Mechanical metamaterial with both positive and negative thermal expansion coefficient and poisson's ratio

Abstract

The present application belongs to the technical field of metamaterials, and particularly relates to a mechanical metamaterial with variable signs of thermal expansion coefficient and Poisson's ratio. Based on the small deformation theory, a structure with variable signs of Poisson's ratio and thermal expansion coefficient is designed by adding a pair of initially contacted triangles of another material into an inner concave hexagon, and the stiffness difference of the structure is obvious when the structure is subjected to tension and compression. The analytical expressions of the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure are calculated by using the relevant method of structural mechanics, and the simulation verification is carried out by using the finite element software. The results show that the accuracy of the analytical solution is very high. The parameter analysis is carried out on the geometric parameters affecting the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure, and then the independent variable interval which can make the material realize the variable signs of Poisson's ratio and thermal expansion coefficient is explicitly given. The structure is likely to be widely used in some important engineering fields (such as space), and some possible inspirations are given for the subsequent research.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metamaterials, and particularly relates to a mechanical metamaterial with variable signs of thermal expansion coefficient and Poisson's ratio. BACKGROUND

[0002] Metamaterials are not materials in the general sense, they are artificially designed, do not exist in nature, and usually have unusual properties because of their micro-geometric structure. Mechanical metamaterials are an important branch of metamaterials, and have received more and more attention in the past decade due to their novel design principles. Mechanical metamaterials can be negative Poisson's ratio materials, negative compressibility materials, negative thermal expansion materials, mode conversion adjustable stiffness materials, origami / cut-paper metasurface materials, etc. Mechanical metamaterials show great application prospects in many fields such as semiconductors, biomedical sensors, space telescopes, etc. Research and development of mechanical metamaterials with multiple singular properties are an important prerequisite for developing intelligent sensors with excellent performance and realizing the multifunctional integration of structures, which is also one of the focuses of the current material and mechanical communities. For example, materials with negative Poisson's ratio and negative thermal expansion properties have great application potential in dental filling materials and solar cell panels.

[0003] Negative Poisson's ratio materials, also known as auxetic materials, have a negative Poisson's ratio, and expand (shrink) in the vertical direction when subjected to tension (compression). Such materials have excellent energy absorption capacity, shear resistance and indentation resistance. According to the geometry and deformation characteristics of the material microstructure (or artificial lattice), the mechanism of auxetic effect can be roughly divided into: concave angle unfolding / folding mechanism, chiral and anti-chiral mechanism, rigid rotation mechanism, and other complex mechanisms, such as origami or cut-paper mechanism, elastic instability mechanism, etc.

[0004] Negative thermal expansion materials are materials with negative thermal expansion coefficients, which show the abnormal phenomenon of 'cold expansion and hot contraction'. It is well known that in the environment with large temperature change, the structure may be destroyed due to excessive thermal stress, and the instrument may lose accuracy due to excessive thermal deformation. If low expansion materials (thermal expansion coefficient close to 0) are used, or positive and negative thermal expansion materials are reasonably matched, this adverse effect can be greatly alleviated. For example, the use of negative thermal expansion connecting devices on satellite structures effectively reduces thermal stress. Since natural negative thermal expansion materials are very rare, and their mechanical properties are usually low and the temperature conditions for realizing negative thermal expansion are harsh, it is difficult to meet the engineering requirements. For the above reasons, the method of preparing negative thermal expansion materials from two or more positive thermal expansion materials has emerged, among which lightweight materials are the main ones. According to the characteristics of lattice thermal expansion deformation, some studies have divided lightweight negative thermal expansion materials into two categories: bending-dominated and tension-dominated. Among them, bending-dominated mainly includes double-material circular arc beam structure and three-dimensional structure derived from it, some ligaments use segmented double-material straight beam chiral lattice and anti-chiral lattice, and concave angle structure composed of two single-material beams. It is worth mentioning that this kind of bending-dominated negative thermal expansion material can often realize the tensile effect at the same time. Bending-dominated negative thermal expansion materials have large flexibility, strong negative thermal expansion effect, and can easily consider the tensile effect when designed, so they are suitable for temperature-sensitive multifunctional intelligent sensors. Tension-dominated mainly includes structures based on double-material triangular units, diamond units, tetrahedral units, ladder units, and a series of structures designed around four-star (regular octagonal) units. Unlike bending-dominated, tension-dominated negative thermal expansion materials often have high rigidity.

