A negative poisson's ratio cellular metamaterial

Abstract

This invention discloses a negative Poisson's ratio honeycomb metamaterial, comprising: a plurality of negative Poisson's ratio metamaterial unit cells; each negative Poisson's ratio metamaterial unit cell includes: a four-pointed star support body and four pairs of double-strut structures connected around the four-pointed star support body; the four-pointed star support body includes four concave edges with concave structures, each concave edge including a concave midpoint and two endpoints; each double-strut structure includes two inner connecting ends and two outer connecting ends, with each concave edge connecting to the two inner connecting ends of a pair of double-strut structures. The four-pointed star support body and the four pairs of double-strut structures connected around the four-pointed star support body proposed in this application improve the structural stability of the metamaterial, mitigate instability during the deformation process of the metamaterial structure, and the double-strut structure also broadens the degree of freedom in structural geometric design and enhances the adjustability of the structural bandgap.

Description

Technical Field

[0001] This invention relates to the field of metamaterials technology, and in particular to a negative Poisson's ratio honeycomb metamaterial. Background Technology

[0002] Cellular metamaterials benefit from advantages such as low density, high tunability, and impact resistance, and are an important branch of the field of mechanical metamaterials. With the development of the manufacturing industry, higher requirements are being placed on the vibration characteristics of structures, and the vibration isolation characteristics of cellular metamaterials have become the mainstream of research in recent years.

[0003] Among existing metamaterial technologies, the "Star-shaped Chiral Negative Poisson's Ratio Structure" (patent publication number CN116292754A) is composed of multiple periodic units arranged in an array along the horizontal and vertical directions. Each periodic unit includes a star-shaped structure and a four-chiral structure. Compared with traditional structures, this structure has better energy absorption capacity. When the structure is subjected to in-plane quasi-static compression, the stress-strain curve exhibits two distinct plateau stages: In the first plateau stage, the vertical cell wall first undergoes bending deformation until the vertical cell wall and the inclined cell wall come into contact, at which point the thickness of part of the cell wall becomes 2t, and the stress value is relatively low. In the second plateau stage, the bending deformation of the star-shaped cell wall and the rotational contraction deformation of the chiral structure are the main components. In this stage, the stress value is significantly increased, which can greatly increase the energy absorption capacity of the structure. Finally, the structure is crushed.

[0004] The aforementioned existing metamaterial technologies are prone to instability when the overall structure undergoes large deformations, resulting in poor structural stability and limiting their engineering applications. Furthermore, the vibration isolation properties of metamaterials are related to their bandgap characteristics, so these characteristics must be considered when designing the structure. However, the aforementioned existing metamaterial technologies have not taken this into account, leading to poor bandgap adjustability. Summary of the Invention

[0005] This invention provides a negative Poisson's ratio honeycomb metamaterial to address the problems in the prior art, such as the lack of a reliable solution for the instability of the overall structure under large deformation, poor structural stability of the metamaterial, and poor bandgap adjustability.

[0006] On one hand, embodiments of the present invention provide a negative Poisson's ratio honeycomb metamaterial, comprising: a plurality of negative Poisson's ratio metamaterial unit cells.

[0007] The negative Poisson's ratio metamaterial unit cell includes: a quadrilateral support body and four pairs of double diagonal rod structures connected around the quadrilateral support body.

[0008] The four-pointed star support body includes four concave edges with concave structures. Each concave edge includes a concave midpoint and two endpoints. The double diagonal bar structure includes two inner connecting ends and two outer connecting ends. Each concave edge connects to the two inner connecting ends of a pair of double diagonal bar structures.

[0009] In one possible implementation, the two inner connecting ends are symmetrically positioned between the midpoint of the corresponding concave side and the two endpoints.

[0010] In one possible implementation, the concave edge is a V-shaped structure or an arc-shaped structure.

