A self-similar hierarchical negative poisson's ratio cell and honeycomb structure thereof

Abstract

The application belongs to the technical field of mechanical metamaterials, and particularly relates to a self-similar layered negative Poisson's ratio cell and a honeycomb structure thereof. The self-similar layered negative Poisson's ratio structure replaces the corner points of the traditional structure with similar star-shaped structures on the basis of the traditional star-shaped structure. When the structure is subjected to low-speed impact, the adjacent cells will first form self-similar star-shaped structures due to the unique configuration, and only after all the self-similar star-shaped structures are formed, the cell walls of the cells will begin to contact each other and deform, so that the self-similar layered negative Poisson's ratio structure can have more superior energy absorption capacity and higher platform stress while maintaining the negative Poisson's ratio effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical metamaterials, and particularly relates to a self-similar layered negative Poisson's ratio cell and a honeycomb structure thereof. BACKGROUND

[0002] Honeycomb structures have been widely used in many engineering fields such as aerospace, automobile, subway and human body protection devices. As a typical lightweight metamaterial, the negative Poisson's ratio honeycomb is concerned because of its excellent performance such as enhanced shear modulus, indentation resistance, high fracture strength, strong impact resistance and excellent energy absorption capacity.

[0003] The configuration of the negative Poisson's ratio honeycomb is derived from the traditional honeycomb structure such as hexagonal, square and circular honeycomb, and thus the common negative Poisson's ratio honeycomb configurations include concave hexagonal structure, star-shaped structure and chiral structure. After years of development, the negative Poisson's ratio honeycomb has many novel structural forms. Through combination of typical structures, layered design, gradient design and configuration optimization, a large number of innovative negative Poisson's ratio honeycomb structures are put on the market, which greatly expands the application prospect of the negative Poisson's ratio structure.

[0004] However, as a lightweight metamaterial, although the negative Poisson's ratio structure has good mechanical properties, its high porosity structural characteristics inevitably weaken the bearing capacity of the structure. Therefore, how to make the honeycomb structure maintain the negative Poisson's ratio effect while having good platform stress and energy absorption characteristics is the goal we pursue.

[0005] Patent 2020111041871 discloses a negative Poisson's ratio structure based on flexible hinges. On the basis of the classic star-shaped honeycomb, the intersection of adjacent structural units is connected by a connecting rod, and a flexible hinge is arranged at the sharp corner position in the structure to reduce stress concentration at the sharp corner and increase the means for adjusting the flexible hinge parameters to change the overall stiffness of the structure. The interference problem of the two rods connected by the flexible hinge after deformation is solved. However, the use of flexible hinges to reduce stress concentration of the structure is difficult in the structure preparation process. Patent 2021111530105 discloses a star-triangle negative Poisson's ratio structure with self-adjusting thickness gradient. The star-shaped honeycomb and the triangular structure are combined, and a self-adjusting thickness gradient design is adopted. When in-plane compression, the deformation process can be divided into two main deformation stages, the stress-strain curve has two platform stages, and the energy absorption capacity is significantly improved. The self-adjusting thickness gradient design of the patent enhances the structural performance, but also increases the manufacturing difficulty, and the structure deformation still has a significant shear band phenomenon, which is not uniform and stable enough. SUMMARY

[0006] In order to solve the above problems, a self-similar hierarchical negative Poisson's ratio cell and a honeycomb structure thereof are provided, which are based on a conventional star-shaped honeycomb structure and obtained by hierarchical design through the adoption of a self-similar structure. The new structure can have superior energy absorption capacity and higher platform stress while maintaining the negative Poisson's ratio effect when subjected to impact load, thereby further enhancing the practicability of the negative Poisson's ratio structure and providing a new train of thought for subsequent structural design work, and solving the problems existing in the prior art.