[0005] Most materials, including negative Poisson's ratio materials and negative thermal expansion materials, have constant signs of Poisson's ratio under tension / compression and thermal expansion coefficient under temperature change. However, recently, researchers have found that metamaterials can be designed to have properties that change sign when the stress direction or temperature change is reversed. For example, Lim designed several structures with variable signs of Poisson's ratio and thermal expansion coefficient (Lim TC. Composite microstructures with Poisson's ratio sign switching upon stress reversal [J]. Composite Structures, 2019, 209: 34-44; Lim T C. Metamaterials with Poisson's ratio sign toggling by means of microstructural duality [J]. SN Applied Sciences, 2019, 1(2); Lim T C. A composite metamaterial with sign switchable elastic and hygrothermal properties induced by stress direction and environmental change reversals [J]. Composite Structures, 2019, 220(JUL.): 185-193.); Peng and Bargmann designed a structure with variable signs of Poisson's ratio by adding initially unconnected rods to a hexagonal honeycomb (Peng X L, Bargmann S. Tunable tension-compression asymmetry and auxeticity in lattice structures by harnessing unilateral contact [J]. Composite Structures, 2021, 278.); Chen et al. designed a structure with variable signs of Poisson's ratio by adding a rope to the diagonal of a parallelogram, and the modulus of the structure changes significantly under tension and compression (Chen M, Fu M, Hu L.Wu et al. achieved the sign-switching of Poisson's ratio by using a spring-like structure (Wu W, Liu P, Kang ZA novel mechanical metamaterial with simultaneous stretching-and compression-expanding properties [J]. Materials & Design, 2021, 208). This type of material may have important potential applications in several key engineering fields. For example, materials that expand regardless of temperature fluctuations could be used in space mechanisms that require permanent locking, ensuring that parts remain self-locking despite significant temperature fluctuations.

[0006] However, current work in the field of sign-shifting metamaterials is still limited and has many limitations, such as anisotropic structures can only achieve sign changes in one direction, sign changes can only be achieved through large deformations, etc. Therefore, the present invention is proposed. Summary of the Invention

[0007] In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio based on small deformation theory by adding a pair of triangles of another material in initial contact in a concave hexagon.

[0008] To achieve the above object, the present invention is implemented through the following technical solutions:

[0009] The present invention provides a mechanical metamaterial with a variable thermal expansion coefficient and Poisson's ratio. The mechanical metamaterial includes multiple unit cell structures, each of which is a concave hexagonal honeycomb structure comprising two horizontal bases and four oblique sides, and isosceles triangles made of another material are connected at two concave points, respectively. The bases of the two isosceles triangles are initially perpendicular to the base of the concave hexagon, and the two isosceles triangles are initially in contact with each other, and a connecting oblique rod is provided between the two isosceles triangles and the vertices of the concave hexagon.

[0010] Preferably, the included angle θ1 between the horizontal base and the hypotenuse of the concave hexagon is 60°-64°.

[0011] Preferably, the included angle θ2 between the horizontal bottom edge of the concave hexagon and the connecting diagonal of the isosceles triangle and the concave hexagon vertex is 30-40°.

[0012] Preferably, the ratio l2 / l1 of half the length of the horizontal bottom edge of the concave hexagon to the length of the diagonal is 1.55-1.9.

[0013] Preferably, the ratio t / l1 of twice the slenderness ratio of the rod constituting the bottom edge of the concave hexagon is 0.05-0.13.

[0014] The present application is based on the small deformation theory, by adding a pair of initial contact triangle of another material in the concave hexagon, a material with variable Poisson's ratio and thermal expansion coefficient is designed, and the stiffness difference of the structure is obvious when subjected to tension and compression. First, the analytical expressions of the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure are calculated by the relevant method of structural mechanics, and then the simulation verification is carried out by using the finite element software, and the results show that the accuracy of the analytical solution is very high. At the same time, the geometric parameters θ1, θ2, l2 / l1 and t / l1 which affect the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure are analyzed, and the influence of the results is studied. The results show that these parameters will significantly affect the properties of the material, and the independent variable interval of the material which can realize the variable Poisson's ratio and thermal expansion coefficient is given. It is worth mentioning that under a relatively wide combination of geometric parameters, the material can realize the variable Poisson's ratio and thermal expansion coefficient at the same time. In addition, the specific stiffness difference of the material is obvious when subjected to tension and compression, and the ratio of the specific stiffness under compression to the specific stiffness under tension can reach 26.24. These strange combinations of properties may be widely used in some important engineering fields (such as space), which may also give some possible inspiration to subsequent research.

