A three-dimensional multicellular structure with adjustable Poisson's ratio and specific energy absorption and its fabrication method

Abstract

This invention relates to a three-dimensional multi-cell structure with adjustable Poisson's ratio and specific energy absorption, and its fabrication method. The three-dimensional multi-cell structure is composed of multiple three-dimensional unit cells arranged periodically in a three-dimensional spatial coordinate system. The three-dimensional unit cells are formed by expanding two-dimensional unit cells through a first spatial transformation or a second spatial transformation. Each two-dimensional unit cell includes two quarter-concave hexagonal structures and a diagonal connecting rod. The two ends of the diagonal connecting rod are connected to a quarter-concave hexagonal structure, and the two quarter-concave hexagonal structures are symmetrical about the centroid of the diagonal connecting rod. This invention, by synergistically adjusting the geometric parameters constituting the unit cell, can flexibly control the negative Poisson's ratio and specific energy absorption of the structure on a macroscopic scale within a wide range, thereby achieving proactive design and optimization of the material's mechanical properties to meet the differentiated requirements for deformation behavior and energy absorption characteristics in different engineering scenarios.

Description

Technical Field

[0001] This invention belongs to the field of mechanical metamaterials technology, specifically relating to a three-dimensional multicellular structure with adjustable Poisson's ratio and specific energy absorption, and its fabrication method. Background Technology

[0002] Metamaterials are composite materials artificially designed to possess extraordinary physical properties not found in natural materials, without violating fundamental laws of physics. They offer significant advantages in energy absorption and dissipation, acoustics, optics, and mechanical properties. The performance of metamaterials is determined not only by the properties of their constituent basic materials but also by their designed structure. Mechanical metamaterials are a major category of metamaterials, referring to man-made materials with counterintuitive mechanical properties, also known as mechanical metamaterials, such as materials with negative Poisson's ratio, negative compressibility, negative thermal expansion, and negative stiffness.

[0003] Negative Poisson's ratio materials, also known as tensile materials, have a negative Poisson's ratio. In conventional materials, when subjected to tension, they typically contract perpendicular to the direction of tension; this phenomenon is known as the positive Poisson's ratio effect. However, negative Poisson's ratio materials exhibit a completely different behavior; when stretched, they expand perpendicular to the direction of tension. This unique property makes negative Poisson's ratio materials potentially valuable in various engineering fields.

[0004] Taking the aerospace field as an example, traditional positive Poisson's ratio materials often experience unnecessary stress concentration in certain directions when subjected to external forces, which can lead to material damage or performance degradation. Negative Poisson's ratio materials, on the other hand, can more effectively disperse these stresses, thereby improving the overall strength and durability of the material. Besides traditional structural components, negative Poisson's ratio materials can also be used in other innovative applications such as vibration and noise reduction in aircraft, and thermal protection. Furthermore, negative Poisson's ratio materials possess excellent energy absorption capabilities, which can significantly improve the impact resistance and fatigue resistance of structures, making them promising for applications in protective equipment and vibration damping materials.

[0005] While some natural materials exhibiting a negative Poisson's ratio exist, their properties often fall short of the requirements for engineering applications. Therefore, it is increasingly important to synthesize materials with superior negative Poisson's ratio properties using advanced materials science and engineering techniques. Summary of the Invention

[0006] The purpose of this invention is to provide a three-dimensional multi-cell structure with adjustable Poisson's ratio and specific energy absorption, and a method for its fabrication. By coordinating the adjustment of the geometric parameters constituting the unit cell, the negative Poisson's ratio coefficient and specific energy absorption of the structure on a macroscopic scale can be flexibly controlled within a wide range, thereby realizing the active design and optimization of the mechanical properties of the material to meet the differentiated requirements for deformation behavior and energy absorption characteristics in different engineering scenarios.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is: a three-dimensional multi-cell structure with adjustable Poisson's ratio and specific energy absorption, wherein the three-dimensional multi-cell structure is composed of multiple three-dimensional single-cell structures arranged periodically in a three-dimensional spatial coordinate system, and the three-dimensional single-cell structure is formed by expanding two-dimensional single cells through a first spatial transformation method or a second spatial transformation method. The two-dimensional unit cell includes two 1 / 4 concave hexagonal structures and an oblique link. The two ends of the oblique link are respectively connected to a 1 / 4 concave hexagonal structure. The two 1 / 4 concave hexagonal structures are symmetrical about the centroid of the oblique link. The first spatial transformation method is as follows: the two-dimensional unit cell located in the xy plane is first mirrored about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis, and then mirrored about a plane that forms an angle of 45° with both the negative x-axis and the positive z-axis. The unit cells obtained by the two mirrorings are connected at common points in space with the original unit cell to form the first type of three-dimensional unit cell structure. The second spatial transformation method is as follows: the two-dimensional unit cell located in the xy plane is mirrored about a plane that makes an angle of 45° with both the positive x-axis and the positive z-axis to obtain the second type of three-dimensional unit cell structure.

