A thermal metastructure device and its topology optimization design method and preparation method

Abstract

The present invention belongs to the technical field related to structural optimization, and discloses a thermal metastructure device and its topology optimization design method and preparation method. The design method includes the following steps: (1) using a full-parameter anisotropic thermal conductivity tensor space to describe an equivalent thermal conductivity tensor set of any mixed material structure, and determining the size and shape of the full-parameter anisotropic thermal conductivity tensor space of the two-phase mixed material; (2) establishing a relationship between the topological functional unit cell configuration of the optimized thermal metastructure device and the macroscopic equivalent thermal conductivity tensor based on a numerical homogenization method, and then establishing a topological functional unit cell design model that can traverse the full-parameter anisotropic space; and at the same time calculating the theoretical thermal conductivity tensor required for the thermal metastructure device to be optimized; (3) designing the topological structure of the metathermal metastructure device based on the topological functional unit cell design model and the calculated theoretical thermal conductivity tensor. The present invention can efficiently and accurately reverse design a topological functional unit cell with specific thermal conductivity tensor properties.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural optimization, and more specifically, relates to a thermal metastructure device and a topology optimization design method and a preparation method thereof. Background Art

[0002] Thermal conductivity, as the fundamental thermal property of materials, determines the diffusion path and magnitude of heat flow in modern industrial products. However, traditional isotropic natural materials are unable to manipulate heat flow. In order to enhance the ability of traditional natural materials to manipulate heat flow, a wider range of equivalent thermal conductivities can be produced by mixing different natural materials. This approach is widely used in the design of thermal metamaterials. When multiple isotropic materials are mixed, due to the different volume fraction ratios and thermal conductivities of the given materials, the equivalent thermal conductivity can have a non-uniform, anisotropic value within the maximum and minimum thermal conductivity range of each given material. Generally, the extraordinary thermal functions of thermal metamaterials rely on the anisotropic thermal conductivity tensor material parameters, and the various components of the thermal conductivity tensor are often interdependent when designing the structure and are confined to a limited parameter space.

[0003] Currently, there are generally two traditional design methods for designing structures with specific values ​​in the full-parameter anisotropic thermal conductivity tensor space: the first is based on the effective medium theory, and through trial and error, the macroscopic equivalent properties of the designed structure are gradually approached to the target thermal conductivity tensor properties. This method has low design efficiency and accuracy, and is affected by empirical design. The second method is to specify the configuration of the mixed material structure in advance, and then select the appropriate material and the appropriate volume fraction ratio. However, the biggest disadvantage of this method is that it may not be possible to find a material with suitable thermal conductivity. Even if a material with suitable thermal conductivity can be found, the contact thermal resistance between the two materials may also be a big problem that needs to be solved. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a thermal metastructure device and a topology optimization design method and preparation method thereof. It adopts a topology optimization method to reversely design a topological functional unit cell corresponding to any value within the boundary of the equivalent thermal conductivity tensor of a two-phase mixed material, utilizes these topological functional unit cells to design thermal metastructure materials, and prepares thermal metastructure devices based on additive manufacturing technology.

[0005] To achieve the above objectives, according to one aspect of the present invention, a topology optimization design method for a thermal metastructure device is provided, the design method comprising the following steps:

[0006] (1) Using the full-parameter anisotropic heat conduction tensor space to describe the equivalent heat conduction tensor set of any mixed material structure, and determining the size and shape of the full-parameter anisotropic heat conduction tensor space for two-phase mixed materials;

[0007] (2) Based on the numerical homogenization method, the relationship between the topological functional unit cell configuration of the optimized thermal metadevice and the macroscopic equivalent thermal conductivity tensor is established, and then a topological functional unit cell design model that can traverse the full parameter anisotropic space is established; at the same time, the theoretical thermal conductivity tensor required for the thermal metadevice to be optimized is calculated;

[0008] (3) Design the topological structure of the super-thermal device based on the topological functional unit cell design model and the calculated theoretical heat conduction tensor.

