阅读说明：本技术 一种自由曲面热超材料结构及其设计和制备方法 (Free curved surface thermal metamaterial structure and design and preparation method thereof ) 是由 胡润 肖蜜 朱展 沙伟 高亮 于 2021-08-04 设计创作，主要内容包括：本发明属于热超材料领域,并具体公开了一种自由曲面热超材料结构及其设计和制备方法,其包括如下步骤：S1、将整体热超材料结构划分为若干个单胞,根据待实现的热学功能确定每个单胞的理想热传导张量；S2、分别对每个单胞进行结构拓扑优化,使每个单胞的等效热传导张量等于其理想热传导张量,得到能够实现相应热学功能的热超材料结构。本发明可以实现任意形状结构、全方位的热学功能,并能通过3D打印技术将热超材料可靠地制造出来；本发明为热超材料的设计与制备提供了一种全新的思路,结构拓扑优化方法给热超材料的设计带来了更大的自由度,3D打印技术给热超材料的制备带来了更高的可靠性。(The invention belongs to the field of thermal metamaterials, and particularly discloses a free curved surface thermal metamaterial structure and a design and preparation method thereof, wherein the free curved surface thermal metamaterial structure comprises the following steps: s1, dividing the integral thermal metamaterial structure into a plurality of unit cells, and determining the ideal heat conduction tensor of each unit cell according to the thermal function to be realized; and S2, respectively carrying out structural topology optimization on each unit cell to enable the equivalent heat conduction tensor of each unit cell to be equal to the ideal heat conduction tensor, and obtaining the thermal metamaterial structure capable of realizing the corresponding thermal function. The invention can realize the omnibearing thermal function with any shape and structure and can reliably manufacture the thermal metamaterial by the 3D printing technology; the invention provides a brand new thought for the design and preparation of the thermal metamaterial, the structural topology optimization method brings greater freedom for the design of the thermal metamaterial, and the 3D printing technology brings higher reliability for the preparation of the thermal metamaterial.)

1. A design method of a free curved surface thermal metamaterial structure is characterized by comprising the following steps:

s1, dividing the integral thermal metamaterial structure into a plurality of unit cells, and determining the ideal heat conduction tensor of each unit cell according to the thermal function to be realized;

and S2, respectively carrying out structural topology optimization on each unit cell to enable the equivalent heat conduction tensor of each unit cell to be equal to the ideal heat conduction tensor, and obtaining the thermal metamaterial structure capable of realizing the corresponding thermal function.

2. The method of claim 1, wherein the finite element method is used to calculate the equivalent thermal conductivity tensor of each unit cellThe calculation formula is as follows:

wherein | V | isTotal volume of functional unit cell, Δ T_eIs the temperature vector difference, N is the total number of finite elements divided in the unit cell;is a unit cell heat-conducting matrix in which,is a matrix of the specific thermal conductivity,κ_material1is the coefficient of thermal conductivity, κ, of the material 1_material2Is the thermal conductivity coefficient of material 2, p is the penalty coefficient, p_eThe range of the design variables allocated to the finite element is 0-1, wherein 0 represents that the finite element is material 1, and 1 represents that the finite element is material 2.

3. The design method of the free-form surface thermal metamaterial structure of claim 2, wherein the structural topology optimization of the unit cell is performed according to a topology optimization model, and the topology optimization model specifically comprises:

an objective function:

K(ρ_e)T＝Q,0≤ρ_e≤1,e＝1,2...N

constraint conditions are as follows:

wherein the content of the first and second substances, in order to be the ideal heat conduction tensor,is the equivalent thermal conduction tensor; k (rho)_e) T, Q are a global heat conduction matrix, a global temperature matrix, and a global heat load matrix, respectively.

4. The design method of the free-form surface thermal metamaterial structure of claim 3, wherein in the topology optimization, the constraint condition G and the objective function C are calculated by a adjoint method to design the variable p_eAnd then updating the optimal design variable ρ with a gradient-based moving asymptote method according to the sensitivity_e。

5. The method of claim 2, wherein a solid isotropic material penalty model is used to interpolate the thermal conductivity coefficients of material 1 and material 2 when calculating the equivalent thermal conductivity tensor for each unit cell using finite element method.

6. The method of designing a free-form surface thermal metamaterial structure as claimed in any one of claims 1 to 5, wherein the ideal thermal conductivity tensor for each unit cell is determined using a coordinate transformation method.

