A method of designing and product of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material

Abstract

The application belongs to the technical field of metamaterials, and discloses a design method and product of a zero / negative thermal expansion coefficient metamaterial composed 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 for isolating the high-pressure gas region and the low-pressure gas region; setting the thermal expansion coefficient and the 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 under the pressure difference between the high-pressure gas region and the low-pressure gas region at a changed temperature in the design domain is equal to the zero thermal or negative thermal expansion of the solid region under the temperature change, thereby obtaining the required shape of the solid region and the gas pressure. Through the application, the thermal expansion performance is accurately controlled, and the application is suitable for aerospace, precision instruments and other application scenarios with high requirements for size thermal stability.

Description

Technical Field

[0001] This invention belongs to the field of metamaterials technology, and more specifically, relates to a design method and product of a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material. Background Technology

[0002] Natural materials universally exhibit dimensional changes during temperature variations, with the vast majority being thermal expansion. In fields such as aerospace, semiconductor manufacturing, precision measurement, and optical devices, where dimensional stability is paramount, errors or stress concentrations caused by thermal deformation can lead to performance degradation or even failure. Therefore, developing materials and structures with zero coefficient of thermal expansion (CTE≈0) or negative coefficient of thermal expansion (CTE<0) has been a crucial research direction in advanced manufacturing and functional materials.

[0003] Existing methods for designing zero / negative thermal expansion metamaterials primarily rely on combinations of materials with different coefficients of thermal expansion to construct complex multiphase structures. For example, according to models such as Gibiansky-Torquato, three materials with different coefficients of thermal expansion are typically required, including at least two different solid materials and one cavity material. While this type of design can achieve macroscopic thermal expansion control, it suffers from the following key problems:

[0004] (1) The thermophysical properties of different solid materials are significantly different, making it difficult to bond at the interface. In particular, under repeated thermal cycles, the interface is prone to debonding or peeling, which affects the reliability of the structure.

[0005] (2) Metamaterials with multiple solid phases usually have complex spatial configurations and require high manufacturing processes. Even with additive manufacturing, it is difficult to form them in one step, which increases the manufacturing difficulty and cost.

[0006] Therefore, continuing with a design approach can solve the above problems. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a design method and product of a zero / negative thermal expansion coefficient metamaterial composed of a single solid material. It aims to solve the problems of interface bonding difficulties (debonding or peeling easily occurs after multiple thermal cycles, affecting structural reliability) and high manufacturing process requirements, difficulty in one-time molding, and increased cost caused by complex spatial configuration of existing multi-material composite zero / negative thermal expansion metamaterials.

[0008] To achieve the above objectives, according to one aspect of the present invention, a method for designing a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material is provided, the method comprising the following steps:

[0009] The design domain is divided into a high-pressure gas region, a low-pressure gas region, and a solid region. The solid region is used to isolate the high-pressure gas region and the low-pressure gas region.

[0010] Set the coefficient of thermal expansion and the elastic modulus of the solid region;

[0011] The shape of the solid region and the gas pressure of the gas region are adjusted so that the deformation of the solid region under the pressure difference between the high-pressure gas region and the low-pressure gas region when the temperature in the design domain is changed is equal to the zero-thermal or negative-thermal expansion of the solid region under temperature change, thereby obtaining the desired shape and gas pressure of the solid region.

[0012] More preferably, the solid region is a metamaterial.

[0013] More preferably, the high-pressure gas region or the low-pressure gas region is surrounded by the solid region to form a closed cavity.

[0014] More preferably, the morphology of the solid region includes: the wall thickness, geometric dimensions, and volume of the solid region.

[0015] More preferably, both the high-pressure gas region and the low-pressure gas region are sealed cavities, and the number of gas moles in the high-pressure gas region cavity and the low-pressure gas region cavity remains constant during temperature changes.

[0016] More preferably, the solid region forms a closed cavity, the high-pressure gas is disposed in the cavity, and a low-pressure gas is disposed outside the cavity to form a low-pressure gas region, which is connected to the outside space and is a vacuum or normal pressure environment.

[0017] More preferably, the solid region forms a closed cavity, the low-pressure gas is disposed in the cavity, and a high-pressure gas is disposed outside the cavity to form a high-pressure gas region, wherein the low-pressure gas region is a vacuum or at atmospheric pressure.

