A design method for functionally graded multi-scale thermal metamaterials for additive manufacturing

Abstract

This application discloses a design method for functionally gradient multi-scale thermal metamaterials for additive manufacturing, including the following steps: S1. Given a level set function, a gradient lattice structure is obtained by controlling the cutting height of a cutting surface; S2. By selecting cutting surfaces at different heights, gradient lattice structures with different volume fractions are obtained, where the volume fraction is the continuous design variable for each design unit in the coarse grid of the lattice structure; S3. Calculating the sample homogenized thermal conductivity coefficient matrix to obtain the equivalent thermal conductivity of the lattice structure configuration; S4. Constructing a proxy model to obtain the proxy model based on the homogenized thermal conductivity coefficients of multiple lattice structure samples obtained by sampling the relative density at a set discrete resolution; S5. Inverse homogenization design to obtain the relative density field distribution at the coarse grid scale; S6. Result reconstruction and post-processing. This application improves the connectivity and manufacturability of the overall structure and can be directly printed using additive manufacturing processes.

Description

Technical Field

[0001] The present application relates to the technical field of thermal metamaterials, and in particular, to a design method for functionally gradient multi-scale thermal metamaterials for additive manufacturing. Background Art

[0002] Thermal metamaterials are a new class of materials that possess extraordinary thermophysical properties not possessed by traditional natural materials. Because their unique properties are primarily determined by their structural configuration, they are referred to as "metamaterials." The concept of thermal metamaterials was first proposed in 2008 and experimentally verified in 2012 as a thermal cloak. Due to their enormous potential applications, research on thermal metamaterials has attracted widespread attention internationally. Typical applications of thermal metamaterials include devices for thermal cloaking, heat concentrating, and thermal rotation, and they hold significant value in aerospace, energy, electronics, and other fields.

[0003] The main design approaches for thermal metamaterials include heat dissipation compensation and transformation thermals. The heat dissipation compensation approach is less flexible and is only suitable for designing relatively simple and regularly shaped thermal metamaterials. The transformation thermal approach offers greater design flexibility, but the resulting thermal metamaterials exhibit uneven thermal conductivity distribution, are often anisotropic, and are difficult to fabricate. To achieve manufacturable complex thermal metamaterials, structural topology optimization methods are increasingly being applied to the design of thermal metamaterials.

[0004] The existing multi-scale thermal metamaterial design method is based on the inverse homogenization method. After obtaining the thermal conductivity distribution field of the thermal metamaterial using transformation thermals, the microstructure configuration at each discrete point is obtained point by point through the inverse homogenization method and assembled to achieve multi-scale thermal metamaterial design. However, this method cannot guarantee the connectivity between unit cells. The materials in some areas where the microstructures intersect are connected, but there are also many areas where the intersections are not connected. The lack of connectivity of the microstructure will destroy the performance of the overall structure and reduce the manufacturability of the structure. Summary of the Invention

[0005] The embodiments of the present application provide a functional gradient multi-scale thermal metamaterial design method for additive manufacturing, which is used to solve the technical problems of low connectivity and manufacturability of the overall structure of the multi-scale thermal metamaterial obtained by the existing multi-scale thermal metamaterial design method.

[0006] The technical solutions adopted in this application are as follows:

[0007] A method for designing functionally graded multi-scale thermal metamaterials for additive manufacturing, comprising the following steps:

[0008] S1. Select a lattice structure, give a level set function, and obtain a lattice structure with gradient changes by controlling the cutting height of the cutting surface;

[0009] S2. According to relative density sampling, by selecting cutting planes at different heights, a gradient lattice structure with different volume fractions is obtained. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density;

[0010] S3. Calculate the sample uniform heat conductivity matrix by finite element method to obtain the equivalent heat conductivity of the lattice structure configuration;

[0011] S4, constructing a proxy model, obtaining the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution;

[0012] S5, inverse homogenization design, taking the relative density of the coarse grid unit as the design variable, and constructing the optimization formula of the surrogate model as the material constitutive model, and then performing iterative solution to obtain the relative density field distribution at the coarse grid scale;

[0013] S6. Result reconstruction and post-processing: convert each coarse grid unit into a corresponding lattice structure and then perform smoothing.