7. A preparation method of a free curved surface thermal metamaterial structure is characterized by comprising the following steps: the design method according to any one of claims 1 to 6 is used for designing a free-form surface thermal metamaterial structure, and the actual free-form surface thermal metamaterial structure is obtained through 3D printing.

8. The method for preparing the free-form curved-surface thermal metamaterial structure as claimed in claim 7, wherein the free-form curved-surface thermal metamaterial structure comprises a substrate and a filling pattern, the material 1 and the material 2 are respectively the substrate material or the filling material according to actual needs, the substrate is printed out by 3D printing of the substrate material, and then the filling material is filled into the substrate gap.

9. The method of claim 8, wherein the base material is a metal and the filler material is an organic polymer.

10. A free-form curved thermal metamaterial structure prepared by the method of any one of claims 7 to 9.

Technical Field

The invention belongs to the field of thermal metamaterials, and particularly relates to a free-curved-surface thermal metamaterial structure and a design and preparation method thereof.

Background

The thermal metamaterial is a novel artificial material, and has unique properties which are not possessed by a natural material, and the unique properties are obtained by designing the natural material in a special mode (such as perforation filling, layered arrangement and the like). The thermal metamaterial often has anisotropic thermal parameters, so that the metamaterial can directionally regulate and control heat flow and has potential application in the fields of efficient thermal management, enhanced heat transfer and the like.

However, the existing thermal metamaterial has some defects, such as insufficient shape adaptability of the thermal metamaterial, difficulty in realizing all-dimensional thermal functions of the thermal metamaterial, and insufficient reliability of experimental preparation of the thermal metamaterial. In order to solve the defects of the thermal metamaterial, expand the application range of the thermal metamaterial and provide a basis for the free design of the thermal metamaterial, a structural design and a preparation method of the free curved surface thermal metamaterial are urgently needed.

Disclosure of Invention

Aiming at the defects or improvement requirements of the prior art, the invention provides a free curved surface thermal metamaterial structure and a design and preparation method thereof, and aims to break through the limitations on the geometric shape, the omnibearing thermal function and the reliable experimental preparation of the thermal metamaterial and improve the design freedom of the thermal metamaterial structure.

To achieve the above object, according to a first aspect of the present invention, a method for designing a free-form curved thermal metamaterial structure is provided, including the steps of:

s1, dividing the integral thermal metamaterial structure into a plurality of unit cells, and determining the ideal heat conduction tensor of each unit cell according to the thermal function to be realized;

and S2, respectively carrying out structural topology optimization on each unit cell to enable the equivalent heat conduction tensor of each unit cell to be equal to the ideal heat conduction tensor, and obtaining the thermal metamaterial structure capable of realizing the corresponding thermal function.

As a further preference it is possible to use,calculating the equivalent heat conduction tensor of each unit cell by adopting a finite element methodThe calculation formula is as follows:

wherein | V | is the total volume of the functional unit cell, Δ T_eIs the temperature vector difference, N is the total number of finite elements divided in the unit cell;is a unit cell heat-conducting matrix in which,is a matrix of the specific thermal conductivity,κ_material1is the coefficient of thermal conductivity, κ, of the material 1_material2Is the thermal conductivity coefficient of material 2, p is the penalty coefficient, p_eThe range of the design variables allocated to the finite element is 0-1, wherein 0 represents that the finite element is material 1, and 1 represents that the finite element is material 2.

Preferably, the unit cell is subjected to structural topology optimization according to a topology optimization model, wherein the topology optimization model specifically comprises:

an objective function:

constraint conditions are as follows:

wherein the content of the first and second substances, in order to be the ideal heat conduction tensor,is the equivalent thermal conduction tensor; k (rho)_e) T, Q are a global heat conduction matrix, a global temperature matrix, and a global heat load matrix, respectively.

More preferably, in topology optimization, the constraint condition G and the objective function C are calculated for the design variable ρ by a concomitant method_eAnd then updating the optimal design variable ρ with a gradient-based moving asymptote method according to the sensitivity_e。

As a further preference, in calculating the equivalent thermal conductivity tensor of each unit cell using the finite element method, the thermal conductivity coefficients of the material 1 and the material 2 are interpolated using the solid isotropic material penalty model.

As a further preferred, the ideal thermal conductivity tensor for each unit cell is determined using a coordinate transformation method.