[0011] In one possible implementation, the two external connecting ends of a pair of double-strut structures of the negative Poisson's ratio metamaterial unit cell are connected to the two external connecting ends of a pair of double-strut structures of an adjacent negative Poisson's ratio metamaterial unit cell, forming an additional concave structure.

[0012] In one possible implementation, half the distance between the midpoints of the two concave sides is l1, half the distance between the two endpoints is l2, half the distance between the two inner connecting ends is l3, half the distance between the two outer connecting ends is l4, the distance from the midpoint of the line connecting the two outer connecting ends to the center point of the four-pointed star support body is L, the ratio of l1 to L is α, the ratio of l2 to L is β, the ratio of l3 to L is γ, the ratio of l4 to L is δ, α < β, γ < β.

[0013] In one possible implementation, α = 0.5β.

[0014] In one possible implementation, α < γ.

[0015] The negative Poisson's ratio honeycomb metamaterial of this invention has the following advantages:

[0016] The proposed quadrangular star support and the four pairs of double-root diagonal braces connected around the quadrangular star support improve the structural stability of the metamaterial and mitigate instability during the deformation process. The double-root diagonal braces also broaden the degree of freedom in the structural geometry design and enhance the adjustability of the structural bandgap. The two external connecting ends of a pair of double-root diagonal braces in the proposed negative Poisson's ratio metamaterial unit cell are connected to the two external connecting ends of a pair of double-root diagonal braces in the adjacent negative Poisson's ratio metamaterial unit cell to form an additional concave structure, which improves the vibration isolation capability of the metamaterial. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of a negative Poisson's ratio honeycomb metamaterial provided in Embodiment 1 of the present invention;

[0019] Figure 2 This is a schematic diagram of the structure of a negative Poisson's ratio metamaterial unit cell provided in Embodiment 1 of the present invention;

[0020] Figure 3 This is a schematic diagram of the vibration frequency response analysis model provided in Embodiment 1 of the present invention;

[0021] Figure 4 This is a schematic diagram of the band structure and frequency response curve provided in Embodiment 1 of the present invention;

[0022] Figure 5 This is a schematic diagram of uniaxial tensile deformation of the structure provided in Embodiment 1 of the present invention;

[0023] Figure 6 This is a schematic diagram of the bandgap distribution under different angle parameters of the inclined bar provided in Embodiment 2 of the present invention;

[0024] Explanation of reference numerals in the attached figures:

[0025] 1- Negative Poisson's ratio metamaterial unit cell, 11- Quadrilateral star supporting main body, 12- Double diagonal bar structure, 111- Concave edge, 1111- Concave midpoint, 1112- End point, 121- Inner connection end, 122- Outer connection end, 2- Additional concave structure. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Example 1:

[0028] Figure 1 This is a schematic diagram of a negative Poisson's ratio honeycomb metamaterial provided in Embodiment 1 of the present invention; Figure 2This is a schematic diagram of the structure of a negative Poisson's ratio metamaterial unit cell provided in Embodiment 1 of the present invention. This embodiment of the present invention provides a negative Poisson's ratio honeycomb metamaterial, comprising: a plurality of negative Poisson's ratio metamaterial unit cells 1.

[0029] The negative Poisson's ratio metamaterial unit cell 1 includes: a quadrilateral support body 11 and four pairs of double diagonal rod structures 12 connected around the quadrilateral support body 11.

[0030] The four-pointed star support body 11 includes four concave edges 111 with concave structures. Each concave edge 111 includes a concave midpoint 1111 and two endpoints 1112. The double diagonal rod structure 12 includes two inner connecting ends 121 and two outer connecting ends 122. Each concave edge 111 connects to the two inner connecting ends 121 of a pair of double diagonal rod structures 12.

[0031] For example, the two inner connecting ends 121 are symmetrically arranged between the concave midpoint 1111 of the corresponding concave edge 111 and the two endpoints 1112.

[0032] For example, the concave edge 111 is a V-shaped structure or an arc-shaped structure.

