb with variable straight wall beam thickness based on Bezier curve proposed in the present invention will produce more plastic hinges when subjected to axial compression, greatly improving the energy absorption characteristics of the structure. The straight wall beams with variable thickness broaden the freedom of structural geometric design.

[0021] Compared with the prior art, the present invention provides a negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve, which has the following beneficial effects:

[0022] (1) The present invention improves the gradient design strategy of negative Poisson's ratio honeycomb metamaterials, thereby increasing the design freedom and energy absorption capacity of the honeycomb structure.

[0023] (2) The Bezier curve-based variable thickness negative Poisson's ratio honeycomb structure proposed in this invention can use straight beam walls as the minimum design unit, greatly increasing the design freedom of the structure. In particular, the straight beam wall thickness design shown in this invention can generate more plastic hinges when the structure is compressed, thereby improving the energy absorption capacity of the concave triangular negative Poisson's ratio honeycomb metamaterial.

[0024] (3) The present invention proposes a variable thickness design for straight-walled beams, where the thickness distribution is defined by a Bezier curve, which can broaden the design space of mechanical metamaterial structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a schematic structural diagram of the negative Poisson's ratio honeycomb structure of the present invention. In the dotted frame in the figure, a closed structure formed by four straight-wall beams connected end to end constitutes a cell.

[0026] Figure 2 for Figure 1 Schematic diagram of the structure of a single cell;

[0027] Figure 3 Schematic diagram of the thickness design of the straight-wall beam based on the Bezier curve in the present invention;

[0028] Figure 4 This is a comparison diagram of the deformation modes of the negative Poisson's ratio structure of the present invention and the existing uniform straight wall beam thickness of the same mass, where Figure 4 4a in the figure is a schematic diagram of the deformation process of the existing negative Poisson's ratio structure with uniform straight wall beam thickness. Figure 4 4b is a schematic diagram of the deformation process of the negative Poisson's ratio honeycomb structure with variable thickness based on the Bezier curve of the present invention;

[0029] Figure 5 This is a comparison diagram of the energy absorption of the negative Poisson's ratio structure of the present invention and the traditional uniform straight-wall beam of the same mass. Among them, model 1 is the energy absorption curve of the negative Poisson's ratio structure of the existing uniform straight-wall beam, and model 2 is the energy absorption curve of the negative Poisson's ratio honeycomb structure of the present invention.

[0030] The meanings of the reference numerals in the figures are:

[0031] 1. Cell; 2. First straight-wall beam; 3. Second straight-wall beam; 4. First control point; 5. Second control point; 6. Third control point; 7. Fourth control point; 8. Fifth control point; 9. Negative Poisson's ratio honeycomb metamaterial with uniform straight-wall beam thickness; 10. Negative Poisson's ratio honeycomb metamaterial with variable thickness based on Bezier curve; 11. Plastic hinge. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0033] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present invention. Meanwhile, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to actual proportional relationships. Technology, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be considered as a part of the specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may also include different values. It should be noted that similar numbers and letters represent similar items in the following drawings, and therefore, once an item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0034] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the protection content of the present invention.

[0035] like Figure 1 As shown, the present invention is a honeycomb metamaterial with a negative Poisson's ratio and variable thickness based on a Bezier curve, which is characterized by being obtained by a single cell 1 of a concave triangular honeycomb structure through several horizontal and vertical arrays.

[0036] like Figure 2 As shown, a single cell 1 is formed by two symmetrically arranged first straight-wall beams 2 and two second straight-wall beams 3 connected end to end. On one side of the axis of symmetry, one first straight-wall beam 2 and one second straight-wall beam 3 meet at an acute angle. The thickness of the straight-wall beams 2 varies along their length, and the thickness distribution is defined by a Bezier curve. The overall thickness trend of the straight-wall beams is relatively uniform, with thickness distribution showing a trend of thickening in the middle and thinning at the edges.

[0037] In a specific implementation of this embodiment, the length of the first straight wall beam 2 is greater than the length of a second straight wall beam 3 .

[0038] The Bezier curve uses a fourth-order Bezier curve, which is a fourth-order polynomial controlled by five control points.

[0039] Among them, the first straight wall beam 2 on one side of the symmetry axis forms an acute angle with the symmetry axis. The angle between the second straight wall beam 3 and the symmetry axis is an acute angle Preferably, .

[0040] like Figure 3 As shown, the expression of the quartic polynomial is: .

[0041] in, is the first control point, is the second control point, is the third control point, is the fourth control point, is the fifth control point, is the control parameter of the Bezier curve.

[0042] There is a one-to-one correspondence between the thickness of a straight-walled beam and the value of the Bezier curve. The thickness of a straight-walled beam at a certain location is equal to the function value of the Bezier curve at the same location plus the initial thickness value, which can be expressed as: , is the thickness distribution expression of the straight beam, is the initial thickness value.

[0043] A fourth-order polynomial controlled by five control points, the coordinates of the first control point are , the coordinates of the second control are , the coordinates of the third control point are , the coordinates of the fourth control point are , the coordinates of the fifth control point are .

[0044] in, is the length of the straight wall beam, is the ordinate of the second control point, is the ordinate of the third control point, In order to ensure the stability of the connection between the first straight wall beam 2 and the second straight wall beam 3, the line connecting the first control point and the fifth control point is a horizontal line. The value of is positively correlated with the thickness of the straight-wall beam at the second control point. The smaller the value, the thinner the thickness of the straight-wall beam in the corresponding part. The value of is positively correlated with the thickness of the straight-wall beam at the third control point. The larger the value, the thicker the straight-wall beam thickness of the corresponding part. The value of is positively correlated with the thickness of the straight-wall beam at the fourth control point. The smaller the value, the smaller the thickness of the straight-wall beam in the corresponding part.

