Design method and product of zero / negative thermal expansion coefficient metamaterial made of single solid material

Abstract

The invention belongs to the related technical field of metamaterials, and discloses a design method and a product of a zero / negative thermal expansion coefficient metamaterial made of a single solid material. The method comprises the following steps: dividing a design domain into a high-pressure gas region, a low-pressure gas region and a solid region, wherein the solid region is used for isolating the high-pressure gas region from the low-pressure gas region; setting a thermal expansion coefficient and an elastic modulus of the solid area; adjusting the form of the solid region and the air pressure of the gas region so that the deformation of the solid region generated under the pressure difference between the high-pressure gas region and the low-pressure gas region is equal to zero heat or negative thermal expansion of the solid region generated under the temperature change under the condition that the temperature in the design region is changed; in this way, the required form and air pressure of the solid area are obtained. According to the invention, the thermal expansion performance is accurately regulated and controlled, and the method is suitable for application scenes with high requirements on size thermal stability, such as aerospace and precise instruments.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of metamaterials, and more particularly relates to a design method and product of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material. BACKGROUND

[0002] Natural materials have the common physical phenomenon of size change during temperature change, and most of them expand when heated. For fields such as aerospace, semiconductor manufacturing, precision measurement, and optical devices that have extremely high requirements for size stability, errors or stress concentrations caused by thermal deformation of the structure can lead to performance degradation or even failure. Therefore, developing materials and structures with zero thermal expansion coefficient (CTE≈0) or negative thermal expansion coefficient (CTE<0) has always been an important research direction in the field of advanced manufacturing and functional materials.

[0003] The existing design method of zero / negative thermal expansion metamaterials mainly relies on the combination of multiple materials with different thermal expansion coefficients to form a complex multi-phase structure. For example, according to the Gibiansky-Torquato model, three materials with different thermal expansion coefficients are usually required, including at least two different solid materials and one cavity material. Although this design can achieve macroscopic thermal expansion regulation, it has the following key problems: (1) The thermal physical properties of different solid materials differ significantly, and the interface bonding is difficult, especially under the action of multiple thermal cycles, which can easily cause interface debonding or peeling, affecting the structural reliability; (2) The design of a multi-solid-phase metamaterial usually has a complex spatial configuration, which requires high manufacturing process, and even with additive manufacturing, it is difficult to form at one time, increasing the manufacturing difficulty and cost; Therefore, a design method is needed to solve the above problems. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a design method and product of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material, aiming to solve the problems of existing multi-material combination type zero / negative thermal expansion metamaterials, such as difficult interface bonding (easy to debond or peel off under multiple thermal cycles, affecting the structural reliability), high manufacturing process requirements due to complex spatial configuration, difficult to form at one time, and increased cost.

[0005] To achieve the above purpose, according to one aspect of the present application, a design method of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material is provided, which includes the following steps: Divide the design domain into a high-pressure gas region, a low-pressure gas region, and a solid region, and the solid region is used to isolate the high-pressure gas region and the low-pressure gas region; Setting the thermal expansion coefficient and elastic modulus of the solid region; Adjusting the shape of the solid region and the gas pressure of the gas region so that the deformation of the solid region caused by the pressure difference between the high-pressure gas region and the low-pressure gas region under the change of temperature in the design domain is equal to the zero thermal or negative thermal expansion of the solid region caused by the change of temperature, thereby obtaining the required shape of the solid region and gas pressure.

[0006] Further preferably, the solid region is a metamaterial.

[0007] Further preferably, the high-pressure gas region or the low-pressure gas region is surrounded by the solid region to form a closed cavity.

[0008] Further preferably, the shape of the solid region includes the wall thickness, geometric size, and volume of the solid region.

[0009] Further preferably, both the high-pressure gas region and the low-pressure gas region are closed cavities, and the number of moles of gas in the high-pressure gas region cavity and the low-pressure gas region cavity remains unchanged during the change of temperature.

[0010] Further preferably, the solid region forms a closed cavity, the high-pressure gas is arranged in the cavity, and the low-pressure gas is arranged outside the cavity to form a low-pressure gas region, which is in communication with the external space and is a vacuum or a normal pressure environment.

[0011] Further preferably, the solid region forms a closed cavity, the low-pressure gas is arranged in the cavity, and the high-pressure gas is arranged outside the cavity to form a high-pressure gas region, and the low-pressure gas region is a vacuum or normal pressure.