According to a second aspect of the present invention, there is provided a method for preparing a free-form curved thermal metamaterial structure, comprising the steps of: and designing to obtain a free-curved-surface thermal metamaterial structure according to the design method, and obtaining an actual free-curved-surface thermal metamaterial structure through 3D printing.

As a further preferred, the free-form surface thermal metamaterial structure comprises a substrate and a filling pattern, wherein whether the material 1 and the material 2 are respectively a substrate material or a filling material is determined according to actual needs, the substrate is printed out by 3D printing by using the substrate material, and then the filling material is filled into the substrate gap.

Further preferably, the base material is a metal, and the filler material is an organic polymer.

According to a third aspect of the invention, a free-form curved-surface thermal metamaterial structure is provided, which is prepared by the preparation method.

Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:

1. the invention makes the equivalent heat conduction tensor of each unit cell equal to the ideal heat conduction tensor thereof by the method of dividing the unit cells and topology optimization, thereby the obtained topological structure can meet the requirement of the ideal anisotropic heat conduction tensor, and the corresponding thermal function is realized; meanwhile, the unit cell of the free-curved-surface thermal metamaterial at each position meets the requirement of ideal heat conduction tensor of the position, so that the designed free-curved-surface thermal metamaterial can break through the limitation of the geometric shape of the thermal metamaterial and realize the omnibearing thermal function.

2. The traditional scale of the layered structure cannot realize the same small finite element dispersion and lower accuracy; meanwhile, different ideal heat conduction tensors exist at different positions, the ideal heat conduction tensor can be achieved only by rotating the laminated structure to a certain degree, and 3D printing is not convenient and fast to manufacture; compared with the traditional laminated structure, the method has higher design freedom degree, and the design method has universality and is suitable for two-dimensional and three-dimensional conditions.

3. The equivalent heat conduction tensor of each unit cell is calculated by adopting a finite element method, the accuracy of data can be improved, and meanwhile, the thermal conductivity coefficient of the material is interpolated by adopting an improved SIMP (Single in line process of materials penalty model), so that the design variable of the finite element is discrete 0 or 1 as far as possible, and the occurrence of intermediate density is avoided; design variables can be driven to 0 and 1 by increasing the penalty coefficient, so that materials at different positions of the structure can be accurately determined.

4. During topology optimization, the volume minimization of the material 2 is taken as an objective function, and whether the material 1 and the material 2 are respectively a substrate material or a filling material is determined according to the material cost or the actual requirement, so that the structural cost can be reduced; meanwhile, the equivalent heat conduction tensor is equal to the ideal heat conduction tensor as the constraint condition, and each finite element can be ensured to meet the condition as much as possible, so that the optimal thermal metamaterial structure is obtained.

5. The free-curved-surface thermal metamaterial is prepared by a 3D printing technology, and has high reliability and manufacturing precision. Meanwhile, the substrate is preferably made of metal materials such as iron and copper, and a reliable frame is provided for the topological structure; the filling material is preferably organic polymer such as polydimethylsiloxane, and the like, and the liquid material is solidified after filling, so that convenience is provided for realizing topological structures with different shapes.

Drawings

FIG. 1 is a schematic diagram of the design and fabrication of a free-form surface thermal metamaterial according to an embodiment of the present invention;

in FIG. 2, a-f are schematic diagrams of free-form curved thermal metamaterial design routes according to embodiments of the present invention;

in FIG. 3, a-f are the thermal aggregation, thermal rotation, thermal stealth structure and its corresponding theoretical simulation temperature field after the topological functional unit cell is integrated according to the embodiment of the present invention;

FIG. 4 is a flow chart of the preparation and experiment of the free-form surface thermal metamaterial according to the embodiment of the invention;

in fig. 5, a to f are graphs showing the structures of three thermal functional devices (thermal aggregation, thermal rotation, thermal stealth) with any shapes and the corresponding experimental temperature field results.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

The design method of the free-form surface thermal metamaterial structure provided by the embodiment of the invention, as shown in fig. 1, comprises the following steps:

s1, dividing the integral thermal metamaterial structure into a plurality of unit cells with certain sizes, preferably square unit cells, wherein the smaller the size of the square unit cell is, the better the realized thermal function effect is; then, the ideal thermal conductivity tensor of each unit cell is determined according to the thermal function to be realized, and preferably, the ideal thermal conductivity tensor of each unit cell is determined by a coordinate conversion method.