[0009] Furthermore, for the two-phase mixed material structure, based on the orthotropic anisotropic heat conduction tensor κ in the plane Wiener limit O , the anisotropic heat conduction tensor κ is calculated by rotating A , and then determine the size and shape of its full-parameter anisotropic heat conduction tensor space. The corresponding formula is:

[0010] κ A =R T (θ)κ O R(θ),

[0011]

[0012]

[0013] R(θ) is the rotation matrix, and θ is the rotation angle.

[0014] Furthermore, the orthotropic heat conduction tensor and the general anisotropic heat conduction tensor can be converted to each other according to κ xy =0 plane can be used to obtain the range of the heat conduction tensor in the entire space.

[0015] Furthermore, the macroscopic equivalent heat conduction tensor κ H The calculation formula is:

[0016]

[0017]

[0018] Where, is the temperature at each finite element node of the topological functional unit cell, which is calculated for each finite element after the initial independent test heat flux is applied; T e is the local temperature field, which is calculated for the entire topological functional unit cell after the initial independent test heat flux is applied; κ(ρ e ) is the thermal conductivity of each finite element, ρ e Represents the density of each cell.

[0019] Furthermore, the unit thermal conductivity κ(ρe ) and the interpolation relationship between the two materials, specifically:

[0020]

[0021] Where, κ material1 and κ material2 are the thermal conductivities of material 1 and material 2, respectively, where material 2 is a high thermal conductivity material relative to material 1; ρ e represents the density of each unit, a continuous design variable ranging from 0 to 1, and p is the penalty factor of the interpolation function, which is generally between 3 and 10.

[0022] Furthermore, the topological functional unit cell design model that can traverse the full parameter anisotropic space is:

[0023]

[0024] st:K(ρ e )T=Q

[0025]

[0026]

[0027] 0≤ρ e ≤1,e=1,2...N e

[0028] Where, K(ρ e ), T and Q are the global heat conduction matrix, global temperature matrix and global heat load matrix of the topological functional unit cell respectively, C is the objective function of the optimization model, G is the constraint function of the optimization model, which is determined by g(.), which is a continuous function used to balance the errors of each component of the input and output heat conduction tensors.

[0029] Furthermore, the heat flux q on the boundary satisfies the following relationship:

[0030]

[0031] where q (in) and q (out) Respectively represent the entry and exit interfaces (j) heat flow, Indicates the heat flow at the interface l (j) directional component; by jointly solving the heat conduction equations of each sub-region, the relationship between the heat conduction tensors of each sub-region can be obtained.

[0032]

[0033] where T represents the temperature field, κ represents the heat conduction tensor, and the superscript i represents the subregion.

[0034] According to another aspect of the present invention, a preparation method is provided, which first uses the topology optimization design method of the thermal metastructure device as described above to design the topology structure of the thermal metastructure device; then, uses 3D printing technology to print the thermal metastructure device.

[0035] Furthermore, the base of the thermal metamaterial printed by 3D printing technology uses polydimethylsiloxane as the filling material and silicone as the background material.

[0036] The present invention also provides a thermal metastructure device prepared by the above-mentioned preparation method of the thermal metastructure device.

[0037] In general, compared with the prior art, the above technical solutions conceived by the present invention have the following beneficial effects:

[0038] 1. The topological functional unit cell design model established in this invention, which can traverse the fully parametric anisotropic space, can efficiently and accurately reverse design topological functional unit cells with specific thermal conductivity tensor properties, solving the problems of low efficiency, reliance on experience, and difficulty in material selection in traditional specific thermal conductivity tensor structure design methods.

[0039] 2. When designing thermal metadevices, a regional scattering cancellation method was proposed to calculate the theoretical thermal conductivity tensor required for each sub-region, developing the scattering cancellation method and improving its design flexibility.

[0040] 3. The concept of a fully parametric anisotropic heat conduction tensor space is proposed to express a set of equivalent heat conduction tensors describing arbitrary hybrid material structures, providing guidance on the feasibility of structural design and material selection to achieve specific thermal properties.

[0041] 4. The thermal metastructure device designed in the present invention is manufactured based on additive manufacturing technology and has strong reliability and manufacturing precision.