[0012] Further preferably, the cavity formed by the solid region includes two structurally identical quadrangular pyramids and a middle cube, the cube is arranged between the two quadrangular pyramids, and the cross section of the cube is the same as the bottom surface of the quadrangular pyramids.

[0013] According to another aspect of the present application, a unit cell structure obtained by using the design method described above is provided.

[0014] According to an aspect of the present application, an isotropic metamaterial is provided, which is formed by combining an array of the unit cell structures described above.

[0015] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects: 1. The present application designs different regions, sets different pressures in different regions, and realizes the deformation caused by the pressure difference by adjusting the gas pressure and the shape of the solid region. The method uses a single solid material for the solid region, which avoids the problem of multi-material interface debonding from the root, and combines the gas pressure control mechanism to drive the solid region to produce compensating deformation using the high and low pressure gas pressure difference caused by temperature change. Finally, the thermal expansion performance is accurately controlled. At the same time, the single material structure is matched with the gas pressure control mechanism, the configuration is simplified, the manufacturing requirements are reduced, and the existing design and manufacturing difficulties and high cost problems are solved. The thermal expansion is accurately controlled, and the engineering application feasibility is improved.

[0016] 2. The present application sets the material of the solid region as a metamaterial, which can be designed to have macroscopic physical properties and flexible response characteristics to temperature and pressure, so that the solid region can isolate high and low pressure gas, and can enhance the sensitivity of the gas pressure difference by optimizing the microstructure (such as wall thickness, geometric shape) to efficiently produce compensating deformation to offset temperature deformation, improve zero / negative thermal expansion control precision and stability, and ensure structure size stability under temperature fluctuations.

[0017] 3. The present application designs the solid region as a closed cavity to stably isolate high and low pressure gas to form a controllable pressure difference, which can avoid gas mixing to ensure stable pressure difference, and can accurately control deformation by adjusting geometric parameters to improve the controllability and reliability of zero / negative thermal expansion performance.

[0018] 4. The present application proposes a systematic design method for realizing zero or negative thermal expansion effect based on a single solid material combined with a gas pressure adjustable control mechanism. Through structure design and thermal-mechanical coupling analysis, the deformation compensation of the solid region caused by the change of gas pressure due to temperature is used to provide a new solution for realizing structure thermal stability, and significantly improve the designability, manufacturability and application feasibility of such metamaterials. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 It is a flow chart of a design method of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material according to the preferred embodiment of the present application.

[0020] Figure 2 It is an axonometric drawing of a zero thermal expansion metamaterial unit cell according to the preferred embodiment of the present application.

[0021] Figure 3is a cross-sectional view of a zero thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present application, wherein (a) is the cross-sectional state of the zero thermal expansion metamaterial unit cell at temperature T1, (b) is the state of the unit cell after the cross-sectional morphology has changed as a result of the deformation of the solid region driven by the pressure difference between the high and low pressure gases when the temperature is raised to T2 (T2>T1).

[0022] Figure 4 is an axonometric view of a negative thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present application.

[0023] Figure 5 is a cross-sectional view of a negative thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present application, wherein (a) is the cross-sectional state of the negative thermal expansion metamaterial unit cell at temperature T1, (b) is the state of the unit cell after the cross-sectional morphology has changed as a result of the reverse deformation of the solid region driven by the pressure difference between the high and low pressure gases when the temperature is raised to T2 (T2>T1).

[0024] Figure 6 is a cross-sectional view of a three-dimensional plate metamaterial T2 lower structure constructed according to a preferred embodiment of the present application.

[0025] In all the drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1 - solid region, 2 - high pressure region, 3 - low pressure region. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely intended to explain the present application and are not intended to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0027] A design method of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material, comprising the following steps: (1) selecting a single solid material with known thermal expansion coefficient and elastic modulus as the solid matrix of the metamaterial, and selecting two gases with known gas constants as the gas matrix of the metamaterial.

[0028] (2), taking the above parameters as the material basic parameters for structural response analysis. In the design domain, three types of functional regions are divided: solid region S, high pressure gas region H and low pressure gas region L. The high pressure gas region H and the low pressure gas region L are completely isolated by the solid region S, and a metamaterial unit cell with thermal driven characteristics is constructed.