[0008] Furthermore, the first type of three-dimensional single-cell structure is mirrored in the y-axis direction, and then the mirrored structure is periodically arranged along the x and z axes to obtain the first type of three-dimensional multi-cell structure.

[0009] Furthermore, the first type of three-dimensional multicellular structure has the same Poisson's ratio in both the x and z directions.

[0010] Furthermore, the second type of three-dimensional unit cell structure is periodically arranged on the x-axis and z-axis to form a single-layer three-dimensional structure, and the single-layer three-dimensional structure is mirrored in the y-axis direction to obtain the second type of three-dimensional multi-cell structure.

[0011] Furthermore, when the second type of three-dimensional unit cell structure is periodically arranged on the x-axis and z-axis, the second type of three-dimensional unit cell structure is arranged sequentially in a forward and reverse alternating manner in the y-axis direction.

[0012] Furthermore, the second type of three-dimensional multicellular structure has the same Poisson's ratio in both the x and z directions.

[0013] Furthermore, the two-dimensional unit cell includes a first ligament, a second ligament, and a third ligament. The first and second ligaments are connected to form a 1 / 4 concave hexagonal structure, and the third ligament is the oblique connecting rod. The first ligament is parallel to the y-axis, the angle between the second and first ligaments is α, and the angle between the third and second ligaments is β.

[0014] Furthermore, by changing the angles α and β, and at least one of the geometric parameters of the first ligament length l1, the second ligament length l2, and the third ligament length l3, the macroscopic negative Poisson's ratio coefficient and specific energy absorption of the three-dimensional multicellular structure can be adjusted.

[0015] This invention also proposes a method for fabricating a three-dimensional multicellular structure, comprising the following steps: S1, providing the aforementioned two-dimensional unit cell, the two-dimensional unit cell being located in the xy plane of a three-dimensional spatial coordinate system; S2, the method for expanding the two-dimensional unit cell structure to obtain a three-dimensional unit cell structure is as follows: first, the two-dimensional unit cell is mirrored about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis, and then mirrored about a plane that forms an angle of 45° with both the negative x-axis and the positive z-axis. The unit cells obtained by the two mirrorings are connected at common points in space with the original unit cell to form a three-dimensional unit cell structure. S3, the three-dimensional single-cell structure is mirrored in the y-axis direction, and then the mirrored structure is periodically arranged along the x and z axes to obtain a three-dimensional multi-cell structure.

[0016] This invention also proposes a method for fabricating a three-dimensional multicellular structure, comprising the following steps: S1, providing the aforementioned two-dimensional unit cell, the two-dimensional unit cell being located in the xy plane of a three-dimensional spatial coordinate system; S2, the method for expanding the two-dimensional unit cell structure to obtain a three-dimensional unit cell structure is: to mirror the two-dimensional unit cell about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis to obtain a three-dimensional unit cell structure; S3, three-dimensional unit cell structures are periodically arranged on the x-axis and z-axis to form a single-layer three-dimensional structure. The single-layer three-dimensional structure is mirrored on the y-axis to obtain a three-dimensional multi-cell structure. When the three-dimensional unit cell structures are periodically arranged on the x-axis and z-axis, the three-dimensional unit cell structures are arranged in a forward and reverse alternating manner on the y-axis.

[0017] The beneficial effects of this invention are as follows: This invention combines two tensile mechanisms to design a highly anisotropic three-dimensional multicellular structure with an adjustable Poisson's ratio, achieving both a negative Poisson's ratio and strong anisotropy with a simple structure. When the material is subjected to tension or compression, the individual members constituting the material undergo axial elongation or shortening. Because the geometric parameters of each member are adjustable, the macroscopic Poisson's ratio of the material can vary. This invention can be applied to designs that improve structural safety and achieve lightweighting. Attached Figure Description

[0018] Figure 1 This is a schematic diagram showing the dimensions of the planar multi-cell structure and the two-dimensional single cell of the present invention.