[0014] Furthermore, the step S1 specifically includes the steps of:

[0015] S11. Define a higher-dimensional level set function α(x). The cutting mathematical expression of the level set function α(x) can be described as:

[0016]

[0017] Where x is the coordinate of any point in the design domain D, Ω is the microstructure domain, is the microstructure boundary, D\Ω refers to the blank area without material, h refers to the cutting height, C(x,h) represents the cutting surface and C(x,h)=h,-1≤h≤1;

[0018] S12. Obtaining a gradient-varying lattice structure configuration by controlling the cutting height of the cutting surface of the level set function α(x).

[0019] Furthermore, the step S3 specifically includes the steps of:

[0020] S31. Using the numerical homogenization method, the equivalent heat conduction coefficient expression of the lattice structure is obtained:

[0021]

[0022] Among them, i and j are the index symbols of the tensor components, |D DE | is the volume of the design unit DE, k lm is the locally varying thermal conductivity, is the preset temperature gradient field, is the temperature gradient field of the response;

[0023] S32, solving the equivalent thermal conductivity expression of the lattice structure by the finite element method to obtain the equivalent thermal conductivity

[0024] Furthermore, the step S4 specifically includes the steps of:

[0025] S41, establishing a mapping relationship between the homogenized heat conductivity coefficient and the relative density ρ;

[0026] S42, sampling the relative density ρ between [0, 1] with an appropriate discrete resolution to obtain a family of lattice structure samples;

[0027] S43. Perform homogenization calculation on each lattice structure sample to obtain the corresponding homogenized heat conduction coefficient

[0028] S44. Perform interpolation fitting on the lattice structure sample to obtain a proxy model.

[0029] Furthermore, the optimization formula in step S5 is:

[0030]

[0031] Where X is the design variable, n is the number of coarse grid elements, the optimization goal is to minimize the total material usage of the structure, that is, the material volume, P refers to the thermal load, T refers to the temperature field result of the finite element solution, and K is the overall heat transfer matrix of the coarse grid scale. is the homogenized equivalent heat transfer matrix of the structure, G describes the difference between the target heat transfer matrix and the equivalent heat transfer matrix, and f is a self-defined metric function defined as needed.

[0032] Furthermore, in step S5, the MMA algorithm is used when iteratively solving the optimization formula.

[0033] On the other hand, the present application provides a functionally graded multi-scale thermal metamaterial design device for additive manufacturing, comprising:

[0034] The lattice structure selection module is used to select the lattice structure. Given a level set function, the lattice structure with gradient changes is obtained by controlling the cutting height of the cutting surface.

[0035] The relative density sampling module is used to obtain gradient lattice structures with different volume fractions by selecting cutting planes at different heights based on relative density sampling. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density;

[0036] The equivalent thermal conductivity calculation module is used to calculate the sample homogenized thermal conductivity matrix using the finite element method to obtain the equivalent thermal conductivity of the lattice structure configuration;

[0037] A proxy model construction module is used to construct a proxy model, and obtain the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution;

[0038] The inverse homogenization design module is used for inverse homogenization design. It uses the relative density of the coarse grid unit as the design variable and uses the surrogate model as the material constitutive model to construct the optimization formula and then iteratively solve it to obtain the relative density field distribution at the coarse grid scale.

[0039] The reconstruction and post-processing module is used for result reconstruction and post-processing, converting each coarse grid unit into a corresponding lattice structure and then performing smoothing.

[0040] On the other hand, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for designing functionally graded multi-scale thermal metamaterials for additive manufacturing are implemented.

[0041] On the other hand, the present application also provides a storage medium, which includes a stored program, and when the program is run, controls the device where the storage medium is located to execute the steps of the functional gradient multi-scale thermal metamaterial design method for additive manufacturing.