[0042] 5. The design method proposed in the present invention is universal and applicable to the design of two-dimensional and three-dimensional topological functional unit cells. The thermal meta-devices prepared are suitable for steady-state and transient conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic flow chart of a topology optimization design method for a thermal metastructure device provided by the present invention;

[0044] Figure 2 a and b are the traversable full-parameter anisotropic heat conduction tensor space and four thermal metadevices respectively;

[0045] Figure 3a, b, and c are schematic diagrams of the size and shape of the full-parameter anisotropic heat conduction tensor space of the phase-mixed material;

[0046] Figure 4 is the plane diagram of the fully parametric orthotropic heat conduction tensor of different two-phase mixed materials;

[0047] Figure 5 It is a schematic diagram of the change in direction of heat flow when it passes through the interface of different materials;

[0048] Figure 6 a, b, c, and d are schematic diagrams of four thermal metastructure designs respectively;

[0049] Figure 7 a, b, c, and d are the structural diagrams of four thermal metamaterials:

[0050] Figure 8 a, b, c, and d are the simulated steady-state temperature field results of four thermal meta-devices;

[0051] Figure 9 a, b, c, and d are schematic diagrams of additive manufacturing samples of four types of thermal metamaterials;

[0052] Figure 10 a, b, c, and d are the experimental temperature field results of four types of thermal meta-devices. DETAILED DESCRIPTION

[0053] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0054] See also Figure 1 and Figure 2 The present invention provides a topology optimization design method for a thermal metastructure device, the design method mainly comprising the following steps:

[0055] Step 1: Use the full-parameter anisotropic heat conduction tensor space to describe the equivalent heat conduction tensor set of any mixed material structure, and determine the size and shape of the full-parameter anisotropic heat conduction tensor space of the two-phase mixed material.

[0056] For two-phase mixed material structures, according to the orthotropic anisotropic heat conduction tensor κ within the Wiener limit in the plane O , the anisotropic heat conduction tensor κ is calculated by rotating A , which determines the size and shape of its fully parametric anisotropic heat conduction tensor space:

[0057] κ A =R T (θ)κ O R(θ),

[0058]

[0059]

[0060] Where R(θ) is the rotation matrix and θ is the rotation angle.

[0061] In this embodiment, since the orthotropic heat conduction tensor and the general anisotropic heat conduction tensor can be converted to each other, according to κ xy = 0 plane, we can get the range of the heat conduction tensor in the entire space. First, for any point It can be considered that this point corresponds to an equivalent heat conduction tensor When the hybrid structure rotates, its equivalent heat conduction tensor κ M Assume that the rotation angle of the hybrid structure is θ, the changed It can be calculated by the following formula:

[0062]

[0063] For analysis The trajectory in space, The position changes in space Figure 3 As shown in . From formula (1), we can see that The sum of the two components on the main diagonal of is always This means that when θ changes from 0 to 180°, The trajectory in space is always in the plane and the straight line of the isotropic heat conduction tensor vertical.

[0064] Based on the above analysis, a two-dimensional coordinate system can be reconstructed, and the orthogonal axes of the coordinate system are κ′ xy Axis and Axis, such as Figure 3 The dotted axis in b is shown in Figure 2. After a simple calculation, we can know that the point to κ′ xy The distance between the axes is:

[0065]

[0066] point arrive The distance between the axes is:

[0067]

[0068] By observing formula (2) and formula (3), we can find that and Has the following relationship:

[0069]

[0070] Therefore, point When the corresponding hybrid structure rotates from 0° to 180°, the trajectory generated in the heat conduction tensor space is an ellipse with the major axis being The short axis is The results are as follows Figure 3 As shown in c in . Therefore, the fully parametric anisotropic heat conduction tensor space for a two-phase material mixture occupies a region similar to an ellipsoid in space. From the above derivation, we can see that the size of the fully parametric anisotropic heat conduction tensor space for a two-phase material mixture is closely related to the range of the orthotropic heat conduction tensor for the two-phase material mixture. Figure 4 The orthotropic heat conduction tensor regions under different material hybrid structures are shown.