[0019] Figure 2 This is a schematic diagram of the first type of three-dimensional unit cell structure in Example 1.

[0020] Figure 3 This is a schematic diagram of the first type of three-dimensional multicellular structure in Example 1.

[0021] Figure 4 This is a schematic diagram of the second type of three-dimensional unit cell structure in Example 2.

[0022] Figure 5 This is a schematic diagram of the single-layer three-dimensional structure in Example 2.

[0023] Figure 6 This is a schematic diagram of the second type of three-dimensional multicellular structure in Example 2.

[0024] Figure 7 The numerical simulation analysis diagram of the three-dimensional multicellular structure in Example 1 shows the change in energy absorption of the structure as α changes.

[0025] Figure 8 The numerical simulation analysis diagram of the three-dimensional multicellular structure in Example 1 shows the changes in Poisson's ratio and specific energy absorption of the structure as α changes. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the embodiments, but this should not be construed as limiting the invention in any way.

[0027] Example 1 The three-dimensional multi-cell structure with adjustable Poisson's ratio and specific energy absorption described in this invention is based on the design of a two-dimensional unit cell structure using a concave-chirality mechanism. A three-dimensional unit cell structure is obtained by spatially arranging several two-dimensional unit cell structures, and then a three-dimensional multi-cell structure is obtained by spatially periodically arranging several three-dimensional unit cell structures.

[0028] Figure 1 (a) is a schematic diagram of the planar multicellular structure of the present invention. Figure 1 (b) is a magnified view and dimensional diagram of the smallest constituent unit (two-dimensional unit cell) cut out based on the periodicity and symmetry of the material's microstructure. For ease of description, a unified Cartesian coordinate system is established: Figure 1 In (b), the origin is established at the centroid of the two-dimensional unit cell, the x-axis points horizontally to the right, the y-axis points vertically upward, and the z-axis points outward perpendicular to the xy-plane (i.e., out of the paper) according to the right-hand rule. Figure 1In the two-dimensional unit cell schematic diagram shown in (b), we only show its projection and size in the xy plane, and all operations and descriptions are based on this xy plane.

[0029] This two-dimensional unit cell can be viewed as consisting of a diagonal link BD connecting the vertices of two symmetrically distributed quarter-concave hexagonal structures (ABC and EDF). The centroid of the diagonal link BD is the centroid of the entire two-dimensional unit cell. The two quarter-concave hexagonal structures are symmetrical about this centroid, ensuring the feasibility of subsequent symmetrical processing along the y-axis. In this design, the arrangement of the diagonal link BD introduces significant chiral characteristics, while the quarter-concave hexagons retain their unique concave angle expansion mechanism. The combination of the two not only enhances the diversity of the structure's deformation modes but also gives it strong anisotropy and extremely low density potential on a macroscopic scale. This composite design is expected to demonstrate unique application value in fields such as energy absorption, flexible devices, and protective structures.

[0030] For ease of subsequent analysis and modeling, the intersections of the ligaments in the two-dimensional unit cell are identified by letters A to F. In this unit cell, ligaments AB and DF have equal lengths and are collectively classified as the first ligament; similarly, ligaments BC and DE are labeled as the second ligament, while ligament BD is defined as the third ligament. Correspondingly, the first, second, and third ligaments are represented by length parameters l1, l2, and l3, respectively. Furthermore, in terms of geometry, the first ligament is arranged vertically, the angle between the second ligament and the vertical direction is denoted as α (∠ABC = α), and the angle between the second and third ligaments is defined as β (∠CBD = β). All ligaments are rectangular rods with a uniform wall thickness denoted as t and an out-of-plane depth of h (t × h). It should be noted that the third ligament is the aforementioned oblique link BD, and the first and second ligaments form the aforementioned 1 / 4 concave hexagonal structure.