[0007] The present application provides one of the following technical solutions:

[0008] A self-similar hierarchical negative Poisson's ratio cell comprises a self-similar star-shaped structure and a transverse ligament, wherein the self-similar star-shaped structure comprises four first concave arrows arranged circumferentially, each first concave arrow being formed by shortening and concaving two inclined cell walls of a second concave arrow of a conventional star-shaped honeycomb structure cell at a node.

[0009] The length of each inclined cell wall of the second concave arrow is l0; and the included angle between the second concave arrow and the horizontal and vertical directions is θ0.

[0010] The length of each inclined cell wall of the first concave arrow is l; the length of each inner arrow is l1; and the included angle between the first concave arrow and the horizontal and vertical directions and the included angle between the inner arrow and the horizontal and vertical directions are θ1.

[0011] θ0=θ1=θ.

[0012] The transverse ligament comprises two symmetrical transverse ligaments arranged on the left and right sides of the self-similar star-shaped structure, and one end of each transverse ligament is connected to the connection point of the adjacent first concave arrow.

[0013] In the formula, l0, l, l1, h and θ satisfy the following relationship:

[0014]

[0015] l=l0(1-2β+βtanθ).

[0016] Further, θ and β satisfy the following relationship:

[0017]

[0018] Further, the conventional star-shaped honeycomb structure cell comprises a four-star-shaped structure, the four-star-shaped structure comprises four second concave arrows arranged circumferentially, and a transverse ligament is connected at the connection point of adjacent second concave arrows. On this basis, the self-similar star-shaped structure is obtained by replacing the self-similar star-shaped structure at the corner position of the four-star-shaped structure and retaining the two transverse ligaments in the transverse direction.

[0019] Further, the inner arrow includes a first inner arrow located at the arrow end of the first inner concave arrow and two symmetrical second inner arrows located at the free end of the first inner concave arrow; the four first inner concave arrows are sequentially connected by the second inner arrows in the circumferential direction.

[0020] The present application provides the following technical solutions two:

[0021] A self-similar hierarchical negative Poisson's ratio honeycomb structure is formed by the arrangement and combination of the self-similar hierarchical negative Poisson's ratio cells as described above.

[0022] Further, the self-similar hierarchical negative Poisson's ratio honeycomb structure is formed by the horizontal connection of the self-similar hierarchical negative Poisson's ratio cells to form a plurality of periodic units, and the plurality of periodic units are arranged in several rows in the longitudinal direction to form a combination.

[0023] Further, the plurality of periodic units in each row are connected by a node of the first inner arrow on the first inner concave arrow.

[0024] Further, the horizontal ligament and the first, second inner concave arrows and the cell wall thickness of the inner arrow are the same, and are t.

[0025] The present application has the following beneficial effects:

[0026] The self-similar hierarchical negative Poisson's ratio structure of the present application has the following significant advantages in energy absorption characteristics:

[0027] (1) When the present application is subjected to impact load, the deformation is uniform, consistent and stable, and the "V" type shear deformation band phenomenon is greatly weakened.

[0028] (2) Compared with the traditional star-shaped honeycomb, the new structure of the present application has higher specific energy absorption at the same relative density, and has greater platform stress and higher strength when impacted.

[0029] (3) Compared with the existing negative Poisson's ratio structure based on flexible hinges, the manufacturing process of the present application is more simple, can be manufactured conveniently and quickly by using 3D printing technology, has lower production cost and higher manufacturing efficiency.

[0030] The self-similar hierarchical negative Poisson's ratio structure of the present application replaces the folded corner part of the star-shaped honeycomb with a self-similar star-shaped structure, and when the new structure is subjected to impact load, adjacent structures will first form a self-similar star-shaped structure due to the unique configuration, and the structure will be crushed only after all the self-similar substructures are formed. Compared with the traditional star-shaped honeycomb, the structure of the present application will enter the densification later, thus maintaining the negative Poisson's ratio effect while having stronger energy absorption capacity and higher platform stress. BRIEF DESCRIPTION OF DRAWINGS

[0031] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:

[0032] Figure 1 Structure diagram of traditional star-shaped honeycomb (SSH) and self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application;

[0033] Figure 2 Structure diagram of traditional star-shaped honeycomb (SSH) and self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application;

[0034] Figure 3 Stress-strain curve comparison of traditional star-shaped honeycomb (SSH) and negative Poisson's ratio structure (VSH) of the present application under impact load;

[0035] Figure 4 Deformation diagram of traditional star-shaped honeycomb (SSH) and self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application under impact load;

[0036] Figure 5 Energy absorption capacity and dynamic Poisson's ratio change diagram of traditional star-shaped honeycomb (SSH) and self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application under impact load;

[0037] Figure 6 Color diagram corresponding to Figure 2 .

[0038] Wherein, Figure 1 (a) is the cell configuration of traditional star-shaped honeycomb (SSH), Figure 1 (b) is the cell configuration of self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application;

[0039] Figure 2 (a) is the cell configuration of traditional star-shaped honeycomb (SSH), Figure 1 (b) is the cell configuration of self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application;

[0040] Figure 4 (a) is the deformation diagram of traditional star-shaped honeycomb (SSH) under impact load; Figure 4 (b) is the deformation diagram of self-similar hierarchical negative Poisson's ratio structure (VSH) of the present application under impact load.

[0041] Reference signs: 1 transverse ligament, 2 first concave arrow, 3 second concave arrow, 4 first inner arrow, 5 second inner arrow. DETAILED DESCRIPTION

[0042] The present invention will be further described below with reference to specific embodiments, but the scope of protection of this application is not limited to these embodiments.

[0043] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0044] See Figures 1-2 , Figure 6 , Figure 1 Figures (a) and (b) show the self-similar hierarchical negative Poisson's ratio (VSH) cell of the present invention and the conventional star-shaped cell (SSH); Figure 2 ( Figure 6 Figures (a) and (b) show the self-similar hierarchical negative Poisson's ratio (VSH) structure of the present invention and the structure derived from the conventional star cell (SSH).

[0045] Wherein, l0 is the length of the second concave arrow inclined cell wall of the traditional star-shaped SSH cell; h is the length of the transverse ligament; l1 is the length of the first concave arrow inclined cell wall of the self-similar layered negative Poisson's ratio (VSH) structure cell of the present invention.

[0046] An embodiment of the present invention provides a self-similar layered negative Poisson's ratio cell, which includes a self-similar star structure and a transverse ligament 1; the self-similar star structure includes four first concave arrows 2 arranged circumferentially, each first concave arrow being obtained by shortening the two inclined cell walls of the second concave arrow 3 of the conventional star honeycomb structure cell and forming an inner arrow at the node.

[0047] The length of each inclined cell wall of the second concave arrow 3 is l0; the angle between the second concave arrow and the horizontal and vertical directions is θ0; the length of each inclined cell wall of the first concave arrow 2 is l; the length of each inner arrow is l1; the angle between the first concave arrow 2 and the horizontal and vertical directions, and the angle between the inner arrow and the horizontal and vertical directions are all θ1; θ0=θ1=θ.

[0048] The aforementioned transverse ligament 1 includes two symmetrically arranged on the left and right sides of the self-similar star-shaped structure, with one end of each transverse ligament connected to the connection point of the adjacent first concave arrow 2.

[0049] The relationship between l0, l, l1 and the transverse ligament lengths h and θ is as follows:

[0050]

[0051] l = l0(1 - 2β + βtanθ).

[0052] θ and β satisfy the following relationship:

[0053]

[0054] The above inner arrow includes a first inner arrow 4 located at the arrow end of the first inner concave arrow 2 and two symmetrical second inner arrows 5 located at the free end of the first inner concave arrow.

[0055] Another embodiment of the present application provides a self-similar hierarchical negative Poisson's ratio honeycomb structure which is formed by transverse connection of the above-mentioned self-similar hierarchical negative Poisson's ratio unit cells into a plurality of periodic units, and the plurality of periodic units are arranged in several rows in the longitudinal direction.