[0033] For example, the two external connecting ends 122 of the pair of double-root diagonal bar structures 12 of the negative Poisson's ratio metamaterial unit cell 1 are connected to the two external connecting ends 122 of the pair of double-root diagonal bar structures 12 of the adjacent negative Poisson's ratio metamaterial unit cell 1 to form an additional concave structure 2.

[0034] For example, half the distance between the midpoints 1111 of the two concave sides 111 is l1, half the distance between the two endpoints 1112 is l2, half the distance between the two inner connecting ends 121 is l3, half the distance between the two outer connecting ends 122 is l4, the distance from the midpoint of the line connecting the two outer connecting ends 122 to the center point of the four-pointed star support body 11 is L, the ratio of l1 to L is α, the ratio of l2 to L is β, the ratio of l3 to L is γ, the ratio of l4 to L is δ, α < β, γ < β.

[0035] δ is the angle parameter of the diagonal bar.

[0036] For example, α = 0.5β.

[0037] For example, α < γ.

[0038] For example, the thickness of the concave edge 111 is t, the ratio of t to L is λ, and λ is the slenderness ratio of the rod.

[0039] The proposed quadrilateral support body and the four pairs of double-root diagonal braces connected around the quadrilateral support body in this embodiment improve the structural stability of the metamaterial and mitigate instability during the deformation process of the metamaterial structure. The double-root diagonal braces also broaden the degree of freedom in the structural geometry design and enhance the adjustability of the structural bandgap. The two external connecting ends of the pair of double-root diagonal braces in the proposed negative Poisson's ratio metamaterial unit cell are connected to the two external connecting ends of the pair of double-root diagonal braces in the adjacent negative Poisson's ratio metamaterial unit cell to form an additional concave structure, which improves the structural vibration isolation capability of the metamaterial.

[0040] In this embodiment, α = 0.4, β = 0.8, γ = 2 / 3, δ = 0.1, λ = 1 / 20, L = 1, and the density of the substrate material constituting the negative Poisson's ratio honeycomb metamaterial is 2700 kg / m³. 3 The Young's modulus is 70 GPa, the Poisson's ratio is 0.33, and the normalized frequency is Ω = ωa / 2πc1, where ω is the angular frequency and a is the lattice constant. The longitudinal wave velocity is denoted by .

[0041] Figure 3 This is a schematic diagram of the vibration frequency response analysis model provided in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the band structure and frequency response curve provided in Embodiment 1 of the present invention. Classical Timoshenko beam elements are used to simulate the members. A unit cell dynamic model is established using Bloch's theorem and the finite element method to obtain the band structure and establish a vibration frequency response analysis model to verify the obtained bandgap characteristics (the bandgap is a unique characteristic of elastic wave propagation in periodic structures; if the elastic wave frequency is within the bandgap frequency band, it indicates that the elastic wave cannot propagate in this structure, thus achieving vibration isolation. Therefore, the bandgap characteristic is a key indicator for evaluating the vibration isolation performance of periodic structures). The band structure is plotted using the first twenty frequencies of the structure. Figure 4 It can be seen that there are three complete band gaps, with frequency ranges of [0.0253, 0.0286], [0.0504, 0.0613], and [0.1157, 0.1986], respectively. The first band gap is located between the fourth and fifth frequency branches, and the widest band gap is located between the sixteenth and seventeenth frequency branches. It can be visually observed that when the excitation frequency is in the band gap band (shaded area), the response acceleration at the structural monitoring point decreases significantly, proving the accuracy of the band structure calculation and verifying the excellent vibration isolation characteristics of the negative Poisson's ratio honeycomb metamaterial. It can be used as a vibration isolation support and a functional element of metamaterial plate and beam structures.