[0071] Step 2: Based on the numerical homogenization method, the relationship between the topological functional unit cell configuration of the optimized thermal metadevice and the macroscopic equivalent thermal conduction tensor is established, and then a topological functional unit cell design model that can traverse the full parameter anisotropic space is established; at the same time, the theoretical thermal conduction tensor required for the thermal metadevice to be optimized is calculated.

[0072] Calculating the macroscopic equivalent heat conduction tensor κ of a topological functional unit cell H , the formula is as follows:

[0073]

[0074]

[0075] in is the temperature at each finite element node of the topological functional unit cell, which is calculated for each finite element after the initial independent test heat flux is applied; T e is the local temperature field, which is calculated for the entire topological functional unit cell after the initial independent test heat flux is applied; κ(ρ e ) is the thermal conductivity of each finite element, ρ e Represents the density of each cell.

[0076] In this embodiment, when constructing the topological functional unit cell design model, first, the modified SIMP scheme is used to construct the unit thermal conductivity κ (ρ e ) and the interpolation relationship between the two materials are as follows:

[0077]

[0078] where κ material1 and κ material2 are the thermal conductivities of material 1 and material 2, respectively, where material 2 is a higher thermal conductivity material than material 1. e Represents the density of each unit, a continuous design variable from 0 to 1, and p is the penalty factor of the interpolation function, which is generally between 3 and 10. In order to obtain a specific heat conduction tensor property of the microstructure Based on the interpolation relationship of formula (5), a topological functional unit cell design model that can traverse the full parameter anisotropic space is established as follows:

[0079]

[0080] Where K(ρ e ), T and Q are the global heat conduction matrix, global temperature matrix and global heat load matrix of the topological functional unit cell, respectively. C is the objective function of the optimization model, and G is the constraint function of the optimization model, which is determined by g(.). g(.) is a continuous function used to balance the errors of each component of the input and output heat conduction tensors. In this embodiment, the value of g(.) is called the relative error, and the specific expression is as follows:

[0081]

[0082] Where a and b are dimensionless numbers, and their values ​​are respectively and size.

[0083] By designing enough topological functional unit cells, their equivalent heat conduction tensors can basically fill the entire fully parametric anisotropic heat conduction tensor space, and finally a traversable fully parametric anisotropic heat conduction space is obtained.

[0084] If the distribution of the temperature field T is known, according to Fourier's law:

[0085] q=-κ·▽T (8)

[0086] By setting a reasonable thermal conductivity tensor κ, the heat flow q can be adjusted to achieve the purpose of controlling the heat flow. In order to control the heat flow and then design the thermal meta-device, we first deduce how the direction of the heat flow vector changes when it passes through the interface of two different materials: Assume that the thermal conductivity tensors at region i and region i+1 are κ (i) and κ (i+1) , the interface between region i and region i+1 is l (j) , Yes (j) The angle between the horizontal plane and the heat flow q in and out of the interface l(j) Use and Indicates that they are related to the interface l (j) The angles are expressed as and According to simple calculations, and The angles with the horizontal plane are and like Figure 5 As shown, where i=1, j=1.

[0087] It is known that the heat flux q is passing through the interface l (j) , its normal component remains unchanged, that is,

[0088]

[0089] in Indicates the heat flow at the interface l (j) The normal component of . According to the relationship between the heat flow angles, we can get:

[0090]

[0091] Substituting formula (10) into formula (9), we can obtain the relationship between the temperature, heat flow and heat conduction tensor of each region:

[0092]

[0093] Where T (i) represents the temperature field of region i, and formula (11) is expanded to obtain:

[0094]

[0095]

[0096] It is obvious from formula (11) that when the temperature gradient in each region is known, the heat flux q (in,out) The heat transfer tensor κ in the two regions can be adjusted (i,i+1) To manipulate. (i,i+1) The desired thermal conductivity tensor can be achieved by designing microstructures through topological optimization, thereby realizing the structural design of thermal metamaterials. Based on the above derivation, four types of thermal metamaterials (heat concentrating, thermally invisible, thermally connected, and thermally reflective metamaterials) were theoretically designed. Specifically, the relationship between the thermal conductivity tensors of each sub-region was calculated based on the temperature gradients of the four thermal metamaterials, thereby obtaining the thermal conductivity tensor distribution of each region.