[0029] (2) Set the boundary conditions of the high-pressure gas region H and the low-pressure gas region L, at least one of which is a sealed cavity, to ensure that the number of moles of gas remains constant during temperature changes. According to the ideal gas state equation , the gas pressure values of each gas region at different temperatures are calculated respectively, and the pressure difference ΔP is calculated as the input thermal load for subsequent analysis.

[0030] (3) Apply the pressure difference ΔP as an equivalent thermal load to the solid region S, and obtain the deformation behavior of the metamaterial under temperature rise or fall conditions through finite element simulation or analytical calculation or experimental testing, to obtain the overall deformation distribution and deformation direction of the solid region.

[0031] (4) According to the results of the finite element simulation or analytical calculation or experimental testing of (3), adjust the metamaterial parameters, including solid wall thickness, cavity volume, initial pressure, and geometry, through an optimization algorithm, and repeat step (3) until the solid region achieves zero thermal expansion (ΔL / L ≈ 0) or negative thermal expansion (ΔL / L < 0) effect in one or more directions under temperature changes.

[0032] (5) When the metamaterial response meets the preset thermal expansion performance indicators, output the current metamaterial unit cell configuration, and can be copied in the three-dimensional direction through orthogonal arrangement to form a metamaterial array with isotropic zero / negative thermal expansion performance.

[0033] In the process of selecting and designing metamaterials, the high-pressure gas region H and the low-pressure gas region L can both be sealed cavities, and the number of moles of gas remains constant throughout the thermal cycle, and the pressure changes proportionally with temperature, suitable for closed environment application scenarios.

[0034] In the process of selecting and designing metamaterials, the high-pressure gas region H is a sealed cavity, while the low-pressure gas region L is connected to the external open space (i.e. the gas pressure remains constant, which can be atmospheric pressure or vacuum), suitable for semi-open system structure design.

[0035] A zero / negative thermal expansion coefficient metamaterial composed of a single solid material, the solid region S can adopt an octahedral unit cell with a cavity inside, the high-pressure gas region H is located inside the center cavity of the unit cell, and the low-pressure gas region L surrounds the periphery, forming a two-way pressure control layout through the cavity position relationship.

[0036] A design method of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material, through finite element simulation or analytical calculation or experimental testing, simulating the structure thermal-force response under different temperature conditions, calculating the overall size change of the solid region S, and drawing the curve, and combining the optimization algorithm to iteratively update the wall thickness, cavity shape, initial pressure and other metamaterial parameters, until the optimal design result is output when the zero / negative thermal expansion performance target is met.

[0037] The present invention will be further described below with reference to specific embodiments.

[0038] Example 1 This embodiment provides a method for designing a three-dimensional metamaterial with zero thermal expansion in a specified direction. The metamaterial is composed of a single solid material, and the aim is to design a metamaterial with an approximately zero thermal expansion coefficient in the Y direction. The method specifically includes the following steps: Material and parameter settings: Select a single solid material with a coefficient of thermal expansion of . The elastic modulus is Set the material's operating temperature range [T] min T max The design goal is to achieve an approximate zero macroscopic thermal expansion coefficient in the Y direction.

[0039] Structural Region Division: An octahedral unit cell structure with internal cavities is constructed within the design domain, dividing it into three regions: solid region S, high-pressure gas region H, and low-pressure gas region L. The high-pressure gas region and the low-pressure gas region are completely separated by the solid region.

[0040] Gas distribution scheme selection: A scheme is selected where the high-pressure gas region is a sealed cavity, and the low-pressure gas region is connected to an open space. The gas pressure in the low-pressure gas region remains constant. (Can be in vacuum or at atmospheric pressure).

[0041] Calculating pressure difference using the ideal gas law: Based on the ideal gas law, calculate the gas pressure in a high-pressure gas region at different temperatures. :

[0042] Pressure difference:

[0043] Thermo-mechanical coupling analysis: ΔP(T) is applied as a thermal load to the solid region, and a finite element model is established to calculate the total deformation of the solid region under the action of ΔP(T) and its own thermal expansion. .

[0044] Structural parameter optimization: Adjusting the thickness of the solid region and the volume of the air cavity. Initial pressure Repeat step (5) with equal parameters, iterating the thermo-mechanical coupling analysis and structural parameter optimization process through the optimization algorithm, so that in hour This ensures that the macroscopic thermal expansion coefficient in the Y direction is close to zero.