[0018] More preferably, the cavity formed by the solid region includes two identical square pyramids and a cube in the middle, with the cube positioned between the two square pyramids and the cross-section of the cube being the same as the base of the square pyramids.

[0019] According to another aspect of the present invention, a unit cell structure obtained using the design method described above is provided.

[0020] According to one aspect of the present invention, an isotropic metamaterial is provided, which is formed by assembling the above-described unit cell structure array.

[0021] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0022] 1. This invention designs different regions with varying pressures. By adjusting the air pressure and the shape of the solid regions, the deformation caused by the pressure difference equals the deformation of the solid regions caused by temperature. This method uses a single solid material for the solid regions, fundamentally avoiding the problem of debonding at multi-material interfaces. Simultaneously, it incorporates a gas pressure control mechanism, utilizing the high and low pressure gas pressure difference caused by temperature changes to drive compensatory deformation in the solid regions, ultimately achieving precise control of thermal expansion performance. Furthermore, the single-material structure combined with the gas pressure control mechanism simplifies the configuration, reduces manufacturing requirements, and facilitates one-time molding, solving the problems of difficult and costly manufacturing in existing designs, achieving precise control of thermal expansion, and improving the feasibility of engineering applications.

[0023] 2. This invention sets the material of the solid region as a metamaterial, utilizing its designable macroscopic physical properties and flexible response characteristics to temperature and pressure. This allows the solid region to not only isolate high and low pressure gases, but also enhance the sensitivity to pressure differences by optimizing the microstructure (such as wall thickness and geometry). This efficiently generates compensating deformation to offset temperature deformation, improves the accuracy and stability of zero / negative thermal expansion control, and ensures the stability of structural dimensions under temperature fluctuations.

[0024] 3. This invention designs the solid region as a closed cavity to stably isolate high and low pressure gases to form a controllable pressure difference. This not only avoids gas mixing and ensures a stable pressure difference, but also allows for precise control of deformation by adjusting geometric parameters, thereby improving the controllability and reliability of zero / negative thermal expansion performance.

[0025] 4. This invention proposes a systematic design method based on a single solid material, combined with a gas pressure controllable mechanism, to achieve zero or negative thermal expansion effects. Through structural design and thermo-mechanical coupling analysis, the deformation compensation of the solid region is generated by the gas pressure change caused by temperature, providing a new solution for achieving structural thermal stability and significantly improving the designability, manufacturability, and application feasibility of this type of metamaterial. Attached Figure Description

[0026] Figure 1 This is a flowchart of a design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material, constructed according to a preferred embodiment of the present invention.

[0027] Figure 2 This is an isometric view of a zero thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present invention.

[0028] Figure 3The diagram shows a cross-sectional view of a zero thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present invention. (a) is the cross-sectional state of the zero thermal expansion metamaterial unit cell at temperature T1, and (b) is the state after the solid region deforms and the unit cell cross-sectional shape changes when the temperature is increased to T2 (T2>T1) under the action of the pressure difference between high and low pressure gases.

[0029] Figure 4 This is an isometric view of a negative thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present invention.

[0030] Figure 5 The diagram shows a cross-sectional view of a negative thermal expansion metamaterial unit cell constructed according to a preferred embodiment of the present invention. (a) is the cross-sectional state of the negative thermal expansion metamaterial unit cell at temperature T1, and (b) is the state after the unit cell cross-sectional shape changes when the temperature rises to T2 (T2>T1) due to the reverse deformation of the solid region driven by the pressure difference between high and low pressure gases.

[0031] Figure 6 This is a cross-sectional view of the three-dimensional plate-type metamaterial T2 structure constructed according to a preferred embodiment of the present invention.

[0032] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0033] 1-Solid region, 2-High pressure region, 3-Low pressure region. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention 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 illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0035] A design method for metamaterials with zero / negative thermal expansion coefficients composed of a single solid material, comprising the following steps:

[0036] (1) Select a single solid material with a known coefficient of thermal expansion and elastic modulus as the solid matrix of the metamaterial, and select two gases with known gas constants as the gas matrix of the metamaterial.

[0037] (2) The above parameters are used as the material basis parameters for structural response analysis. The design domain is divided into three functional regions: 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, constructing a metamaterial unit cell with thermally driven characteristics.