[0042] Compared with the existing technology, this application has the following beneficial effects:

[0043] The present application provides a functional gradient multi-scale thermal metamaterial design method for additive manufacturing, including the following steps: S1, selecting a lattice structure, giving a level set function, and obtaining a gradient-changing lattice structure by controlling the cutting height of the cutting surface; S2, sampling according to relative density, obtaining gradient lattice structures with different volume fractions by selecting cutting surfaces of different heights, wherein the volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density; S3, calculating the sample homogenized thermal conductivity coefficient matrix by the finite element method to obtain the equivalent thermal conductivity coefficient of the lattice structure configuration; S4, constructing a proxy model, obtaining the proxy model based on the homogenized thermal conductivity coefficient of multiple lattice structure samples obtained after sampling the relative density according to the set discrete resolution; S5, inverse homogenization design, taking the relative density of the coarse grid unit as the design variable, and constructing the proxy model as the material constitutive optimization formula and then iteratively solving it to obtain the relative density field distribution at the coarse grid scale; S6, result reconstruction and post-processing, converting each coarse grid unit into the corresponding lattice structure and then smoothing it.

[0044] Compared with the existing solutions, in the traditional single-scale solution, in order to obtain a structural topology with clear and smooth boundaries and that can be manufactured, the present application needs to increase the discrete resolution of the structure as much as possible, and adopt appropriate numerical processing methods to eliminate intermediate density units. However, in this case, there may be less material at the boundary of the microstructure, and the microstructure configurations obtained by optimizing different target thermal conductivity tensors at different macroscopic positions are quite different, making connectivity difficult to ensure. This solution adopts the idea of ​​functional gradient design, and uses a multi-scale microstructure with functional gradient to replace the single-scale microstructure in the traditional method, allowing the existence of intermediate density, and does not require a clear macroscopic topological structure, that is, it does not require a high macroscopic grid discrete resolution. Therefore, while achieving the design goals, the connectivity and manufacturability of the overall structure are significantly improved, and it can be directly printed using an additive manufacturing process.

[0045] In addition to the above-described purposes, features and advantages, the present application has other purposes, features and advantages. The present application will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the functionally graded multi-scale thermal metamaterial design method according to a preferred embodiment of the present application.

[0047] Figure 2 Schematic diagrams of 9 typical two-dimensional lattice structure prototypes.

[0048] Figure 3 It is a schematic diagram of obtaining a gradient lattice structure at different cutting heights in a preferred embodiment of the present application.

[0049] Figure 4 This is a schematic diagram of sampling and fitting results in a preferred embodiment of the present application, wherein:

[0050] Figure 4 (a) Schematic diagram of the gradient configuration obtained by discrete sampling of relative density for the selected type of microstructure.

[0051] Figure 4 (b) Schematic diagram of the discrete sampling results and fitting curve of the level set function cutting height corresponding to the selected type of gradient microstructure based on relative density.

[0052] Figure 4 (c) is a schematic diagram of the discrete sampling results and fitting curve of element 1 in the homogenized thermal conductivity matrix corresponding to the selected type of gradient microstructure based on relative density.

[0053] Figure 4 (d) is a schematic diagram of the discrete sampling results and fitting curve of element 2 in the homogenized thermal conductivity matrix corresponding to the selected type of gradient microstructure based on relative density.

[0054] Figure 5 This is a schematic diagram of an example design of a functional gradient lattice unit cell according to a preferred embodiment of the present application.

[0055] Figure 6 Schematic diagram of the effect of traditional design method.

[0056] Figure 7 This is a schematic diagram comparing the effects of the design methods of the preferred embodiment of the present application.

[0057] Figure 8 This is a schematic diagram of the module of the functionally graded multi-scale thermal metamaterial design device according to the preferred embodiment of the present application.

[0058] Figure 9 This is a schematic block diagram of an electronic device entity according to a preferred embodiment of the present application.