[0015] Preferably, the plurality of unit cell structures are periodically arranged and connected to each other.

[0016] More preferably, the same bottom edge is shared between the upper and lower adjacent unit cell structures, and the same two diagonal edges are shared between the left and right adjacent unit cell structures, thereby forming a plurality of unit cell structures.

[0017] Preferably, the material of the concave hexagonal honeycomb structure and the connecting diagonal is selected from Invar alloy, and the material of the isosceles triangle is selected from aluminum.

[0018] More preferably, the Invar alloy has α1=1.1ppm / ℃, E1=144Gpa, v1=0.29, ρ1=7.18g / cm 3 ; the aluminum has α3=23.1ppm / ℃, E3=70Gpa, v3=0.33, ρ3=2.7g / cm 3 .

[0019] Compared with the prior art, the present application has the beneficial effects that:

[0020] The present application is based on the small deformation theory, and a structure with variable Poisson's ratio and thermal expansion coefficient is designed by adding a pair of initially contacted triangles of another material in the inner concave hexagon, and the stiffness difference of the structure is obvious when the structure is subjected to tension and compression. The analytical expressions of the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure are calculated by using the relevant method of structural mechanics, and the simulation verification is carried out by using the finite element software, and the results show that the accuracy of the analytical solution is very high. The parameter analysis is carried out on the geometric parameters affecting the equivalent Poisson's ratio, modulus and thermal expansion coefficient of the structure, and then the independent variable interval which can make the material realize the variable Poisson's ratio and thermal expansion coefficient is clearly given. The mechanical metamaterial with variable Poisson's ratio and thermal expansion coefficient designed by the present application is expected to be widely used in some important engineering fields (such as space), and lays a foundation for subsequent research. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 Fig. 1 is a schematic diagram of the structure of the new mechanical metamaterial: (a) unit cell; (b) multi-cell;

[0022] Figure 2 Fig. 3 is a schematic diagram of the mechanism for realizing the variable sign of the new mechanical metamaterial, wherein (a) tension and compression along the y-axis, indicating that the material is subjected to the y-direction axial load, (b) temperature rise and fall, indicating that the material is subjected to the temperature load, (c) tension and compression along the x-axis, indicating that the material is subjected to the x-direction axial load, wherein the dashed box represents the contour before being subjected to the load.

[0023] Figure 3 Fig. 6 is the influence of the change of θ1 on the material properties: (a) thermal expansion coefficient; (b) Poisson's ratio and Young's modulus when tension and compression in the y-direction; (c) Poisson's ratio and Young's modulus when tension and compression in the x-direction; (d) specific stiffness: S represents the specific stiffness when tension, and C represents the specific stiffness when compression.

[0024] Figure 4 Fig. 7 is the influence of the change of θ2 on the material properties: (a) thermal expansion coefficient; (b) Poisson's ratio and Young's modulus when tension and compression in the y-direction; (c) Poisson's ratio and Young's modulus when tension and compression in the x-direction; (d) specific stiffness: S represents the specific stiffness when tension, and C represents the specific stiffness when compression.

[0025] Figure 5 Fig. 8 is the influence of the change of l2 / l1 on the material properties: (a) thermal expansion coefficient; (b) Poisson's ratio and Young's modulus when tension and compression in the y-direction; (c) Poisson's ratio and Young's modulus when tension and compression in the x-direction; (d) specific stiffness: S represents the specific stiffness when tension, and C represents the specific stiffness when compression.