[0097] (4.1) Design of heat-concentrating metamaterials based on regional scattering cancellation

[0098] For heat-concentrating metamaterials, a region with a large temperature gradient can be created in its center while the temperature of the background area does not change. The size of the thermal metamaterial is as follows: Figure 6 As shown, the white straight line is the isotherm. Since the heat-concentrating metamaterial is symmetrical about the center, only one-quarter of the area needs to be considered during design. Figure 6 As shown in a, a quarter of the heat is concentrated in the metamaterial by the two interfaces l (1) and l (2) It is divided into three areas: Area 1, Area 2 and Area 3. Figure 6 From the information in the figure, we can know that the function and shape of the entire heat-concentrating metamaterial are determined by the parameters |CB|, |DC|, |OD|, and Decide.

[0099] When implementing the heat concentration function, the temperature gradient of each area can be calculated based on the isotherm. The temperature gradient of area 1 in the x and y directions is:

[0100]

[0101] The temperature gradient of region 2 in the x and y directions is:

[0102]

[0103] The temperature gradient of region 3 in the x and y directions is:

[0104]

[0105] According to formula (10), the heat flow satisfies the following relationship when passing through interface 1:

[0106]

[0107] The heat flow through interface 2 satisfies the following relationship:

[0108]

[0109] Among them, κ b is the thermal conductivity of region 1, i.e., the thermal conductivity of the background region. Substituting equations (17) and (18) into equation (13), we can obtain the general relationship between the thermal conductivity tensors of each subregion:

[0110]

[0111] When setting |DC|=2|OD|=2|CB|=25mm, and The above formula can be simplified as:

[0112]

[0113] (4.2) Design of thermal stealth metamaterial based on regional scattering cancellation

[0114] For thermal stealth metamaterials, an area with extremely low temperature gradient can be created in its center while the temperature of the background area does not change. The size of the thermal metamaterial device is as follows: Figure 6 As shown in b, the white straight line is the isotherm. Since the thermal stealth metamaterial is symmetrical about the center, only one-quarter of the area needs to be considered during design. Figure 6 As shown in b, one quarter of the thermal stealth metamaterial is covered by two interfaces l (1) and l (2) It is divided into three areas: Area 1, Area 2 and Area 3. Figure 6 From the information in b, we can know that the function and shape of the entire thermal stealth metamaterial are determined by the parameters |CB|, |OB|, and Decide.

[0115] When achieving thermal stealth, the temperature gradient of each region can be calculated based on the isotherm. The temperature gradient of region 1 in the x and y directions is:

[0116]

[0117] The temperature gradient of region 2 in the x and y directions is:

[0118]

[0119] The temperature gradient of region 3 in the x and y directions is:

[0120]

[0121] Where ξ is a small positive decimal. According to formula (10), the heat flow satisfies the following relationship when passing through interface 1:

[0122]

[0123] The heat flow through interface 2 satisfies the following relationship:

[0124]

[0125] Among them, κ b is the thermal conductivity of region 1, i.e., the thermal conductivity of the background region. Substituting equations (17) and (18) into equation (13), we can obtain the general relationship between the thermal conductivity tensors of each subregion:

[0126]

[0127] When |OB| = 2|CB| = 50 mm is set, and The above equation can be simplified to:

[0128]

[0129] (4.3) Theoretical design of thermally connected metamaterials based on regional scattering cancellation

[0130] For thermally connected metamaterials, the temperature gradient can connect the two ends of the structure without loss, and the size of its thermal metamaterial device is as shown in c in Figure 6 To design thermally connected metamaterials, the entire design area is divided into four sub-regions, namely Region 1, Region 2, Region 3, and Region 4, by three interfaces l (1) , l (2) and l (3) According to the information in c in Figure 6 , the function and shape of the entire thermally connected metamaterial are determined by the parameters β1 and β2.