Specifically, in order to prove the feasibility of the method provided by the invention, numerical simulation and experimental verification are respectively carried out, and three thermal aggregation devices, thermal rotation devices and thermal stealth devices in any shapes are selected for verification. In order to realize different thermal functions (thermal aggregation, thermal rotation and thermal stealth), the ideal thermal conduction tensor of the unit cell at different positions can be calculated by a coordinate conversion method, and the ideal thermal conduction tensor of the unit cell is measured to be the ideal thermal conduction tensor at the midpoint of the unit cell.

(1) Heat concentrator, its geometry is as follows:

where θ' is the different azimuth angle, R₁(θ′)，R₂(θ′)，R₃(θ') are the structural parameters shown in FIG. 2, respectively, representing the geometric dimensions of the thermal concentrator, the radius of the thermal concentrator varying with azimuthal angle, and the irregular structure of the thermal concentrator.

For thermal aggregation, the inner region R' is ≦ R₁The ideal thermal conductivity tensor calculation formula of (θ') is as follows:

wherein the content of the first and second substances,representing the ideal heat conduction tensor of the inner region of the heat concentrator,is a rotation matrix, R (theta')^TIs the transposed matrix of R (θ'),. kappa._bIs the background thermal conductivity.A₁Is an intermediate variable in the calculation process. Andthese are the four components of the ideal thermal conduction tensor, which are both radius and azimuth dependent, i.e., the ideal thermal conduction tensor for the unit cell is different at different locations.

The outer region R' is ≧ R₁The ideal thermal conductivity tensor calculation formula of (θ') is as follows:

wherein the content of the first and second substances,the ideal thermal conductivity tensor representing the outer region of the thermal concentrator,is a rotation matrix, R (theta')^TIs the transposed matrix of R (θ'),. kappa._bIs the background thermal conductivity.A₂And b is an intermediate variable in the calculation process. Is the four components of the ideal thermal conductivity tensor at locations in the outer region of the thermal concentrator. Likewise, these four components are both related to radius and azimuth.

(2) The thermal rotator has the following geometrical dimensions:

where θ' is the different azimuth angle, θ₀Is the heat flow rotation angle, R, of the thermal rotator₁(θ′)，R₂(θ') is a structural parameter shown in fig. 2, which represents the geometric dimension of the thermal rotator, the radius of the thermal rotator varies with the variation of the azimuth angle, and the thermal rotator is represented by an irregular structure.

For thermal rotation, the ideal heat conduction tensor calculation formula at different positions is as follows:

wherein, κ^BIs the ideal heat conduction tensor for the thermal rotator,is a rotation matrix, R (theta')^TIs the transposed matrix of R (θ'),. kappa._bIs the background thermal conductivity of the material,B₁，B₂is an intermediate variable in the calculation process.Andrespectively, four components of the ideal thermal conduction tensor of the thermal rotator, which are both related to radius and azimuth, i.e. the ideal thermal conduction tensor of the unit cell at different positions is different.

(3) The thermal stealth device has the following geometrical dimensions:

where θ' is the different azimuth angle. R₁(θ′)，R₂(θ') is a structural parameter shown in fig. 2, which represents the geometric dimension of the thermal stealth device, and the radius of the thermal stealth device changes with the change of the azimuth angle, which represents that the thermal stealth device is an irregular structure.

For thermal stealth, the ideal heat conduction tensor calculation formula at different positions is as follows:

wherein, κ^CIs the ideal heat conduction tensor for the thermal stealth device,is a rotation matrix, R (theta')^TIs the transposed matrix of R (θ'),. kappa._bIs the background thermal conductivity.C is an intermediate variable in the calculation process.Andthese are the four components of the ideal thermal conduction tensor of the thermal stealth, respectively, which are both related to radius and azimuth, i.e. the ideal thermal conduction tensor of the unit cell is different at different locations.

S2, calculating each of the obtained data by finite element methodThe equivalent heat conduction tensor of the unit cells is that each unit cell is divided into a plurality of finite elements, and the equivalent heat conduction tensor of each unit cell is calculated by using a finite element methodThe calculation formula is as follows:

wherein | V | is the total volume of the functional unit cell; delta T_eIs the difference in the vector of the temperature, is the node temperature vector, T, under uniform test heat flow_eThe node temperature field is obtained through finite element analysis and calculation; n is the total number of finite elements divided in the unit cell.Is a unit cell heat-conducting matrix in which,is a matrix of unity thermal conductivity, N is the shape interpolation function in finite element analysis, V_eIs the volume of a single finite element;κ_material1is the coefficient of thermal conductivity, κ, of the material 1_material2Is the thermal conductivity coefficient of material 2, p is the penalty coefficient, increasing the penalty coefficient can drive the design variable towards 0 and 1; each finite element is assigned a continuous design variable p_eThe variation range is 0-1, wherein 0 represents that the finite element is a material 1, and 1 represents that the finite element is a material 2.