[0038] (2) Set boundary conditions for the high-pressure gas region H and the low-pressure gas region L, where at least one is a closed cavity to ensure that the number of gas moles remains constant during temperature changes. Based on the ideal gas law... The gas pressure values ​​of each gas region at different temperatures are calculated, and the pressure difference ΔP is obtained as the input thermal load for subsequent analysis.

[0039] (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 heating or cooling conditions through finite element simulation, analytical calculation or experimental testing, and obtain the overall deformation distribution and deformation direction of the solid region.

[0040] (4) Based on the finite element simulation or analytical calculation or experimental test results of (3), adjust the metamaterial parameters, including solid wall thickness, cavity volume, initial air pressure, and geometry, by optimizing the 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 change.

[0041] (5) When the metamaterial response meets the preset thermal expansion performance index, the current metamaterial unit cell configuration is output, and it can be replicated in three dimensions through orthogonal arrangement to form a metamaterial array with isotropic zero / negative thermal expansion performance.

[0042] In the process of selecting and designing metamaterials, both the high-pressure gas region H and the low-pressure gas region L can be closed cavities. The number of gas moles remains constant throughout the entire thermal cycle, and the pressure changes proportionally with the temperature, making it suitable for applications in closed environments.

[0043] In the process of selecting and designing metamaterials, the high-pressure gas region H is a closed cavity, while the low-pressure gas region L is connected to the external open space (i.e., the gas pressure is kept constant, which can be atmospheric pressure or vacuum), which is suitable for the design of semi-open system structures.

[0044] A metamaterial with zero / negative thermal expansion coefficient composed of a single solid material, wherein the solid region S can be an octahedral unit cell with an internal cavity, the high-pressure gas region H is located inside the central cavity of the unit cell, and the low-pressure gas region L surrounds its periphery, forming a bidirectional pressure control layout through the cavity position relationship.

[0045] A design method for metamaterials with zero / negative thermal expansion coefficients composed of a single solid material is proposed. Through finite element simulation, analytical calculation, or experimental testing, the thermo-mechanical response of the structure under different temperature conditions is simulated, the overall size change of the solid region S is calculated and the curve is plotted, and the metamaterial parameters such as wall thickness, cavity shape, and initial pressure are iteratively updated by combining optimization algorithms until the zero / negative thermal expansion performance target is met, and the optimal design result is output.

[0046] The present invention will be further described below with reference to specific embodiments.

[0047] Example 1

[0048] 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:

[0049] 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.

[0050] 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.

[0051] 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).

[0052] 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. :

[0053]

[0054] Pressure difference:

[0055] 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. .

[0056] 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.

[0057] Simulation verification: The optimized structure was verified through finite element simulation. The results show that in [T min T max Within the temperature range, the macroscopic coefficient of thermal expansion of the structure in the Y direction. .

[0058] The above embodiments yield a metamaterial unit cell configuration with macroscopic zero thermal expansion in the Y direction. The unit cell is an octahedral structure with an internal cavity, and key parameters such as the wall thickness of the suitable solid region, the initial gas pressure of the high-pressure gas region, and the cavity volume are determined.

[0059] Example 2

[0060] This embodiment provides a three-dimensional plate-like metamaterial unit cell exhibiting negative thermal expansion in a single direction. Its structure undergoes overall contraction upon heating, making it suitable for high-precision thermal stability control scenarios. This embodiment further optimizes Embodiment 1, with the design goal of achieving a negative thermal expansion coefficient in the Y direction. The specific differences are as follows:

[0061] By reducing the wall thickness of the solid region S, under the same pressure difference ΔP(T), a more significant concave or bending deformation is induced; this deformation direction is opposite to the intrinsic thermal expansion direction of the material, thus producing a negative thermal expansion effect in the Y direction on a macroscopic scale. .

[0062] The above embodiments yield a three-dimensional plate-type metamaterial unit cell configuration exhibiting a stable negative thermal expansion effect in the Y direction. The wall thickness of its solid region is thinner than that of Embodiment 1, and it matches the initial gas pressure and cavity volume of the corresponding high-pressure gas region.

[0063] Example 3

[0064] This embodiment provides a design method for an isotropic metamaterial structure that achieves zero thermal expansion response in multiple directions simultaneously. The structure is composed of symmetrically arranged single material unit cells and is suitable for three-dimensional thermally stable application scenarios.