[0131] When implementing the thermal connection function, the temperature gradients of each region can be calculated according to the isotherm. The temperature gradients of Region 1 to Region 4 in the x and y directions are both:

[0132]

[0133] According to formula (10), the heat flux satisfies the following relationship when passing through interface 1:

[0134]

[0135] The heat flux satisfies the following relationship when passing through interface 2:

[0136]

[0137] The heat flux satisfies the following relationship when passing through interface 3:

[0138]

[0139] where κ b is the thermal conductivity of Region 1, i.e., the thermal conductivity of the background region. Subsequently, substituting formula (29), formula (30), and formula (31) into formula (13), the general relationship between the thermal conduction tensors of each sub-region can be obtained. When cotβ1 = 1, cotβ2 = 1 and are set, Finally, we can get:

[0140]

[0141] (4.4) Theoretical design of heat-reflecting metamaterials based on regional scattering cancellation

[0142] For thermal reflective metamaterials, the heat flow can be deflected without loss of temperature gradient, just like light encountering mirror reflection. The size of the thermal metamaterial device is as follows: Figure 6 In order to design the required thermal function, the entire design area is divided into three interfaces l (1) , l (2) and l (3) It is divided into four sub-areas, namely Area 1, Area 2, Area 3 and Area 4. Figure 6 From the geometric information in d, we can see that the function and shape of the entire heat-reflective metamaterial are determined by parameters β1, β2, β3 and β4.

[0143] When realizing the heat reflection function, the temperature gradient of each area can be calculated based on the isotherm. The temperature gradient of area 1 and area 2 in the x and y directions are:

[0144]

[0145] The temperature gradient of region 3 in the x and y directions is:

[0146]

[0147] The temperature gradient of region 4 in the x and y directions is:

[0148]

[0149] According to formula (10), the heat flow satisfies the following relationship when passing through interface 1:

[0150]

[0151] The heat flow through interface 2 satisfies the following relationship:

[0152]

[0153] The heat flow across interface 3 satisfies the following relationship:

[0154]

[0155] Among them, κ b is the thermal conductivity of region 1, i.e. the thermal conductivity of the background region. Then, by substituting formula (36), formula (37) and formula (38) into formula (13), we can obtain the general relationship between the thermal conductivity tensors of each sub-region. When setting cotβ1=3,β2=90°,β3=45°,β4=45°, and Finally, we can get:

[0156]

[0157] Step three: Design the topological structure of the super-thermal device based on the topological functional unit cell design model and the calculated theoretical heat conduction tensor.

[0158] The relationship between the thermal conductivity tensors of each sub-region of the four thermal metamaterials was calculated by the regional scattering cancellation method, as shown in formulas (20), (27), (32) and (39). Under the premise of considering the reciprocity of the thermal conductivity tensor and the second law of thermodynamics, when the thermal conductivity of the background material is 13Wm -1 K -1 The feasible solutions of the thermal conductivity tensors of various thermal metamaterial sub-regions are shown in Table 1. According to the distribution of thermal conductivity tensors in each region in Table 1, the structure of the non-background region is optimized domain by domain through the topological functional unit cell design method that can traverse the full-parameter anisotropic space. The materials selected for optimization are copper and PDMS. There are two reasons for choosing these two materials: 1) The full-parameter anisotropic thermal conductivity tensor space composed of copper and PDMS contains the thermal conductivity tensors in the above-mentioned sub-regions. 2) Pure copper structures can be manufactured through 3D printing. PDMS is a liquid glue at room temperature. When heated, it can have good contact with the solid, which can reduce the thermal resistance of the two materials and ensure that the thermal metamaterial can be prepared.

[0159] Table 1 Feasible solutions of the heat conduction tensor for various thermal metamaterial sub-regions

[0160] Feasible solution of heat conduction tensor for heat-concentrating and stealthy metamaterial sub-regions

[0161]

[0162] Feasible solution of the thermal conductivity tensor of thermally connected and reflective metamaterial sub-regions

[0163]

[0164] The size of the topological functional unit cell is set to 5mm×5mm. After obtaining the optimal topological functional unit cell of each sub-region, the optimized topological functional unit cells are periodically arrayed, and then the topological functional unit cells of the array are cut into the shape of the sub-region and assembled, and finally the corresponding multi-scale structure of the thermal metamaterial can be obtained. Figure 7 shown.