[0056] In order to illustrate that the self-similar hierarchical negative Poisson's ratio honeycomb structure of the present application has better negative Poisson's ratio effect, deformation stability and plateau stress compared with the traditional star-shaped honeycomb, the stress-strain, deformation mode and Poisson's ratio of the self-similar hierarchical negative Poisson's ratio honeycomb structure under impact load are studied and compared with those of the traditional star-shaped honeycomb.

[0057] Referring to Figure 3 , a comparison diagram of nominal stress-strain curves of the traditional star-shaped honeycomb (SSH) and the new structure of the present application under low-speed impact is shown. It can be seen that the nominal stress of the self-similar hierarchical negative Poisson's ratio honeycomb structure of the present application is higher, and therefore the plateau stress is also higher.

[0058] Referring to Figure 4 , a deformation mode diagram of the new structure of the present application and the traditional star-shaped honeycomb (SSH) under low-speed impact is shown. It can be seen that the self-similar hierarchical negative Poisson's ratio honeycomb structure of the present application only forms a weak upper and lower symmetrical "V"-shaped shear deformation band in the initial deformation stage, and the overall deformation is more stable. The unit cells of the traditional star-shaped honeycomb (SSH) are in contact with each other in a short time, which leads to overall deformation and weakens the stability.

[0059] Referring to Figure 5 , a comparison diagram of energy absorption characteristics and dynamic Poisson's ratio of the new structure of the present application and the traditional star-shaped honeycomb (SSH) is shown. It can be seen that the self-similar hierarchical negative Poisson's ratio honeycomb structure of the present application can maintain the negative Poisson's ratio effect while having higher energy absorption per unit mass under different impact speeds: 2m / s, 25m / s and 100m / s.

[0060] The above merely illustrates the embodiments of the present application, and the protection scope of the present application is not limited to these specific embodiments, but determined by the claims of the present application. The present application can have various changes and modifications for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the technical thought and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A self-similar hierarchical negative Poisson's ratio cell, characterized in that, The self-similar star structure comprises four first concave arrows arranged in a circumferential direction, each first concave arrow being formed by shortening and concaving two inclined cell walls of a second concave arrow of a four-order star-shaped honeycomb structure at a node; The length of each inclined cell wall of the second concave arrowhead is l 0 ; the included angle between the second concave arrowhead and the horizontal and vertical directions is ; The length of each inclined cell wall of the first inner concave arrow is l ; the length of each wall of the inner arrow is l 1 ; the included angle between the first inner concave arrow and the horizontal and vertical directions and the included angle between the inner arrow and the horizontal and vertical directions are both ; ; The lateral ligament comprises two symmetrical lateral ligaments arranged on the left and right sides of the self-similar star structure, and one end of each lateral ligament is connected to the connection point of the adjacent first concave arrow; wherein l 0 , l , l 1 Relationship of the length of the transverse ligament h、 to the length of the transverse ligament ； with satisfies the following relationship: ； The inner arrow comprises a first inner arrow located at the arrow end of the first concave arrow and two symmetrical second inner arrows located at the free end of the first concave arrow; the four first concave arrows are connected in sequence along the circumferential direction through the second inner arrows.

2. A self-similar hierarchical negative Poisson's ratio cellular structure characterized in that, The self-similar hierarchical negative Poisson's ratio cell arrangement is formed by the self-similar hierarchical negative Poisson's ratio cell arrangement of claim 1.

3. The self-similar hierarchical negative Poisson's ratio honeycomb structure of claim 2, wherein, The plurality of periodic units formed by the lateral connection of the self-similar hierarchical negative Poisson's ratio cell are arranged in several rows in the longitudinal direction.

4. The self-similar hierarchical negative Poisson's ratio cellular structure of claim 3, wherein, Each row of the plurality of periodic units is connected through a node of the first inner arrow on the first concave arrow.

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