[0031] The process of arranging the two-dimensional unit cell structure into a three-dimensional unit cell structure through spatial arrangement is as follows: First, the two-dimensional unit cell located in the xy plane is mirrored about a plane forming a 45° angle with both the positive x-axis and positive z-axis. The resulting two-dimensional unit cell is located in the zy plane and connected to the original unit cell. Then, it is mirrored again about a plane forming a 45° angle with both the negative x-axis and positive z-axis. The unit cells obtained from these two mirrorings are connected at a common point in space with the original unit cell. The resulting spatial structure includes four two-dimensional unit cells connected at the same location, i.e. Figure 2 The first type of three-dimensional unit cell structure is shown.

[0032] The process of obtaining a first-class three-dimensional multi-cell structure from several first-class three-dimensional unit cell structures through spatial periodic arrangement is as follows: The obtained first-class three-dimensional unit cell structures are mirrored along the y-axis, and then the mirrored structures are periodically arranged along the x and z axes, resulting in the following: Figure 3 The first type of three-dimensional multicellular structure is shown.

[0033] Example 2 This embodiment still uses the two-dimensional single cell described in Embodiment 1, but designs a second type of three-dimensional multi-cell structure according to a different spatial splicing method than Embodiment 1.

[0034] Specifically, by mirroring the two-dimensional unit cell located in the xy plane about a plane that forms a 45° angle with both the positive x-axis and the positive z-axis, a second type of three-dimensional unit cell structure is obtained, such as... Figure 4 The darker part in the image. The second type of three-dimensional unit cell structure is flipped 180° along the y-axis to obtain a reversed three-dimensional unit cell whose spatial orientation is upside down; subsequently, using the connection point of two two-dimensional unit cells in the second type of three-dimensional unit cell structure as the starting point, the reversed three-dimensional unit cells are connected along the x-axis and z-axis to obtain... Figure 4 The spatial structure is shown. Then, following the above-described alternating arrangement along the x and z axes in the y-axis direction, multiple second-type three-dimensional unit cell structures are arranged to obtain... Figure 5 The single-layer three-dimensional structure shown is then mirrored along the y-axis to obtain... Figure 6 The second type of three-dimensional multicellular structure is shown.

[0035] Based on the deformation symmetry relationship of the two-dimensional unit cell in Examples 1 and 2, the resulting three-dimensional multi-cell structure has the same Poisson's ratio in the x and z directions.

[0036] The following example uses the three-dimensional multi-cell structure of Example 1. The three-dimensional multi-cell structure model is imported into ABAQUS for finite element analysis. The model size is as follows: four layers of two-dimensional unit cells along the x and z axes, and two layers of two-dimensional unit cells along the y axis. The element type is C3D8R. The material parameters used are Future 7100Pro nylon, i.e., E1=E2=1500MPa, υ1=υ2=0.3. The cross-sectional area of ​​the rods constituting the two-dimensional unit cells is taken as 1.6×1.6mm. 2 Where l1=20mm, l2=24mm, l3=16mm, β=45°, and α takes values ​​of 26°, 28°, 30°, 32°, and 34°. When performing numerical simulation to solve the mechanical response, the structure is compressed along the negative y-axis, and the total compression is set to 50% strain. The Poisson's ratio υ and energy absorption EA of the model are measured.

[0037] The results of the numerical simulation analysis are as follows Figure 7 , 8 As shown, Figure 7 The graphs show the changes in energy absorption as a function of strain during the compression of models of different sizes. It can be seen that as the angle α increases, the energy absorption of the model gradually increases, and the overall trend is not significantly different. Figure 8 The diagram comparing the compression Poisson's ratio and specific energy absorption of models of different sizes shows that as the angle α increases, the absolute value of the compression Poisson's ratio υ gradually decreases, that is, the tensile effect gradually decreases, while the specific energy absorption gradually increases, that is, the energy absorption of the same mass of the structure gradually increases.

[0038] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the specific implementation of the present invention with reference to the above embodiments. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the pending claims.