[0042] Figure 5 This is a schematic diagram of the uniaxial tensile deformation of the structure provided in Embodiment 1 of the present invention. The structural deformation of the negative Poisson's ratio honeycomb metamaterial is simulated and predicted using uniaxial static tension (with only the tensile direction degree of freedom constrained at the bottom nodes, tensile force applied to the top nodes, and the remaining boundary nodes being free nodes). Figure 5It can be seen that under axial tensile load, the lateral dimension increases along with the axial dimension, exhibiting a tensile expansion phenomenon, which is a characteristic imparted by the negative Poisson's ratio. The macroscopic Poisson's ratio of this structure was measured to be -0.3. The negative Poisson's ratio is one of the unique mechanical properties of mechanical metamaterials, and numerous studies have shown that structures with negative Poisson's ratio exhibit excellent performance in terms of impact resistance, shear resistance, and energy absorption.

[0043] Example 2:

[0044] In this embodiment, α = 0.4, β = 0.8, γ = 2 / 3, λ = 1 / 20, L = 1, and the angle parameter δ of the diagonal bar varies from 0.1 to 0.7.

[0045] Figure 6 This is a schematic diagram of the bandgap distribution under different inclined rod angle parameters provided in Embodiment 2 of the present invention. Figure 6 It can be seen that the bandgap distribution of the negative Poisson's ratio honeycomb metamaterial structure changes significantly under different inclined bar angle parameters, with six bandgaps appearing sequentially. The width of the low-frequency bandgap gradually decreases with the increase of δ. When δ = 0.19 and 0.40, the first and second bandgaps disappear respectively. When δ = 0.15, the third bandgap begins to appear, and its width first increases and then decreases with the increase of δ, until it disappears completely at δ = 0.59. The lower boundary of the fourth bandgap is adjacent to the upper boundary of the third bandgap, and its overall width also shows a trend of first increasing and then decreasing. The fifth bandgap changes drastically with δ, but it always exists except when δ is in the range of [0.52, 0.54]. The sixth bandgap reappears at δ = 0.53, and its center frequency is somewhat higher than when it first appeared at δ = 0.21. In summary, this characteristic can be used to carry out parameterized control of the bandgap, obtain the target vibration isolation frequency bandgap, and further improve the tunability of the structural bandgap.

[0046] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0047] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A negative Poisson's ratio cellular metamaterial, characterized in that, include: Several negative Poisson's ratio metamaterial unit cells; The negative Poisson's ratio metamaterial unit cell includes: a quadrilateral support body and four pairs of double diagonal rod structures connected around the quadrilateral support body; The four-pointed star support body includes four concave edges with concave structures. Each concave edge includes a concave midpoint and two endpoints. The double diagonal bar structure includes two inner connecting ends and two outer connecting ends. Each concave edge connects to the two inner connecting ends of a pair of double diagonal bar structures. The two inner connecting ends are symmetrically arranged between the midpoint of the corresponding concave side and the two endpoints; The two external connecting ends of a pair of double-strut structures in the negative Poisson's ratio metamaterial unit cell are connected to the two external connecting ends of a pair of double-strut structures in the adjacent negative Poisson's ratio metamaterial unit cell, forming an additional concave structure.

2. A negative Poisson's ratio honeycomb metamaterial according to claim 1, wherein, The concave edge has a V-shaped structure or an arc-shaped structure.

3. The negative Poisson's ratio honeycomb metamaterial according to claim 1, characterized in that, Half the distance between the midpoints of the two opposite concave sides is l 1. Half the distance between the two endpoints is l 2. Half the distance between the two inner connection ends is l 3. Half of the distance between the two external connection ends is l 4. The distance from the midpoint of the line connecting the two external connecting ends to the center point of the four-pointed star support body is... L , l 1 and L The ratio is α , l 2 and L The ratio is β , l 3 and L The ratio is γ , l 4 and L The ratio is δ , α < β , γ < β .

4. The negative Poisson's ratio honeycomb metamaterial according to claim 3, characterized in that, α =0.5 β 。 5. The negative Poisson's ratio honeycomb metamaterial according to claim 3, characterized in that, α < γ 。

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