Three-dimensional structure unit cell configuration multi-physical field performance coupling regulation and control method and system

Abstract

The invention relates to a three-dimensional structure unit cell configuration multi-physical field performance coupling regulation and control method and system, and belongs to the field of electric digital data processing. And constructing a multi-scale self-similar microstructure unit cell through a fractal geometry theory. The fractal dimension is quantitatively represented by adopting a box-counting dimension method, a mapping relation model of the fractal dimension and electromagnetic, mechanical, optical and other physical properties is established, and directional regulation and control of macroscopic physical properties are realized. The material meets the requirements of multiple fields such as electromagnetic wave absorption, vibration suppression and light field regulation and control through parameterized design, the limitation of cross-physical field regulation and control of traditional materials is solved, and a universal framework is provided for mathematical design of functional materials.

Description

Technical Field

[0001] This invention pertains to the field of electronic digital data processing and relates to a mathematically defined material based on fractal geometry theory. This material achieves quantitative control of electromagnetic, mechanical, and optical properties through microstructure unit cell organization with a specific fractal dimension. This material overcomes the limitations of traditional functional materials' single-physical-field design by establishing a mathematical mapping relationship between fractal geometric parameters and macroscopic physical properties, providing a universal method for the digital design of cross-domain functional materials. Background Technology

[0002] The design of traditional functional materials relies on trial and error, making it difficult to achieve synergistic performance control across multiple physics fields. For example, the absorption peak frequency of electromagnetic absorbing materials and the resonant frequency band of mechanically damping materials lack unified characterization parameters, and the asymmetry control of optical transmission materials cannot be compatible with thermal protection performance. Although fractal geometry theory has been applied to single physics fields (such as mechanical fractal structures and electromagnetic fractal structures), a unified mathematical model across disciplines has not yet been formed: on the one hand, there is a lack of quantitative correlation equations between fractal dimension and different physical performance parameters; on the other hand, a universal design framework considering multi-scale structure-physical field coupling has not been established. How to find a parameter to uniformly characterize multiphysics field performance remains a key challenge restricting the development of mathematically defined materials. Summary of the Invention

[0003] The purpose of this invention is to provide a method for coupling and controlling the multi-physics properties of a three-dimensional single-cell structure, which can achieve coupled control of electromagnetic, mechanical, and optical properties.

[0004] The technical solution of this invention is: a method for coupling and controlling the multiphysics field performance of a three-dimensional single-cell structure, comprising: Based on the initially given specific three-dimensional structural unit cell configuration, calculate the fractal dimension of the overall configuration and determine the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; determine whether the currently calculated fractal dimension is greater than or equal to 2.5. If it is, continue the subsequent processing; otherwise, adjust the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.5. A unified parameterized model of multiphysics is constructed. Based on the pre-designed thickness, electromagnetic properties, mechanical properties and optical properties as constraints, the common geometric characteristic parameters of the structure, namely fractal dimension, duty cycle of each layer and thickness of each layer, are iteratively optimized to obtain the optimal three-dimensional structural unit cell configuration that simultaneously satisfies the electromagnetic properties, mechanical properties and optical properties.

[0005] Preferably, the fractal dimension is calculated in the following manner: Construct a geometric model of a three-dimensional structural unit cell configuration, and use cubic meshes of different scales to contain the three-dimensional space occupied by the geometric model; Calculate the number of cubic meshes containing objects, Nr; right and In least squares regression analysis, the slope of the fitted line is the fractal dimension. Where r is the side length of the cubic grid, and r decreases by a factor of 10 to cover at least 3 orders of magnitude.

[0006] Preferably, the unified parameterized model of multiple physics fields includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

[0007] Preferably, the impedance transfer equation derived based on transmission line theory is as follows: ,in Impedance gradient correction factor , Let the impedance be the wave impedance of the k-th layer. The impedance of the (k-1)th layer is... The intrinsic impedance of the material, Let be the complex propagation constant. Let be the thickness of the k-th layer, D be the fractal dimension of the configuration, D1 be the reference fractal dimension, α be the material constant with a value ranging from 1 to 10, and p be the duty cycle of the k-th layer.

[0008] Preferably, the fractal damping model based on mechanical wave theory is as follows: for each layer of the configuration, the loss factor... Among them, the equivalent stiffness Damping coefficient ; in, For material stiffness, Let fractal dimension be the number of ... D1 is the duty cycle of the calculation layer, D1 is the baseline fractal dimension, and β is the material constant, with a value range of 0-1.

[0009] Preferably, the fractal light transmission model constructed based on Fresnel diffraction theory is as follows: for each layer of the configuration, the transmittance... , The reference transmittance; Impedance gradient correction factor Where D1 is the reference fractal dimension, ε is a material constant ranging from 1 to 10, and the optical attenuation coefficient is... Where λ is the wavelength of light and the equivalent refractive index is... ,in , Where is the refractive index of the material and the porosity, and K is the extinction coefficient. d represents the duty cycle and thickness of the calculation layer.