[0065] Using the optimized unit cell obtained in Example 1 as the basic building block, a three-dimensional lattice structure was constructed by orthogonally arranging it along the X, Y, and Z directions, ensuring consistent gas arrangement, cavity structure, and pressure difference distribution in all directions. The results were verified through full-structure finite element analysis, confirming that the macroscopic thermal expansion coefficients in any direction met the requirements. .

[0066] The above embodiments yield an isotropic metamaterial array that achieves zero thermal expansion response in the X, Y, and Z directions. This array is composed of zero thermal expansion unit cells optimized in Embodiment 1 arranged orthogonally along three-dimensional directions, and the gas arrangement, cavity structure, and pressure difference distribution in each direction remain consistent.

[0067] Example 4

[0068] This embodiment provides an isotropic metamaterial structure composed of orthogonally arranged negative thermal expansion unit cells, which can produce macroscopic contraction effects in the X, Y, and Z directions under heating conditions, and is suitable for multiaxial thermal stability control applications.

[0069] The optimized unit cell structure from Example 2 was used as the constituent unit. It was orthogonally arranged along the X, Y, and Z directions to construct a three-dimensional lattice structure; the gas distribution and pressure settings remained consistent in all directions. Full-structure finite element simulation verified that this three-dimensional structure could achieve macroscopic negative thermal expansion characteristics in all directions, satisfying… .

[0070] The above embodiments yield an isotropic metamaterial array with macroscopic negative thermal expansion characteristics in the X, Y, and Z directions. The array is composed of the negative thermal expansion unit cells optimized in Embodiment 2, arranged orthogonally in three dimensions, and the gas distribution and pressure settings in each direction are kept uniform.

[0071] Example 5

[0072] To verify the effectiveness of the method of the present invention, the implementation method of the present invention will be described in detail below with reference to the accompanying drawings.

[0073] Using aluminum alloy ( , As solid material 1, the design temperature range is 20°C to 120°C. High-pressure gas region 2: a sealed cavity, initial temperature 20°C, initial pressure 0.1 MPa, volume... Low-pressure gas region 3: an open space with a constant pressure of 0.1 MPa (atmospheres).

[0074] Objective: To determine the change in length in the Y direction under a temperature increase of 100°C. (Zero thermal expansion target).

[0075] After multiple rounds of parameter optimization, the final result was a solid region thickness of 1.2 mm and a high-pressure chamber volume of [missing information]. Design, such as Figure 2 and Figure 3 As shown, solid material is represented by region 1, high-pressure gas region by region 2, and low-pressure gas region by region 3. The finite element calculation results are displayed... The coefficient of thermal expansion in the Y direction within the range is The coefficient of thermal expansion is reduced by 115 times, meeting the (near) zero thermal expansion design requirements and realizing the design of zero thermal expansion metamaterials.

[0076] After further reducing the thickness of the solid region to 0.8 mm, as follows: Figure 4 and Figure 5As shown, solid material is represented by region 1, high-pressure gas region by region 2, and low-pressure gas region by region 3. The simulation results show that the coefficient of thermal expansion in the Y direction is... This led to the design of metamaterials with negative thermal expansion.

[0077] The aforementioned zero thermal expansion metamaterial ( Figure 2 )according to Figure 6 By arranging them in a certain way, a supermaterial with an isotropic coefficient of thermal expansion of zero can be obtained. The aforementioned negative thermal expansion supermaterial ( Figure 4 )according to Figure 6 By arranging them in a certain way, we can obtain supermaterials with negative isotropic thermal expansion coefficients.

[0078] like Figure 2 The axonometric view of the zero thermal expansion metamaterial unit cell is shown. The three-dimensional view shows the zero thermal expansion metamaterial unit cell. The solid region (1) has a wall thickness that is adapted. The internal high-pressure gas region (2) is isolated from the external low-pressure gas region (3), reflecting the zero-direction deformation design characteristics.

[0079] like Figure 3 The cross-sectional diagrams of the zero thermal expansion metamaterial unit cell are shown in (a) and (b). The cross-sectional states at different temperatures are compared to show the deformation of the solid region (1) and the volume change of the high-pressure gas region (2), reflecting the zero thermal expansion mechanism.

[0080] like Figure 4 The axonometric view of the negative thermal expansion metamaterial unit cell is shown. The three-dimensional view shows that the solid region (1) of the negative thermal expansion metamaterial unit cell has a thin wall thickness, and the internal high-pressure gas region (2) is isolated from the external low-pressure gas region (3), reflecting the negative deformation design characteristics.