[0059] Figure 10 It is a schematic diagram of the internal structure of a computer device according to a preferred embodiment of the present application. DETAILED DESCRIPTION

[0060] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0061] Reference Figure 1 The preferred embodiment of the present application provides a method for designing functionally graded multi-scale thermal metamaterials for additive manufacturing, comprising the steps of:

[0062] S1. Select the lattice structure, give the level set function, and obtain the lattice structure with gradient change by controlling the cutting height of the cutting surface, such as Figure 2 As shown, there are 9 types of lattice structures;

[0063] S2. According to relative density sampling, by selecting cutting planes at different heights, gradient lattice structures with different volume fractions (i.e., the volume ratio of the material volume to the volume of the structural design domain, ranging from 0 to 1) can be obtained. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density, with Figure 2 Taking type (2) in as an example, we can get Figure 3 Gradient lattice structures are obtained at different cutting heights as shown;

[0064] S3. Calculate the sample uniform heat conductivity matrix by finite element method to obtain the equivalent heat conductivity of the lattice structure configuration;

[0065] S4, constructing a proxy model, obtaining the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution;

[0066] S5, inverse homogenization design, taking the relative density of the coarse grid unit as the design variable, and constructing the optimization formula of the surrogate model as the material constitutive model, and then performing iterative solution to obtain the relative density field distribution at the coarse grid scale;

[0067] S6. Result reconstruction and post-processing: convert each coarse grid unit into a corresponding lattice structure and then perform smoothing.

[0068] This embodiment provides a functional gradient multi-scale thermal metamaterial design method for additive manufacturing. The basic design concept of the functional gradient multi-scale microstructure is to discretize the design domain into two levels: coarse and fine grids. Each coarse grid unit corresponds to a functional gradient lattice unit cell, which is obtained by the level set function cutting method, including the following steps: S1, selecting a lattice structure, giving a level set function, and obtaining a gradient-changing lattice structure by controlling the cutting height of the cutting surface; S2, according to relative density sampling, obtaining gradient lattice structures with different volume fractions by selecting cutting surfaces of different heights, and the volume fraction is the volume fraction of each design unit in the coarse grid in the lattice structure. Continuous design variables: relative density; S3. Calculate the sample homogenized thermal conductivity matrix using the finite element method to obtain the equivalent thermal conductivity of the lattice structure configuration; S4. Construct a proxy model, and obtain the proxy model based on the homogenized thermal conductivity of multiple lattice structure samples obtained by sampling the relative density according to the set discrete resolution; S5. Inverse homogenization design, the relative density of the coarse grid unit is used as the design variable, and the proxy model is used as the material constitutive optimization formula and then iteratively solved to obtain the relative density field distribution at the coarse grid scale; S6. Result reconstruction and post-processing, converting each coarse grid unit into the corresponding lattice structure and then smoothing it.

[0069] Compared with the existing solutions, in the traditional single-scale solution, in order to obtain a structural topology with clear and smooth boundaries and that can be manufactured, the present embodiment needs to increase the discrete resolution of the structure as much as possible, and adopt appropriate numerical processing methods to eliminate intermediate density units. However, in this case, there may be less material at the boundary of the microstructure, and the microstructure configurations obtained by optimizing different target thermal conductivity tensors at different macroscopic positions are quite different, making connectivity difficult to ensure. This solution adopts the idea of ​​functional gradient design, and uses a multi-scale microstructure with functional gradient to replace the single-scale microstructure in the traditional method, allowing the existence of intermediate density, and does not require a clear macroscopic topological structure, that is, does not require a high macroscopic grid discrete resolution. Therefore, while achieving the design goals, the connectivity and manufacturability of the overall structure are significantly improved, and it can be directly printed using an additive manufacturing process.

[0070] Preferably, the step S1 specifically includes the steps of:

[0071] S11. Define a higher-dimensional level set function α(x). The cutting mathematical expression of the level set function α(x) can be described as:

[0072]

[0073] Where x is the coordinate of any point in the design domain D, Ω is the microstructure domain, is the microstructure boundary, D\Ω refers to the blank area without material, h refers to the cutting height, C(x,h) represents the cutting surface and C(x,h)=h,-1≤h≤1;

[0074] S12. Obtaining a gradient-varying lattice structure configuration by controlling the cutting height of the cutting surface of the level set function α(x).