[0026] Figure 6Effects of the variation of t / l1 on material properties: (a) thermal expansion coefficient; (b) Poisson's ratio and Young's modulus in the y direction under tension and compression; (c) Poisson's ratio and Young's modulus in the x direction under tension and compression; (d) specific stiffness: S represents the specific stiffness under tension, and C represents the specific stiffness under compression. DETAILED DESCRIPTION

[0027] The specific embodiments of the present application will be further described below. It should be noted that the description of these embodiments is used to help understand the present application, but does not constitute a limitation on the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0028] The experimental methods in the following examples are all conventional methods unless otherwise specified. The test materials used in the following examples are all commercially available unless otherwise specified.

[0029] Example 1 Design and verification of a mechanical metamaterial with variable signs of thermal expansion coefficient and Poisson's ratio

[0030] 1. Design of a mechanical metamaterial

[0031] Figure 1 The structure of the new mechanical metamaterial proposed in the present application is shown in the following figure, which includes a plurality of unit cell structures, Figure 1 a is a single unit cell structure, and a schematic diagram of the arrangement of multiple cells of the structure is shown in Figure 1 b. Each unit cell structure is a classic concave hexagonal honeycomb structure ABCDEF, and two isosceles triangles composed of another material are connected at concave points C and F, wherein the base GH, IJ of the triangle is initially perpendicular to the base AB, ED of the concave hexagon, and GH and IJ are initially in contact with each other, Figure 1 a is only to show the structural details and does not represent the actual state. Among them, the upper and lower adjacent unit cell structures share the same base, and the left and right adjacent unit cell structures share the same two oblique sides, thereby forming a plurality of unit cell structures. In addition, a connecting diagonal rod is provided between the inner triangle and the concave hexagon vertex.

[0032] The principle of realizing the variable signs of Poisson's ratio and thermal expansion coefficient is as follows (as shown in Figure 2GH and IJ will have a tendency to move towards each other, causing the two rods to stick together all the time, and the whole structure will finally stretch in the x direction, at this time the Poisson's ratio and the x direction thermal expansion coefficient are positive. While the structure is in the y direction tension or the ambient temperature decreases, GH and IJ will have a tendency to move away from each other and eventually lead to the separation of the two rods, the movement of the rod will bring the whole structure to finally stretch in the x direction, at this time the Poisson's ratio and the x direction thermal expansion coefficient are negative, thus realizing the sign change of the Poisson's ratio and the x direction thermal expansion coefficient Figure 2 a,b). While the structure is in the x direction compression, GH and IJ will also have a tendency to move towards each other, causing the two rods to stick together all the time, and the whole structure will finally stretch in the y direction, at this time the Poisson's ratio is positive; on the contrary, in the x direction tension, the two rods are separated and bring the whole structure to stretch in the y direction, the Poisson's ratio is negative, thus also realizing the sign change of the Poisson's ratio Figure 2 c). It is worth mentioning that under certain specific geometric parameters, the y direction thermal expansion coefficient can also realize the sign change.

[0033] 2、Results verification and parameter analysis

[0034] 2.1、The influence of θ1

[0035] First of all, the influence of the change of the angle θ1 between the horizontal bottom edge and the inclined edge of the concave hexagon (such as the angle between AF and AB) on the material properties is explored. The range of θ1 is 60°-88°, among which the six edges of the concave hexagonal honeycomb structure, the inclined rod between the isosceles triangle and the concave hexagonal vertex, and the connecting rod between the two unit structures are selected from invar (represented by CF rod), α1=1.1ppm / ℃, E1=144Gpa, v1=0.29, ρ1=7.18g / cm 3 ; the three edges of the isosceles triangle are selected from aluminum (represented by BG rod), α3=23.1ppm / ℃, E3=70Gpa, v3=0.33, ρ3=2.7g / cm 3 . The geometric dimensions are l1=10mm, l2=16mm, θ1=60°, θ2=45°, t=1mm. Among them, l1 is half of the length of the bottom edge of the concave hexagon, l2 is the length of the inclined edge of the concave hexagon. E1 and E3, α1 and α3, v1 and v3 represent the Young's modulus, thermal expansion coefficient and Poisson's ratio of invar and aluminum respectively. t represents the thickness of the rod.