Preferably, a modified SIMP (solid isotropic material penalty model) is used to interpolate the thermal conductivity coefficients of material 1 and material 2.

And S3, constructing a mathematical model for topology optimization based on the formula (8) to obtain the topological cell structure with the specific heat conduction tensor. The structural topology optimization is carried out on each unit cell, so that the equivalent heat conduction tensor of each unit cell is equal to the ideal heat conduction tensor, and the thermal metamaterial structure capable of realizing the corresponding thermal function is obtained.

Specifically, structural topology optimization is performed on the unit cell according to a topology optimization model, the volume minimization of the material 2 is taken as an objective function, and when the material 1 and the material 2 are actually applied, whether the material 1 and the material 2 are respectively a substrate material or a filling material is determined according to the material cost or the actual requirement;

the topology optimization model specifically comprises:

wherein the content of the first and second substances, in order to be the ideal heat conduction tensor,for the equivalent heat conduction tensor, f is a continuous function for balancing the equivalent heat conduction tensorAnd ideal heat conduction tensorThe error between; k (rho)_e) T, Q are a global heat conduction matrix, a global temperature matrix, a global heat load matrix, K (ρ)_e) And Q can be obtained by calculation,

preferably, the constraint G and the objective function C are calculated by an adjoint method for the design variable ρ_eThe sensitivity of (2) is to update the design variables in the optimization problem by using the gradient-based moving asymptote method and the calculated sensitivity, and it can be found from equation (9) that the optimized unit cell structure has an ideal equivalent thermal conductivity tensor when the constraint G is satisfied.

After the unit cells with different structures are obtained by a topology optimization method, the unit cells are assembled into the free-curved-surface thermal metamaterial, and the equivalent heat conduction tensor of each unit cell meets the requirement of an ideal heat conduction tensor, so that different thermal functions can be realized. In order to eliminate the contact thermal resistance when different unit cells are assembled, four corners of each unit cell are fixed by base materials so as to ensure that adjacent unit cells can be connected. The topological optimization design process of the free-curved surface thermal metamaterial functional unit cell is shown in FIG. 2.

In the simulations and experiments, the overall dimensions were 100mm by 100mm, and the background thermal conductivity was 2.3Wm^-1K^-1(ii) a The size of each unit cell was set to 2.5mm by 2.5 mm. One unit cell is divided into 100 x 100 finite elements. Material 1 is a base material, in particular steel (H13, kappa)_H13＝31W m^-1K^-1) The material 2 is a filler material, in particular polydimethylsiloxane (PDMS, kappa)_PDMS＝0.16W m^-1K^-1). The left and right boundaries were set to 393K and 293K, respectively, in the simulation, and the other boundaries were set to be thermally insulating. Fig. 3 shows the heat collection, heat rotation, and heat hiding structure after unit cell integration and the corresponding theoretical simulation temperature field, and it can be seen that by integrating unit cells of different structures, the free curved surface heat metamaterial realizes different thermal functions in different heat flow directions, the external temperature field is not affected by devices and remains parallel, and the heat collection, heat hiding, and heat rotation effects are respectively realized inside the external temperature field. FIG. 4 shows the experimental preparation process of the free-form curved-surface thermal metamaterial, first using 5mm thick steel (H13, K.)_H13＝31W m^-1K^-1) Substrates were constructed and then the voids between the substrates were filled with polydimethylsiloxane. To match background thermal conductivity in the simulation, a cured silicone sealant (ACC AS1802,2.3 Wm) was chosen^-1K^-1) As background material. Peltier heating and cooling modules were fixed at both ends of the curing background plate to create a linear temperature gradient to meet the simulation conditions. The experimentally prepared devices were covered with polyvinyl chloride (PVC) tape, having a thickness of 0.1mm, to maintain the same surface emissivity under an infrared camera. Fig. 5 shows different thermal functional effects of three free-curved-surface thermal metamaterials prepared by experiments, and it is found that similar to simulation results, the external temperature field is hardly influenced by devices, and the internal parts respectively realize thermal aggregation, thermal stealth and thermal rotation effects.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.