[0165] After obtaining the multi-scale structures of the four thermal metamaterials, finite element simulations were then carried out. The simulation conditions were set as follows: the thermal conductivity of the background materials of the four thermal metamaterial devices was set to 13Wm -1 K-1 For heat concentrating and thermally stealthy meta-devices, the left boundary of the device is high temperature, fixed at 423K; the right boundary is low temperature, fixed at 273K; and the upper and lower boundaries are set as thermal insulation boundaries. For heat connecting and heat reflecting meta-devices, the left boundary of the device is high temperature, fixed at 363K; the right boundary is low temperature, fixed at 273K; and the other boundaries are set as thermal insulation boundaries. After simulation calculations, the simulated steady-state temperature fields of various thermal meta-materials are as follows Figure 8 shown.

[0166] The present invention also provides a method for preparing a thermal metastructure device. The preparation method first uses the above-mentioned thermal metastructure device topology optimization design method to design the topological structure of the thermal metastructure device; then, 3D printing technology is used to print the thermal metastructure device.

[0167] Specifically, four thermal metastructure devices were prepared by using a base of thermal metastructure material printed using 3D printing technology, polydimethylsiloxane as the filling material, and silicone as the background material.

[0168] In order to reduce the impact of air convection on the experimental verification of thermal metamaterials, the designed two-dimensional thermal metamaterial multi-scale structure is longitudinally stretched to 5 mm thick, its STL model is exported, and the thermal metamaterial multi-scale structure is manufactured using additive manufacturing technology. Figure 9 3D printed structural samples are displayed, among which a is a heat-concentrating metamaterial sample, b is a thermal stealth metamaterial sample, c is a thermal connection metamaterial sample, and d is a heat-reflecting metamaterial sample. The black line shows the standard scale. After printing each thermal metamaterial sample, PDMS needs to be added to the printed sample substrate and the air in the glue needs to be evacuated to reduce the contact thermal resistance and air convection of the two materials, copper and PDMS. First, the printed sample is placed in a container made of acrylic board, PDMS is poured into the container, and then after vacuum degassing, uniform heating and cutting of excess material, the thermal metamaterial used in the experiment is completed. After that, the preparation of the entire thermal metamaterial device began. In the experiment, the background material selected was a thermal conductivity of 13Wm -1 K -1 , 5mm thick solid silicone plate, this silicone is soft and can be cut into any shape with a knife. In order to reduce the contact thermal resistance, a thermal conductivity of 13Wm is filled between the background silicone and the thermal metamaterial. -1 K -1 Semi-solid thermal grease is applied, and the entire thermal superstructure device is thus prepared.

[0169] The above article briefly describes the preparation process of the thermal metadevice, and then conducts experiments to test the performance of the thermal metadevice. In the experiment, the entire thermal metadevice was embedded in an insulating foam to reduce the impact of air convection on the experiment. The heat source and cold source of the experiment used a heating belt and a refrigerator to heat and cool the two ends of the thermal metadevice respectively. The temperature was controlled by a thermocouple and was the same as the temperature set in the numerical simulation. The temperature field of the entire thermal metadevice was recorded by a thermal infrared camera fixed above the device. In the experiment, in order to ensure that the thermal emissivity of the entire thermal metadevice was the same, the entire surface of the device was covered with a layer of black 0.1mm thick PVC tape.

[0170] The experimental test begins when the heat source and the cold source are working. When the temperature distribution of the entire thermal metastructure device basically does not change, it can be considered that the thermal metastructure device has reached a steady-state temperature field. At this time, the temperature field of each thermal metastructure device is recorded, and the obtained temperature distribution is as follows: Figure 10 As shown in the figure, a is the temperature distribution of the heat-concentrating metadevice, b is the temperature distribution of the heat-stealing metadevice, c is the temperature distribution of the heat-connecting metadevice, and d is the temperature distribution of the heat-reflecting metadevice. The temperature distributions show that the experimentally obtained temperature field is similar to the simulated temperature field. The four thermal metadevices respectively achieve the extraordinary functions of heat concentrating, heat-stealing, heat-connecting, and heat-reflecting.

[0171] The present invention also provides a thermal metastructure device, which is prepared by using the above-mentioned preparation method of the thermal metastructure device.