[0036] Figure 3(a) is the effect of the change of θ1 on the thermal expansion coefficients of the material in two directions, where AM represents the result of the analytical solution, and FEM represents the result of the finite element. H and C represent the results of the heating and cooling, respectively. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of not more than 0.15%, indicating that the analytical solution has high accuracy. Among them, the error calculation method is as follows: the absolute value of the difference between the analytical solution and the finite element result, divided by the absolute value of the maximum of the analytical solution obtained in the process of changing the independent variable. Second, it can be seen that the thermal expansion coefficient in the x direction is monotonically increasing, whether it is heating or cooling, while the thermal expansion coefficient in the y direction first increases and then decreases. In addition, when heating, the expansion coefficients in two directions are positive, while when cooling, negative thermal expansion coefficients appear in a certain interval, among which when θ1 takes about 60°-64°, the expansion coefficients of the material in two directions can realize the singular characteristic of changing sign when heating and cooling.

[0037] Figure 3 (b) is the effect of the change of θ1 on the Poisson's ratio and Young's modulus of the material in the y direction when tension and compression, where S and C represent the results of tension and compression, respectively. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of not more than 0.41%, indicating that the analytical solution has high accuracy. Second, it can be seen that whether tension or compression, or Poisson's ratio, monotonically increases with the increase of θ1, and in the whole independent variable interval, the Poisson's ratio of tension and compression is opposite in sign. That is, combined with the properties under temperature load, it can be known that the material can realize the change of sign of thermal expansion coefficient and Poisson's ratio at the same time when θ1 takes about 60°-64°. The Young's modulus monotonically increases when tension and increases first and then decreases when compression. It is worth noting that the Young's modulus of the material in the y direction when tension and compression is significantly different, when θ1 = 60°, the modulus when compression is 10.8 times the modulus when tension, which is also not a common property.

[0038] Figure 3 (c) shows the effect of the change of θ1 on the Poisson's ratio and Young's modulus of the material in the x direction when tension and compression, similarly, the analytical solution results and the finite element results agree well, with a maximum error of not more than 0.55%, and whether tension or compression, or Poisson's ratio and modulus, monotonically increases with the increase of θ1, and in the whole independent variable interval, the Poisson's ratio of tension and compression is opposite in sign. Considering that the density of the material at different angles is different, as shown in Figure 3 (d) can be seen that the specific stiffness of the material in two directions monotonically increases with θ1 when tension and compression, and when θ1 = 88°, the specific stiffness in the y direction when compression can reach a relatively large value of 0.36.

[0039] 2.2, the effect of θ2

[0040] Next, the influence of the change of the angle θ2 between the horizontal base of the concave hexagon and the connecting diagonal between the isosceles triangle and the vertex of the concave hexagon (such as the angle between AG and AB) on the material properties is considered. The range of variation of θ2 is 5°-40°.

[0041] Figure 4 (a) is the influence of the change of θ2 on the thermal expansion coefficients of the material in two directions. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of no more than 1.1%. Second, it can be seen that when heated, the expansion coefficients in both directions first increase and then decrease, and are all positive; while when cooled, they all monotonically decrease, and negative thermal expansion coefficients appear in a certain interval; among them, when θ2 takes about 30°-40°, the expansion coefficients of the material in two directions can realize the sign change when heated and cooled.

[0042] Figure 4 (b) is the influence of the change of θ2 on the Poisson's ratio and Young's modulus of the material when stretched and compressed in the y direction. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of no more than 0.24%. Second, it can be seen that whether stretched or compressed, the Poisson's ratio and Young's modulus all monotonically increase with the increase of θ2, and in the entire interval of the independent variable, the material is a negative Poisson's ratio. Compared with the case in 2.1, the Young's modulus of the material in the y direction when stretched and compressed does not show a significant difference when θ2 changes. Figure 4 (c) shows the influence of the change of θ2 on the Poisson's ratio and Young's modulus of the material when stretched and compressed in the x direction, and similarly, the analytical solution results and the finite element results agree well, with a maximum error of no more than 0.28%, in addition, when stretched, the Poisson's ratio monotonically decreases, while when compressed, it first decreases and then increases, and the Young's modulus monotonically increases with the increase of θ2 whether stretched or compressed. However, from Figure 4 (d) it can be seen that the specific stiffness of the material in both directions when stretched and compressed monotonically increases with θ2, and when θ2=40°, the specific stiffness when compressed can reach 8.9 times that when stretched, which reflects the huge difference in strength of the material when stretched and compressed. Compared with compression, the change of specific stiffness in two directions when stretched is not obvious.