[0045] Simulation verification: The optimized structure was verified through finite element simulation. The results show that in [T min T maxThe macroscopic thermal expansion coefficient of the structure in the Y direction in the temperature range .

[0046] The above embodiment obtains a metamaterial unit cell configuration with macroscopic zero thermal expansion performance in the Y direction. The unit cell is an octahedral structure with an internal cavity. Key parameters such as the wall thickness of the solid region, the initial gas pressure of the high-pressure gas region, and the cavity volume are determined.

[0047] Embodiment 2 The present embodiment provides a three-dimensional plate-type metamaterial unit cell that exhibits negative thermal expansion effect in a single direction. The structure shrinks as a whole when heated, and is suitable for high-precision thermal stability control scenarios. The present embodiment is further optimized based on Embodiment 1, and the design goal is to achieve negative thermal expansion coefficient in the Y direction. The specific differences are: By reducing the wall thickness of the solid region S, under the action of the same pressure difference ΔP(T), more significant inward concave or bending deformation is induced. The deformation direction is opposite to the intrinsic thermal expansion direction of the material, thereby producing a negative thermal expansion effect in the Y direction on the macroscopic level, making .

[0048] The above embodiment obtains a three-dimensional plate-type metamaterial unit cell configuration that exhibits stable negative thermal expansion effect in the Y direction. The wall thickness of the solid region is thinner than that of Embodiment 1, and the corresponding initial gas pressure of the high-pressure gas region and the cavity volume are matched.

[0049] Embodiment 3 The present embodiment provides an isotropic metamaterial structure design method that simultaneously achieves zero thermal expansion response in multiple directions. The structure is composed of a single material unit cell arranged symmetrically, and is suitable for three-dimensional size thermal stability application scenarios.

[0050] The unit cell optimized in Embodiment 1 is used as the basic component. It is arranged orthogonally along the X, Y, and Z directions to construct a three-dimensional lattice structure. The gas arrangement, cavity structure, and pressure difference distribution in each direction are ensured to be consistent. The results are verified by full-structure finite element analysis, and the macroscopic thermal expansion coefficient in any direction satisfies .

[0051] The above embodiment obtains an isotropic metamaterial array that achieves zero thermal expansion response in the X, Y, and Z directions. The array is composed of the zero thermal expansion unit cell optimized in Embodiment 1 arranged orthogonally in three-dimensional directions, and the gas arrangement, cavity structure, and pressure difference distribution in each direction remain consistent.

[0052] Embodiment 4 The present embodiment provides an isotropic metamaterial structure composed of negative thermal expansion unit cells arranged orthogonally. It can produce a macroscopic shrinkage effect in the X, Y, and Z directions under heating conditions, and is suitable for multi-axial thermal stability control occasions.

[0053] The single cell structure optimized in Example 2 is used as a constituent unit. It is arranged orthogonally along the X, Y, and Z directions to construct a three-dimensional lattice structure; the gas distribution and pressure setting are kept consistent in each direction. After full-structure finite element simulation verification, the three-dimensional structure can achieve macroscopic negative thermal expansion characteristics in each direction, meeting the .

[0054] The isotropic metamaterial array with macroscopic negative thermal expansion characteristics in the X, Y, and Z directions is obtained in the above example. The array uses the negative thermal expansion single cell optimized in Example 2 as a constituent unit, is arranged orthogonally along the three-dimensional direction, and the gas distribution and pressure setting in each direction are kept uniform.

[0055] Example 5 To verify the effectiveness of the method of the present application, the implementation method of the present application is specifically described below in combination with the drawings.

[0056] Aluminum alloy (Al 6061) , ) is used as the solid material 1, and the design temperature range is 20°C to 120°C. The high-pressure gas region 2: a closed cavity, initial temperature 20°C, initial pressure 0.1 MPa, volume . The low-pressure gas region 3: a connected open space, with a constant gas pressure of 0.1 MPa (atmospheric pressure).

[0057] Objective: Y-direction length change under 100°C temperature rise (zero thermal expansion target).

[0058] After multiple rounds of parameter optimization, the solid region thickness is finally 1.2 mm, the high-pressure cavity volume , as shown in Figure 2 and Figure 3 , the solid material is 1, the high-pressure gas region is 2, and the low-pressure gas region is 3. The finite element calculation result shows that the Y-direction thermal expansion coefficient is in the range of , the thermal expansion coefficient is reduced by 115 times, meeting the (near) zero thermal expansion design requirement, and realizing the zero thermal expansion metamaterial design.