Claims

1. A three-dimensional multicellular structure with adjustable Poisson's ratio and specific energy absorption, characterized in that, The three-dimensional multi-cell structure is composed of multiple three-dimensional single-cell structures arranged periodically in a three-dimensional spatial coordinate system. The three-dimensional single-cell structure is formed by expanding two-dimensional single cells through a first spatial transformation method or a second spatial transformation method. The two-dimensional unit cell includes two 1 / 4 concave hexagonal structures and an oblique link. The two ends of the oblique link are respectively connected to a 1 / 4 concave hexagonal structure. The two 1 / 4 concave hexagonal structures are symmetrical about the centroid of the oblique link. The first spatial transformation method is as follows: the two-dimensional unit cell located in the xy plane is first mirrored about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis, and then mirrored about a plane that forms an angle of 45° with both the negative x-axis and the positive z-axis. The unit cells obtained by the two mirrorings are connected at common points in space with the original unit cell to form the first type of three-dimensional unit cell structure. The second spatial transformation method is as follows: the two-dimensional unit cell located in the xy plane is mirrored about a plane that makes an angle of 45° with both the positive x-axis and the positive z-axis to obtain the second type of three-dimensional unit cell structure.

2. The three-dimensional multicellular structure according to claim 1, characterized in that, The first type of three-dimensional single-cell structure is mirrored in the y-axis direction, and then the mirrored structure is periodically arranged along the x and z axes to obtain the first type of three-dimensional multi-cell structure.

3. The three-dimensional multicellular structure according to claim 2, characterized in that, The first type of three-dimensional multicellular structure has the same Poisson's ratio in the x and z directions.

4. The three-dimensional multicellular structure according to claim 1, characterized in that, The second type of three-dimensional unit cell structure is periodically arranged on the x-axis and z-axis to form a single-layer three-dimensional structure. The single-layer three-dimensional structure is mirrored in the y-axis direction to obtain the second type of three-dimensional multi-cell structure.

5. The three-dimensional multicellular structure according to claim 4, characterized in that, When the second type of three-dimensional unit cell structure is periodically arranged on the x-axis and z-axis, the second type of three-dimensional unit cell structure is arranged in a staggered manner in the y-axis direction.

6. The three-dimensional multicellular structure according to claim 1, characterized in that, The second type of three-dimensional multicellular structure has the same Poisson's ratio in the x and z directions.

7. The three-dimensional multicellular structure according to claim 1, characterized in that, The two-dimensional unit cell includes a first ligament, a second ligament, and a third ligament. The first and second ligaments are connected to form a 1 / 4 concave hexagonal structure, and the third ligament is the oblique connecting rod. The first ligament is parallel to the y-axis, the angle between the second and first ligaments is α, and the angle between the third and second ligaments is β.

8. The three-dimensional multicellular structure according to claim 7, characterized in that, By changing the angles α and β, and at least one of the geometric parameters of the first ligament length l1, the second ligament length l2, and the third ligament length l3, the macroscopic negative Poisson's ratio coefficient and specific energy absorption of the three-dimensional multicellular structure can be adjusted.

9. A method for fabricating a three-dimensional multicellular structure, characterized in that, Includes the following steps: S1, providing a two-dimensional unit cell as described in claim 1, wherein the two-dimensional unit cell is located in the xy plane of a three-dimensional spatial coordinate system; S2, the method for expanding the two-dimensional unit cell structure to obtain a three-dimensional unit cell structure is as follows: first, the two-dimensional unit cell is mirrored about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis, and then mirrored about a plane that forms an angle of 45° with both the negative x-axis and the positive z-axis. The unit cells obtained by the two mirrorings are connected at common points in space with the original unit cell to form a three-dimensional unit cell structure. S3, the three-dimensional single-cell structure is mirrored in the y-axis direction, and then the mirrored structure is periodically arranged along the x and z axes to obtain a three-dimensional multi-cell structure.

10. A method for fabricating a three-dimensional multicellular structure, characterized in that, Includes the following steps: S1, providing a two-dimensional unit cell as described in claim 1, wherein the two-dimensional unit cell is located in the xy plane of a three-dimensional spatial coordinate system; S2, the method for expanding the two-dimensional unit cell structure to obtain a three-dimensional unit cell structure is: to mirror the two-dimensional unit cell about a plane that forms an angle of 45° with both the positive x-axis and the positive z-axis to obtain a three-dimensional unit cell structure; S3, three-dimensional unit cell structures are periodically arranged on the x-axis and z-axis to form a single-layer three-dimensional structure. The single-layer three-dimensional structure is mirrored on the y-axis to obtain a three-dimensional multi-cell structure. When the three-dimensional unit cell structures are periodically arranged on the x-axis and z-axis, the three-dimensional unit cell structures are arranged in a forward and reverse alternating manner on the y-axis.

Images