[0043] 2.3, the influence of l2 / l1

[0044] Then the influence of the change of the ratio of half the length of the horizontal base of the concave hexagon to the length of the diagonal l2 / l1 on the material properties is considered. The range of variation of l2 / l1 is 1.2-1.9, and the rest of the geometric parameters remain unchanged. Figure 5(a) is the effect of the change of l2 / l1 on the thermal expansion coefficients of the material in two directions. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of no more than 0.83%. Second, it can be seen that the expansion coefficients in both directions are positive during heating, and the x-direction first decreases slightly and then increases significantly, while the y-direction increases monotonously, and during cooling, they all decrease from positive to negative, and then increase to positive again, wherein when l2 / l1 is about 1.55-1.9, the expansion coefficients of the material in both directions can change sign during heating and cooling.

[0045] Figure 5 (b) is the effect of the change of l2 / l1 on the Poisson's ratio and Young's modulus of the material in the y-direction under tension and compression. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of no more than 1.2%. Second, it can be seen that the Poisson's ratio decreases monotonously with the increase of l2 / l1 under tension, and is always negative, while under compression, the Poisson's ratio increases from positive to negative. Thus, it can also be known that when l2 / l1 is about 1.55-1.7, the material can simultaneously achieve the change of sign of the thermal expansion coefficient and the Poisson's ratio. The modulus first increases and then decreases under tension and compression. Similar to the case in 2.1, the Young's modulus of the material in the y-direction under tension and compression differs significantly when l2 / l1 changes, and when l2 / l1 = 1.9, the modulus under compression is 25.9 times that under tension, which is a surprising difference. Figure 5 (c) shows the effect of the change of l2 / l1 on the Poisson's ratio and Young's modulus of the material in the x-direction under tension and compression, and similarly, the analytical solution results and the finite element results agree well, with a maximum error of no more than 0.19%, in addition, under tension, the Poisson's ratio monotonously increases, while under compression, the trend is opposite, and the Poisson's ratio decreases from positive to negative, the modulus monotonously decreases with the increase of l2 / l1 under tension and compression, and when l2 / l1 = 1.9, the modulus under compression is 20.2 times that under tension. And from Figure 5 (d) it can be seen that the specific stiffness of the material in the y-direction under tension and compression both first increases and then decreases with the increase of l2 / l1, while the x-direction monotonously decreases, and when l2 / l1 = 1.9, the specific stiffness under compression can reach 26.24 times that under tension, which again reflects the huge difference in strength of the material under tension and compression.

[0046] 2.4, the effect of t / l1

[0047] Finally, the effect of the change of twice the slenderness ratio of the rod AB (the rod used to form the bottom side of the concave hexagon) t / l1 (the slenderness ratio refers to the ratio of the thickness of the rectangular rod (the thickness of the short side of the rectangle) to the length of AB rod) on the material properties is considered. Let the change range of t / l1 be 0.05-0.19, and the rest of the geometric parameters remain unchanged. Figure 6(a) is the effect of the change of t / l1 on the thermal expansion coefficients of the material in two directions. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of not more than 0.69%. Second, it can be seen that when the temperature rises, the expansion coefficients in two directions are positive, and both monotonically decrease with the increase of t / l1, while when the temperature drops, they all monotonically increase from negative values, and when t / l1 takes about 0.05-0.13, the expansion coefficients of the material in two directions can realize the sign change when the temperature rises and drops.

[0048] Figure 6 (b) is the effect of the change of t / l1 on the Poisson's ratio and Young's modulus of the material when stretched and compressed in the y direction. First, it can be seen that the analytical solution results and the finite element results agree well, with a maximum error of not more than 1.7%. Second, it can be seen that the Poisson's ratio monotonically increases with the increase of t / l1, and is negative when stretched and positive when compressed. Thus, when t / l1 takes about 0.05-0.13, the material can realize the sign change of the thermal expansion coefficient and the Poisson's ratio at the same time. The modulus also monotonically increases whether stretched or compressed. Similarly, the Young's modulus of the material in the y direction when stretched and compressed changes significantly when t / l1 changes, and when t / l1=0.05, the modulus when compressed is 13.6 times the modulus when stretched, which is also a surprising difference.