[0059] After further reducing the solid region thickness to 0.8 mm, as shown in Figure 4 and Figure 5 , the solid material is 1, the high-pressure gas region is 2, and the low-pressure gas region is 3. The simulation result shows that the Y-direction thermal expansion coefficient is , realizing the negative thermal expansion metamaterial design.

[0060] The aforementioned zero thermal expansion metamaterial ( Figure 2 ) is arranged according to Figure 6The negative thermal expansion coefficient isotropic material is obtained by arranging the negative thermal expansion coefficient material (1000) according to the arrangement shown in the isometric view of the negative thermal expansion coefficient material unit cell (1000). Figure 4 The negative thermal expansion coefficient isotropic material is obtained by arranging the negative thermal expansion coefficient material (1000) according to the arrangement shown in the isometric view of the negative thermal expansion coefficient material unit cell (1000). Figure 6 The negative thermal expansion coefficient isotropic material is obtained by arranging the negative thermal expansion coefficient material (1000) according to the arrangement shown in the isometric view of the negative thermal expansion coefficient material unit cell (1000).

[0061] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figure 2 As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature.

[0062] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figure 3 As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature.

[0063] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figure 4 As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature.

[0064] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figure 5 As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature.

[0065] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figure 6 As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature.

[0066] As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. As shown in the isometric view of the zero thermal expansion coefficient material unit cell, the solid area (1) is thick, and the high-pressure gas area (2) is isolated from the low-pressure gas area (3), which reflects the zero thermal expansion design feature. Figures 2-5By showing the structural deformation of zero / negative thermal expansion cells at different temperatures (the size of zero thermal expansion cell is approximately unchanged, and the negative thermal expansion cell shrinks), the "zero / negative" characteristics are further intuitively presented, and the "zero / negative thermal expansion coefficient" in the title is fully embodied.

[0067] Those skilled in the art will easily understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of designing a zero / negative thermal expansion coefficient metamaterial composed of a single solid material, characterized in that, The method comprises the following steps: The design domain is divided into high-pressure gas region, low-pressure gas region and solid region, the solid region is made of single solid material, and is used for isolating the high-pressure gas region and the low-pressure gas region; The thermal expansion coefficient and the elastic modulus of the solid region are set; The shape of the solid region and the gas pressure of the gas region are adjusted, so that the deformation of the solid region caused by the pressure difference between the high-pressure gas region and the low-pressure gas region under the change of the temperature in the design domain is equal to the zero thermal or negative thermal expansion of the solid region caused by the change of the temperature, so as to obtain the required shape of the solid region and the gas pressure.

2. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 1, wherein, The solid region is a metamaterial.

3. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 1, wherein, The shape of the solid region comprises the wall thickness, the geometric size and the volume of the solid region.

4. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 3, wherein, The high-pressure gas region or the low-pressure gas region is surrounded by the solid region to form a closed cavity.

5. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 4, wherein, The high-pressure gas region and the low-pressure gas region are both closed cavities, and the number of moles of the gas in the high-pressure gas region cavity and the low-pressure gas region cavity remains unchanged during the change of the temperature.

6. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 4, wherein, The solid region forms a closed cavity, the high-pressure gas is arranged in the cavity, and the low-pressure gas is arranged outside the cavity to form a low-pressure gas region, the low-pressure gas region is in communication with the external space, and is a vacuum or a normal pressure environment.

7. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 4, wherein, The solid region forms a closed cavity, the low-pressure gas is arranged in the cavity, and the high-pressure gas is arranged outside the cavity to form a high-pressure gas region, and the low-pressure gas region is a vacuum or a normal pressure.

8. A method of designing a zero / negative thermal expansion coefficient metamaterial made of a single solid material as claimed in claim 1 or 4, wherein, The cavity formed by the solid region comprises two four-prism structures with the same structure and a cubic body arranged between the two four-prism structures, and the cross section of the cubic body is the same as the bottom surface of the four-prism structure.

9. A unit cell structure obtained by using the design method in any one of claims 1-8.

10. An isotropic metamaterial, characterized in that, The isotropic metamaterial is formed by combining the unit cell structure array in claim 9.

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