[0075] The traditional level set method is to keep the cutting surface fixed and realize the structural evolution by updating the level set function. The idea adopted in this application is to obtain a gradient-changing lattice structure configuration by controlling the cutting height of the cutting surface given a level set function. This is a classic method for obtaining a gradient-changing lattice structure, that is, obtaining a family of lattice structure configurations with similar shapes, geometric dimensions and performance gradients. In the sampling stage, only simple cases are considered, and the cutting surface is defined as:

[0076] C(x,h)=h,-1≤h≤1

[0077] Therefore, we can obtain different styles of microstructure prototypes by defining different level set functions α(x). For example, Figure 2 shown.

[0078] The solution of cutting with a level set function in this embodiment can efficiently obtain a microstructure configuration with a gradual gradient, and can freely and flexibly obtain various types of functionally gradient microstructure prototypes by changing the level set function.

[0079] Preferably, the step S3 specifically includes the steps of:

[0080] S31. Using the numerical homogenization method, the equivalent heat conduction coefficient expression of the lattice structure is obtained:

[0081]

[0082] Among them, i and j are the index symbols of the tensor components, |D DE | is the volume of the design unit DE, k lm is the locally varying thermal conductivity, is the preset temperature gradient field, is the temperature gradient field of the response;

[0083] S32, solving the equivalent thermal conductivity expression of the lattice structure by the finite element method to obtain the equivalent thermal conductivity

[0084] In this embodiment, the numerical homogenization method has a rigorous theoretical basis, has high calculation accuracy for functional gradient structures, and transmits information unidirectionally between different scales. The calculation process is simple, which is conducive to establishing a corresponding structural configuration-equivalent thermal conductivity matrix database and establishing a corresponding proxy model.

[0085] Preferably, the step S4 specifically includes the steps of:

[0086] S41, establishing a mapping relationship between the homogenized heat conductivity coefficient and the relative density ρ;

[0087] S42, sampling the relative density ρ between [0, 1] with an appropriate discrete resolution to obtain a family of lattice structure samples;

[0088] S43. Perform homogenization calculation on each lattice structure sample to obtain the corresponding homogenized heat conduction coefficient Discrete-based Data, by polynomial fitting, to establish the uniform heat transfer coefficient Mapping between and relative density ρ:

[0089]

[0090]

[0091] Among them, k 11 and k 22 They represent the two components at the main diagonal of the homogenized equivalent heat conduction tensor, y = 1, 2; d0 is the predetermined polynomial order, and p is the corresponding polynomial coefficient;

[0092] S44. Perform interpolation fitting on the lattice structure sample to obtain a proxy model.

[0093] Taking type (2) in 2 as an example, we sampled with a discrete resolution of [0, 0.05, 0.1, ..., 0.90, 0.95, 1] ​​to obtain 21 configuration samples, and performed homogenization calculations to obtain the corresponding 21 sets of homogenized heat transfer coefficients. Then interpolate and fit the samples to obtain the proxy model, and the results are as follows Figure 4 (a)-4(d) shown.

[0094] Preferably, the optimization formula in step S5 is:

[0095]

[0096] Where X is the design variable, n is the number of coarse grid elements, the optimization goal is to minimize the total material usage of the structure, that is, the material volume, P refers to the thermal load, T refers to the temperature field result of the finite element solution, and K is the overall heat transfer matrix of the coarse grid scale. is the homogenized equivalent heat transfer matrix of the structure, G describes the difference between the target heat transfer matrix and the equivalent heat transfer matrix, and f is a self-defined metric function defined as needed.

[0097] Preferably, in step S5, an MMA algorithm (the method of moving asymptotes) is used when iteratively solving the optimization formula.

[0098] Figure 5 An example of functional gradient lattice unit cell design is shown. Input the heat transfer matrix k of a target Output , we can use the solution proposed in this application to design the equivalent heat transfer matrix k H Close to k Output It can be seen that this functionally graded multi-scale thermal metamaterial does not require too high a coarse grid discrete resolution, nor does it need to eliminate intermediate density units to obtain a design with performance close to that of a good effect.