[0045] In a specific implementation of this embodiment, , , for the first straight wall beam 2, ; For the second straight wall beam 3, , , , .

[0046] like Figure 4 As shown, a negative Poisson's ratio honeycomb metamaterial 9 of uniform thickness and a negative Poisson's ratio honeycomb metamaterial 10 of variable thickness based on a Bezier curve of equal mass were subjected to quasi-static compression. The deformation patterns show that when compressed, both structures contract toward the center, indicating that the Poisson's ratio of the indented triangular honeycomb metamaterial is negative. When the negative Poisson's ratio honeycomb metamaterial 9 of uniform thickness is compressed, the bottom of the structure deforms first, and the first straight-walled beam 2 is squeezed in the middle, generating a plastic hinge 11. When the negative Poisson's ratio honeycomb metamaterial 10 of variable thickness based on a Bezier curve is compressed, the bottom deforms first, and the contraction trend in the middle is more pronounced, indicating that the negative Poisson's ratio effect of this structure is more advantageous. Unlike the negative Poisson's ratio honeycomb metamaterial 9 of uniform thickness, the first straight-walled beam 2 of the present invention, when squeezed, generates two plastic hinges 11 on both sides of the first straight-walled beam 2. Figure 4 The middle circle indicates the location of the plastic hinge 11. Figure 4 4b plastic hinge 11 Figure 4 There are more plastic hinges 11 in 4a. Producing more plastic hinges 11 means that the structure can absorb more energy under the same mass, that is, the negative Poisson's ratio honeycomb metamaterial 10 with variable thickness based on Bezier curve of the present invention can absorb more energy.

[0047] like Figure 5 As shown, Figure 5 Model 1 is a negative Poisson's ratio honeycomb metamaterial with uniform thickness 9, and model 2 is a negative Poisson's ratio honeycomb metamaterial with variable thickness based on Bezier curve 10. Figure 5 It can be seen that, under the same mass, Model 2 has a larger peak force than Model 1. The closed area enclosed by the curve and the horizontal axis represents the amount of energy absorption. It can be seen that the Bezier curve-based variable thickness negative Poisson's ratio honeycomb metamaterial 10 of the present invention improves the energy absorption capacity of the structure.

[0048] It should be noted that: Figure 5 In the embodiment of the present invention, when the compression distance is about 60 mm, the force of Model 2 (the honeycomb structure with a negative Poisson's ratio of the present invention) is lower than that of Model 1 (the honeycomb structure in the prior art). This is because the straight-walled beams of uniform thickness contained in Model 1 will produce plastic hinges 11 in the middle of the straight-walled beams when deformed, so that the first straight-walled beam contacts the second straight-walled beam earlier. Model 1 enters the densification stage earlier than Model 2. This situation will only occur briefly and will not affect the overall adsorption capacity of the present invention and the greater peak force.

[0049] It should be noted that, in this application, relational terms such as first and second, etc. are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article, or device. In the absence of further restrictions, an element defined by the statement "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0050] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A negative Poisson's ratio honeycomb structure with variable thickness based on a Bezier curve, characterized by: The invention comprises a cell, wherein the cell is a concave triangular structure, and the cell is arranged in a horizontal and vertical array to form a honeycomb structure; the cell is a symmetrical structure, including a straight-wall beam, wherein the straight-wall beam includes a first straight-wall beam and a second straight-wall beam; the first straight-wall beam and the second straight-wall beam are respectively provided on both sides of the symmetry axis of the cell, and the first straight-wall beam and the second straight-wall beam are connected at an acute angle; the thickness of the straight-wall beam varies along the length direction of the straight-wall beam, and the thickness distribution is defined by a Bezier curve; The length of the first straight wall beam is greater than the length of the second straight wall beam; The first straight wall beam on one side of the symmetry axis forms an acute angle with the symmetry axis The angle between the second straight wall beam and the symmetry axis is an acute angle. The angle between The Bezier curve is a fourth-order Bezier curve, which is a fourth-order polynomial and is controlled by five control points. The thickness of the straight-walled beam has a one-to-one correspondence with the function value of the Bezier curve, that is, the thickness of the straight-walled beam is equal to the function value of the Bezier curve at the same position plus the initial thickness value, which can be expressed as: ;in, is the thickness distribution expression of the straight beam, is the initial thickness value, is the function expression of the Bezier curve, is the control parameter of the Bezier curve.

2. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 1, characterized in that: The expression of the quartic polynomial is: ; in, is the function expression of the Bezier curve, is the first control point, is the second control point, is the third control point, is the fourth control point, is the fifth control point, is the control parameter of the Bezier curve.

3. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 2, characterized in that: The coordinates of the first control point are , the coordinates of the second control are , the coordinates of the third control point are , the coordinates of the fourth control point are , the coordinates of the fifth control point are ;in, is the length of the straight wall beam, is the ordinate of the second control point, is the ordinate of the third control point, is the vertical coordinate of the fourth control point.

4. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 3, characterized in that: The value of is positively correlated with the thickness of the straight-wall beam at the second control point. The smaller the value, the thinner the thickness of the straight-wall beam at the corresponding part. The value of is positively correlated with the thickness of the straight wall beam at the third control point. The larger the value, the thicker the straight wall beam thickness of the corresponding part. The value of is positively correlated with the thickness of the straight-wall beam at the fourth control point. The smaller the value, the thinner the thickness of the straight-wall beam in the corresponding part.

5. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 1, characterized in that: Initial thickness value , .

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