Negative Poisson's ratio honeycomb structure based on bezier curve variable thickness

Abstract

The invention relates to the technical field of mechanical metamaterials, and discloses a Bessel curve variable thickness-based negative Poisson's ratio honeycomb structure, the structure is formed by a plurality of times of transverse and longitudinal arrays of a single cell of a concave triangular honeycomb structure, and the single cell is formed by connecting two first straight wall beams and two second straight wall beams which are symmetrically arranged end to end; a first straight wall beam and a second straight wall beam are arranged on the two sides of the symmetry axis respectively, and the first straight wall beam and the second straight wall beam are connected in an acute angle mode. The thickness of each straight-wall beam changes in the length direction of the straight-wall beam, the distribution trend of the thickness is defined through a Bezier curve, and compared with uniform thickness distribution, the overall trend of the thickness of the straight-wall beam is thicker in the middle and thinner on the two sides. The design freedom degree and the energy absorption capacity of the honeycomb structure can be improved.

Description

Technical Field

[0001] The 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 structure is an important branch of mechanical metamaterials. Compared with positive Poisson's ratio materials, it has the special mechanical property of expanding (contracting) in the transverse direction under longitudinal tension (compression). Because of its excellent surface isotropy, anti-shear performance and energy absorption and vibration isolation effects, it has always been the focus of research and can be widely used in aerospace, automotive and military fields.

[0003] For the design strategy of negative Poisson's ratio honeycomb structure, there is a hybrid design strategy at the macro level, which refers to combining different types of unit cells. At the micro scale, there are hierarchical design and gradient design. The hierarchical design strategy is to embed small-sized unit cells into large-sized unit cells. The gradient design strategy refers to connecting several unit cells with gradient designs in geometric parameters. The introduction of these strategies increases the degree of freedom of design of negative Poisson's ratio honeycomb structure and can obtain mechanical properties different from 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, which includes a number of curved concave hexagonal cells arranged gradiently around the central axis of the truncated cone tube structure and along the generatrix direction of the truncated cone tube. 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] In the past, gradient honeycomb designs 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 deficiencies in the prior art, 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 comprises a cell, wherein the cell is an inwardly concave triangular structure, and there are a plurality of cells, which are arranged in a horizontal and vertical array to form a honeycomb structure; the cell is a symmetrical structure, comprising a straight-wall beam, wherein the straight-wall beam comprises a first straight-wall beam and a second straight-wall beam; the first straight-wall beam and the second straight-wall beam are respectively arranged 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 distribution of the thickness is defined by a Bezier curve, and 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 adopts 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, It is the control parameter of 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, It is the control parameter of 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 ordinate 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] Further, 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 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 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] When the negative Poisson's ratio honeycomb with variable straight wall beam thickness based on Bezier curve proposed by the present invention is subjected to axial compression, the straight wall beams will produce more plastic hinges under the pressure, which greatly improves 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 negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve proposed in the present invention can use the straight beam wall as the minimum design unit, which greatly increases the design freedom of the structure. In particular, the straight beam wall thickness design shown in the present 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 to design a straight-wall beam with variable thickness, and 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 The schematic diagram of the structure of the negative Poisson's ratio honeycomb structure of the present invention is shown in the dotted line frame in the figure. The closed structure formed by four straight wall beams connected end to end is a cell.

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

[0027] Figure 3 It is a 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 of the same mass, where Figure 4 a is a schematic diagram of the deformation process of the existing negative Poisson's ratio structure with uniform straight wall beam thickness. Figure 4 b is a schematic diagram of the deformation process of the negative Poisson's ratio honeycomb structure based on Bezier curve variable thickness according to the present invention;

[0029] Figure 5 It is a comparison diagram of the negative Poisson's ratio structure energy absorption between the present invention and the traditional uniform straight-wall beam of the same mass, wherein model 1 is the negative Poisson's ratio structure energy absorption curve of the existing uniform straight-wall beam thickness, and model 2 is the negative Poisson's ratio honeycomb structure energy absorption curve 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 be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work 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. The 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 reference numerals and letters represent similar items in the following drawings, and therefore, once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0034] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply 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, a negative Poisson's ratio honeycomb metamaterial with variable thickness based on Bezier curve of the present invention 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, and a first straight wall beam 2 and a second straight wall beam 3 are connected at an acute angle on one side of the symmetry axis. The thickness of the straight wall beam 2 varies along the length direction of the straight wall beam, and the distribution of the thickness is defined by a 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 uniform thickness distribution.

[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 quartic polynomial controlled by five control points.

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

[0040] like Figure 3 As shown, the quartic polynomial expression 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, It is the control parameter of Bezier curve.

[0042] There is a one-to-one correspondence between the thickness of the straight-walled beam and the value of the Bezier curve. The thickness of the straight-walled beam at a certain point is equal to the function value of the Bezier curve at the same position 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, is the ordinate of the fourth 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 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 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, the negative Poisson's ratio honeycomb metamaterial 9 of uniform thickness and the negative Poisson's ratio honeycomb metamaterial 10 of variable thickness based on the Bezier curve of the same mass are subjected to quasi-static compression respectively. From the deformation mode, it can be seen that when the two structures are compressed, the structures shrink toward the center, indicating that the Poisson's ratio of the concave 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 wall beam 2 is squeezed in the middle position, generating a plastic hinge 11. When the negative Poisson's ratio honeycomb metamaterial 10 of variable thickness based on the Bezier curve is compressed, the bottom deforms first, and the trend of shrinkage in the middle is more obvious, 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 wall beam 2 of the present invention will generate two plastic hinges 11 on both sides of the first straight wall beam 2 when it is squeezed. Figure 4 The middle circle indicates the position of the plastic hinge 11. Figure 4 B plastic hinge 11 Figure 4 There are more plastic hinges 11 in a. Producing more plastic hinges 11 means that the structure can absorb more energy under the same mass, that is to say, 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, and the closed area enclosed by the curve and the horizontal axis represents the amount of energy absorption. It can be seen that the negative Poisson's ratio honeycomb metamaterial 10 based on Bezier curve variable thickness of the present invention improves the energy absorption capacity of the structure.

[0048] It should be noted that: Figure 5 In the figure, when the compression distance is about 60 mm, the force of Model 2 (the negative Poisson's ratio honeycomb structure 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 included in Model 1 will produce plastic hinges 11 in the middle of the straight-walled beams when deformed, so that the first straight-walled beams will contact with the second straight-walled beams 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 and greater peak force of the present invention.

[0049] It should be noted that, in this application, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or equipment including 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 equipment. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or equipment including the elements.

[0050] Although 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 the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve, characterized in that: It includes a cell, which is a concave triangular structure, and there are a plurality of cells, which are arranged in a horizontal and vertical array to form a honeycomb structure; the cell is a symmetrical structure, including a straight-wall beam, and 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 arranged 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 distribution of the thickness is defined by a 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 length of the first straight wall beam is greater than the length of the second straight wall beam.

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

4. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 1, characterized in that: The Bezier curve adopts a fourth-order Bezier curve, which is a fourth-order polynomial and is controlled by five control points.

5. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 4, 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, It is the control parameter of Bezier curve.

6. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 4, characterized in that: 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, It is the control parameter of Bezier curve.

7. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 4, 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 ordinate of the fourth control point.

8. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 7, characterized in that: The line connecting the first control point and the fifth control point is a horizontal line.

9. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 7, 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 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 fourth control point. The smaller the value, the thinner the thickness of the straight-wall beam in the corresponding part.

10. The negative Poisson's ratio honeycomb structure with variable thickness based on Bezier curve according to claim 6, characterized in that: Initial thickness value , .

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