[0081] like Figure 5 The cross-sectional diagrams of the negative thermal expansion metamaterial unit cell are shown in (a) and (b). The cross-sectional states at different temperatures are compared to show the deformation of the solid region (1) and the volume change of the high-pressure gas region (2), reflecting the negative thermal expansion mechanism.

[0082] like Figure 6 The structural cross-section of the three-dimensional plate metamaterial under T2 is shown, which shows an array of multiple unit cells arranged orthogonally. Each region (1), (2), and (3) is regularly distributed and structurally symmetrical, reflecting the macroscopic layout of isotropic zero / negative thermal expansion.

[0083] By dividing the design domain into solid, high-pressure, and low-pressure gas regions, and adjusting the morphology and pressure of the solid region, the deformation of the solid region driven by the pressure difference during temperature changes is made to cancel out (achieve zero) or inversely superimpose (achieve negative) the intrinsic thermal expansion deformation of the material. Zero thermal expansion coefficient is embodied in Example 1, which aims for an approximately zero macroscopic thermal expansion coefficient in the Y direction; in Example 5, the zero thermal expansion unit cell... The coefficient of thermal expansion in the internal Y direction reaches (Near zero), and the formation of isotropic zero thermal expansion metamaterials after unit cell arraying; the negative thermal expansion coefficient is reflected in Example 2, which aims for a thermal expansion coefficient <0 in the Y direction, and in Example 5, the negative thermal expansion unit cell has a thermal expansion coefficient in the Y direction within the same temperature range of . (less than 0), forming an isotropic negative thermal expansion metamaterial after arraying; simultaneously, attached Figure 2-5 By demonstrating the structural deformation of zero / negative thermal expansion unit cells at different temperatures (zero thermal expansion unit cells have approximately unchanged size, while negative thermal expansion unit cells shrink), the "zero / negative" characteristics are presented more intuitively, fully reflecting the "zero / negative thermal expansion coefficient" in the title.

[0084] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for metamaterials with zero / negative thermal expansion coefficients composed of a single solid material, characterized in that, The method includes the following steps: The design domain is divided into a high-pressure gas region, a low-pressure gas region, and a solid region. The solid region uses a single solid material to isolate the high-pressure gas region and the low-pressure gas region. Set the coefficient of thermal expansion and the elastic modulus of the solid region; The shape of the solid region and the gas pressure of the gas region are adjusted so that the deformation of the solid region under the pressure difference between the high-pressure gas region and the low-pressure gas region when the temperature in the design domain is changed is equal to the zero-thermal or negative-thermal expansion of the solid region under temperature change, thereby obtaining the desired shape and gas pressure of the solid region.

2. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 1, characterized in that, The solid region is a metamaterial.

3. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 1, characterized in that, The morphology of the solid region includes: the wall thickness, geometric dimensions, and volume of the solid region.

4. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 3, characterized in that, The high-pressure gas region or the low-pressure gas region is surrounded by the solid region to form a closed cavity.

5. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 4, characterized in that, Both the high-pressure gas region and the low-pressure gas region are closed cavities, and the number of gas moles in the high-pressure gas region and the low-pressure gas region remains constant during temperature changes.

6. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 4, characterized in that, The solid region forms a closed cavity, the high-pressure gas is placed in the cavity, and a low-pressure gas is placed outside the cavity to form a low-pressure gas region. This low-pressure gas region is connected to the outside space and is a vacuum or normal pressure environment.

7. The design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 4, characterized in that, The solid region forms a closed cavity, the low-pressure gas is disposed in the cavity, and a high-pressure gas is disposed outside the cavity to form a high-pressure gas region. The low-pressure gas region is a vacuum or at atmospheric pressure.

8. A design method for a metamaterial with zero / negative thermal expansion coefficient composed of a single solid material as described in claim 1 or 4, characterized in that, The cavity formed by the solid region includes two identical square pyramids and a cube in the middle. The cube is positioned between the two square pyramids, and the cross-section of the cube is the same as the base of the square pyramids.

9. A unit cell structure obtained using the design method according to any one of claims 1-8, the unit cell structure comprising a solid region, a high-pressure gas region, and a low-pressure gas region.

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

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