[0049] Figure 6 (c) shows the effect of the change of t / l1 on the Poisson's ratio and Young's modulus of the material when stretched and compressed in the x direction, and similarly, the analytical solution results and the finite element results agree well, with a maximum error of not more than 3.8%, in addition, the Poisson's ratio and modulus in two directions monotonically increase with the increase of t / l1, and the signs of the Poisson's ratio when stretched and compressed are always opposite. From Figure 6 (d), it can be seen that the specific stiffness of the material in two directions when stretched and compressed monotonically increases with t / l1, and when t / l1=0.05, the specific stiffness when compressed in the y direction can also reach 13.6 times that when stretched, which again reflects the huge difference in strength of the material when stretched and compressed.

[0050] From the above 4 groups of different parameter analysis, it can be seen that the error between the analytical solution and the finite element results is very small, which shows the accuracy of the analytical solution derived by the present application, at the same time, it also gives a plurality of parameter intervals that can realize the sign change of the thermal expansion coefficient / Poisson's ratio, and it is found that the stiffness of the material also changes significantly when stretched and compressed. These novel and unique properties will make the proposed material have a wider application space.

[0051] The embodiments of the present application are described in detail above, but the present application is not limited to the described embodiments. Various changes, modifications, replacements, and variations of the embodiments can be made by those skilled in the art without departing from the principles and spirit of the present application, and still fall within the scope of the present application.

Claims

1. A mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio, characterized in that: The mechanical metamaterial includes a plurality of unit cell structures, each of which is a concave hexagonal honeycomb structure comprising two horizontal bases and four oblique sides, and isosceles triangles made of another material are connected at two concave points, the two isosceles triangles are connected to the concave points at their vertices, the bases of the two isosceles triangles are initially perpendicular to the base of the concave hexagon, and the two isosceles triangles are initially in contact with each other, and a connecting diagonal rod is provided between the base angles of the two isosceles triangles and the vertices of the concave hexagon; The fact that both the thermal expansion coefficient and Poisson's ratio can change sign means that when the structure is compressed in the y-direction or the ambient temperature rises, the bases of the two isosceles triangles tend to move toward each other, causing the two rods to remain stuck together and the entire structure to eventually elongate in the x-direction. At this time, both the Poisson's ratio and the thermal expansion coefficient in the x-direction are positive. However, when the structure is stretched in the y-direction or the ambient temperature drops, the bases of the two isosceles triangles tend to move away from each other and eventually separate the two rods. The movement of the rods will drive the entire structure to eventually stretch in the x-direction. At this time, the Poisson's ratio and the thermal expansion coefficient in the x-direction are both negative, thereby achieving a change in the sign of the Poisson's ratio and the thermal expansion coefficient in the x-direction.

2. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: Multiple unit cell structures are arranged periodically and connected to each other.

3. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 2, characterized in that: The upper and lower adjacent unit cell structures share the same bottom edge, and the left and right adjacent unit cell structures share the same two oblique edges, thus forming multiple unit cell structures.

4. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: The material of the inwardly concave hexagonal honeycomb structure and the connecting oblique rods is selected from Invar alloy, and the material of the isosceles triangle is selected from aluminum.

5. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 4, characterized in that: The Invar alloy has α1=1.1ppm / ℃, E1=144GPa, ν1=0.29, and ρ1=7.18g / cm 3 ; The aluminum α3 = 23.1ppm / ℃, E3 = 70Gpa, ν3 = 0.33, ρ3 = 2.7g / cm 3 .

6. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: The included angle θ1 between the horizontal base and the hypotenuse of the concave hexagon is 60°-64°.

7. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: The included angle θ2 between the horizontal base of the indented hexagon and the connecting diagonal rod between the isosceles triangle and the vertex of the indented hexagon is 30°-40°.

8. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: The ratio of half the length of the horizontal base of the concave hexagon to the length of the hypotenuse, l2 / l1, is 1.55-1.

9.

9. The mechanical metamaterial with variable thermal expansion coefficient and Poisson's ratio according to claim 1, characterized in that: The double of the slenderness ratio t / l1 of the rod constituting the base of the concave hexagon is 0.05-0.13.

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