[0099] at last, Figure 6 A simple design case is shown. Using traditional design methods, it can be seen that it is difficult to connect the unit cells at many points, which will greatly reduce the performance of the combined structure and make the structure manufacturability poor. Figure 7 The same design was carried out using the scheme proposed in this application. The total volume of the materials was similar, and the results were k H Approximation k Output While the effect is good, the assembly structure has good connectivity. After structural post-processing, the connectivity advantage of the assembly structure is further enhanced, the manufacturability of the overall structure is guaranteed, and it can be directly processed and manufactured using the additive manufacturing method.

[0100] like Figure 8 As shown, another preferred embodiment of the present application provides a functionally graded multi-scale thermal metamaterial design device for additive manufacturing, comprising:

[0101] The lattice structure selection module is used to select the lattice structure. Given a level set function, the lattice structure with gradient changes is obtained by controlling the cutting height of the cutting surface.

[0102] The relative density sampling module is used to obtain gradient lattice structures with different volume fractions by selecting cutting planes at different heights based on relative density sampling. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density;

[0103] The equivalent thermal conductivity calculation module is used to calculate the sample homogenized thermal conductivity matrix using the finite element method to obtain the equivalent thermal conductivity of the lattice structure configuration;

[0104] A proxy model construction module is used to construct a proxy model, and obtain the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution;

[0105] The inverse homogenization design module is used for inverse homogenization design. It uses the relative density of the coarse grid unit as the design variable and uses the surrogate model as the material constitutive model to construct the optimization formula and then iteratively solve it to obtain the relative density field distribution at the coarse grid scale.

[0106] The reconstruction and post-processing module is used for result reconstruction and post-processing, converting each coarse grid unit into a corresponding lattice structure and then performing smoothing.

[0107] like Figure 9 As shown, a preferred embodiment of the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the functional gradient multi-scale thermal metamaterial design method for additive manufacturing in the above-mentioned embodiment are implemented.

[0108] like Figure 10 As shown, the preferred embodiment of the present application further provides a computer device, which can be a terminal or a liveness detection server, and its internal structure diagram can be as shown in FIG. Figure 10 As shown. The computer device includes a processor, a memory and a network interface connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with other external computer devices via a network connection. When the computer program is executed by the processor, the steps of the above-mentioned functional gradient multi-scale thermal metamaterial design method for additive manufacturing are implemented.

[0109] Those skilled in the art will understand that Figure 10 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0110] A preferred embodiment of the present application also provides a storage medium, which includes a stored program, and when the program is run, controls the device where the storage medium is located to execute the steps of the functional gradient multi-scale thermal metamaterial design method for additive manufacturing in the above embodiment.

[0111] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0112] If the functions described in the method of this embodiment are implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a storage medium readable by one or more computing devices. Based on this understanding, the part of the embodiment of the present application that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for enabling a computing device (which can be a personal computer, server, mobile computing device or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program code.

[0113] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0114] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0115] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0116] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0117] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0118] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A design method for functionally graded multi-scale thermal metamaterials for additive manufacturing, characterized by: Including steps: S1. Select a lattice structure, give a level set function, and obtain a lattice structure with gradient changes by controlling the cutting height of the cutting surface; S2. According to relative density sampling, by selecting cutting planes at different heights, a gradient lattice structure with different volume fractions is obtained. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density; S3. Calculate the sample uniform heat conductivity matrix by finite element method to obtain the equivalent heat conductivity of the lattice structure configuration; S4, constructing a proxy model, obtaining the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution; S5, inverse homogenization design, taking the relative density of the coarse grid unit as the design variable, and constructing the optimization formula of the surrogate model as the material constitutive model, and then performing iterative solution to obtain the relative density field distribution at the coarse grid scale; S6. Result reconstruction and post-processing: convert each coarse grid unit into the corresponding lattice structure and then perform smoothing.