[0172] It will be easily understood by those skilled in the art 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 in the scope of protection of the present invention.

Claims

1. A topology optimization design method for a thermal metastructure device, characterized in that: The method comprises the following steps: (1) Using the full-parameter anisotropic heat conduction tensor space to describe the equivalent heat conduction tensor set of any mixed material structure, and determining the size and shape of the full-parameter anisotropic heat conduction tensor space for two-phase mixed materials; (2) Based on the numerical homogenization method, the relationship between the topological functional unit cell configuration of the optimized thermal metadevice and the macroscopic equivalent thermal conductivity tensor is established, and then a topological functional unit cell design model that can traverse the full parameter anisotropic space is established; at the same time, the theoretical thermal conductivity tensor required for the thermal metadevice to be optimized is calculated; (3) Design the topological structure of the super-thermal device based on the topological functional unit cell design model and the calculated theoretical heat conduction tensor; Macroscopic equivalent heat conduction tensor κ H The calculation formula is: Where, is the temperature at each finite element node of the topological functional unit cell, which is calculated for each finite element after the initial independent test heat flux is applied; T e is the local temperature field, which is calculated for the entire topological functional unit cell after the initial independent test heat flux is applied; κ(ρ e ) is the thermal conductivity of each finite element, ρ e represents the density of each unit; The heat flux q on the boundary satisfies the following relationship: where q (in) and q (out) Respectively represent the entry and exit interfaces (j) heat flow, Indicates the heat flow at the interface l (j) The directional component of ; by jointly solving the heat conduction equations of each sub-region, the relationship between the heat conduction tensors of each sub-region can be obtained: where T represents the temperature field, κ represents the heat conduction tensor, and the superscript i represents the subregion.

2. The topology optimization design method for a thermal metadevice according to claim 1, wherein: For two-phase mixed material structures, the orthotropic heat conduction tensor κ is calculated based on the Wiener limit in the plane. O , the anisotropic heat conduction tensor κ is calculated by rotating A , and then determine the size and shape of its full-parameter anisotropic heat conduction tensor space. The corresponding formula is: k A =R T (i)k O R(θ), R(θ) is the rotation matrix, and θ is the rotation angle.

3. The topology optimization design method for a thermal metastructure device according to claim 2, wherein: The orthotropic heat conduction tensor and the general anisotropic heat conduction tensor can be converted to each other according to κ xy =0 plane can be used to obtain the range of the heat conduction tensor in the entire space.

4. The topology optimization design method for a thermal metastructure device according to claim 1, wherein: Building block thermal conductivity κ(ρ e ) and the interpolation relationship between the two materials, specifically: Where, κ material1 and κ material2 are the thermal conductivities of material 1 and material 2, respectively, where material 2 is a high thermal conductivity material relative to material 1; ρ e represents the density of each unit, a continuous design variable ranging from 0 to 1, and p is the penalty factor of the interpolation function, which is generally between 3 and 10.

5. The topology optimization design method for a thermal metastructure device according to claim 4, wherein: The topological functional unit cell design model that can traverse the full parameter anisotropic space is: s.t.:K(ρ e )T=Q 0≤ρ e ≤1,e=1,2...N e Where, K(ρ e ), T and Q are the global heat conduction matrix, global temperature matrix and global heat load matrix of the topological functional unit cell respectively, C is the objective function of the optimization model, G is the constraint function of the optimization model, which is determined by g(.), which is a continuous function used to balance the errors of each component of the input and output heat conduction tensors.

6. A method for preparing a thermal metastructure device, characterized in that: The preparation method first adopts the topology optimization design method of the thermal metastructure device according to any one of claims 1 to 5 to design the topology structure of the metastructure device; then, the thermal metastructure device is printed using 3D printing technology.

7. The method for preparing a thermal metastructure device according to claim 6, wherein: The base of the thermal metamaterial is printed using 3D printing technology. The filling material is polydimethylsiloxane and the background material is silicone.

8. A thermal metastructure device, characterized in that: The thermal metastructure device is prepared by using the preparation method of the thermal metastructure device according to claim 7.

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