2. The design method of functionally graded multi-scale thermal metamaterials for additive manufacturing according to claim 1, characterized in that: The step S1 specifically includes the following steps: S11. Define a higher-dimensional level set function α(x). The cutting mathematical expression of the level set function α(x) is described as: Where x is the coordinate of any point in the design domain D, Ω is the microstructure domain, is the microstructure boundary, D\Ω refers to the blank area without material, h refers to the cutting height, C(x, h) represents the cutting surface and C(x, h) = h, -1≤h≤1; S12. Obtaining a gradient-varying lattice structure configuration by controlling the cutting height of the cutting surface of the level set function α(x).

3. The design method of functionally graded multi-scale thermal metamaterials for additive manufacturing according to claim 2, characterized in that: The step S3 specifically includes the following steps: S31. Using the numerical homogenization method, the equivalent heat conduction coefficient expression of the lattice structure is obtained: Among them, i and j are the index symbols of the tensor components, |D DE | is the volume of the design unit DE, k lm is the locally varying thermal conductivity, is the preset temperature gradient field, is the temperature gradient field of the response; S32, solving the equivalent thermal conductivity expression of the lattice structure by the finite element method to obtain the equivalent thermal conductivity 4. The design method of functionally graded multi-scale thermal metamaterials for additive manufacturing according to claim 3, characterized in that: The step S4 specifically includes the following steps: S41, establishing a mapping relationship between the homogenized heat conductivity coefficient and the relative density ρ; S42, sampling the relative density ρ between [0, 1] with an appropriate discrete resolution to obtain a family of lattice structure samples; S43. Perform homogenization calculation on each lattice structure sample to obtain the corresponding homogenized heat conduction coefficient S44. Perform interpolation fitting on the lattice structure sample to obtain a proxy model.

5. The design method of functionally graded multi-scale thermal metamaterials for additive manufacturing according to claim 4, characterized in that: The optimization formula in step S5 is: Where X is the design variable, n is the number of coarse grid elements, the optimization goal is to minimize the total material usage of the structure, that is, the material volume, P refers to the thermal load, T refers to the temperature field result of the finite element solution, and K is the overall heat transfer matrix of the coarse grid scale. is the homogenized equivalent heat transfer matrix of the structure, G describes the difference between the target heat transfer matrix and the equivalent heat transfer matrix, and f is a self-defined metric function defined as needed.

6. The design method of functionally graded multi-scale thermal metamaterials for additive manufacturing according to claim 5, characterized in that: In step S5, the MMA algorithm is used to iteratively solve the optimization formula.

7. A functionally graded multi-scale thermal metamaterial design device for additive manufacturing, characterized in that: include: The lattice structure selection module is used to select the lattice structure. Given a level set function, the lattice structure with gradient changes is obtained by controlling the cutting height of the cutting surface. The relative density sampling module is used to obtain gradient lattice structures with different volume fractions by selecting cutting planes at different heights based on relative density sampling. The volume fraction is the continuous design variable of each design unit in the coarse grid in the lattice structure: relative density; The equivalent thermal conductivity calculation module is used to calculate the sample homogenized thermal conductivity matrix using the finite element method to obtain the equivalent thermal conductivity of the lattice structure configuration; A proxy model construction module is used to construct a proxy model, and obtain the proxy model according to the uniformized heat conductivity coefficient of a plurality of lattice structure samples obtained after sampling the relative density according to a set discrete resolution; The inverse homogenization design module is used for inverse homogenization design. It uses the relative density of the coarse grid unit as the design variable and uses the surrogate model as the material constitutive model to construct the optimization formula and then iteratively solve it to obtain the relative density field distribution at the coarse grid scale. The reconstruction and post-processing module is used for result reconstruction and post-processing, converting each coarse grid unit into a corresponding lattice structure and then performing smoothing.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the functional gradient multi-scale thermal metamaterial design method for additive manufacturing as described in any one of claims 1 to 6 are implemented.

9. A storage medium comprising a stored program, characterized in that: When the program is running, the device where the storage medium is located is controlled to execute any one of steps 1 to 6 of the method for designing functionally graded multi-scale thermal metamaterials for additive manufacturing.

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