[0010] A three-dimensional single-cell configuration multiphysics field performance coupling control system includes: The preprocessing module calculates the fractal dimension of the overall configuration based on the initially given specific three-dimensional structural unit cell configuration, and determines the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; it determines whether the currently calculated fractal dimension is greater than or equal to 2.5. If it is, it continues the subsequent processing; otherwise, it adjusts the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.5. The optimization module constructs a unified parameterized model of multiple physics fields. Based on the pre-designed thickness, electromagnetic performance, mechanical performance and optical performance indicators as constraints, iteratively optimizes the common geometric characteristic parameters of the structure, namely fractal dimension, duty cycle of each layer and thickness of each layer, to obtain the optimal three-dimensional structural unit cell configuration that simultaneously satisfies the electromagnetic performance, mechanical performance and optical performance indicators.

[0011] Preferably, the unified parameterized model of multiple physics fields includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

[0012] A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for coupling and controlling the multiphysics properties of a three-dimensional single-cell configuration.

[0013] A computer software product includes: a processor and a storage device; Storage device for storing one or more programs. When the one or more programs are executed by one or more processors, the one or more processors implement the three-dimensional structural unit cell configuration multiphysics field performance coupling control method.

[0014] The advantages of this invention compared to the prior art are as follows: 1. Based on research findings that the geometric complexity (fractal dimension D) of fractal structures is correlated with physical phenomena such as mechanical wave loss, electromagnetic wave absorption, and light scattering, this invention establishes a fractal-performance mapping relationship for multiple physics fields. The requirement for multi-field coupling and control is satisfied by limiting the fractal dimension. Electromagnetic, mechanical, and optical properties are uniformly characterized using a fractal dimension D (2.5-3.0).

[0015] 2. A unified parameterized model for multiple fields is proposed: using fractal dimension D, duty cycle p, and layer thickness d as core parameters, and fractal correction coefficient G as a multi-field coupling factor, multi-domain characterization equations are constructed. In the electromagnetic field, the impedance transfer equation of the fractal structure is derived based on transmission line theory; in the mechanical field, a fractal damping model is established based on mechanical wave theory; and in the optical field, a fractal optical transmission model is constructed based on Fresnel diffraction theory, achieving the design goal of "same structural parameters - multi-field performance prediction".

[0016] 3. Constructing a mathematically defined material design system: Starting from fractal dimension screening, a closed-loop process of "geometric parameter calculation - physical performance prediction - multi-field collaborative optimization" is formed. Materials designed through this process can have their fractal structure parameters customized according to target requirements (such as electromagnetic stealth + vibration suppression composite function), ensuring multi-field performance control accuracy ≤5%. An application example of a composite functional device shows that the fractal material simultaneously achieves ≥10dB absorption in the 10-18GHz range and ≥15dB vibration attenuation in the 100-800Hz range, verifying the effectiveness of multi-field control. Attached Figure Description

[0017] Figure 1: Unified flowchart for calculating the fractal dimension using box-counting dimension Figure 2 : Schematic diagram of multi-field collaborative design process. Detailed Implementation

[0018] The following is in conjunction with the appendix Figure 1-2 This invention provides a detailed description of a method for coupling and controlling the multiphysics properties of a three-dimensional single-cell structure, such as... Figure 2 As shown, the steps are as follows: (1) Based on the specific three-dimensional structural unit cell configuration, calculate the fractal dimension of the overall configuration and determine the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; determine whether the currently calculated fractal dimension is greater than or equal to 2.5. If it is greater than or equal to 2.5, continue the subsequent processing; otherwise, adjust the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.5. like Figure 1 As shown, the fractal dimension is calculated in the following way: Construct a geometric model of a three-dimensional structural unit cell configuration, and use cubic meshes of different scales to contain the three-dimensional space occupied by the geometric model; Calculate the number of cubic meshes containing objects, Nr; right and In least squares regression analysis, the slope of the fitted line is the fractal dimension. Where r is the side length of the cubic grid, and r decreases by a factor of 10 to cover at least 3 orders of magnitude.

[0019] When D is greater than 2.5, the space filling rate of the fractal structure exceeds 80%, satisfying the requirements for multi-field coupling control. The electromagnetic, mechanical, and optical properties are uniformly characterized by the fractal dimension D (2.5-3.0). For example, when D=2.96, -20dB reflection loss is achieved in the electromagnetic field at 10GHz, a loss factor of 0.8 is achieved in the mechanical field at 500Hz, and a transmission asymmetry of 30% is achieved in the optical field at 550nm.

[0020] (2) Select the fractal dimension, duty cycle of each layer and thickness of each layer as design parameters to construct a unified parameterized model of multiple physics fields; and perform iterative optimization based on the pre-designed thickness, electromagnetic performance, mechanical performance and optical performance indicators as constraints to obtain the optimal three-dimensional structural unit cell configuration that meets the electromagnetic performance, mechanical performance and optical performance indicators.

[0021] The unified parameterized model of multiphysics includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

[0022] The impedance transfer equation derived from transmission line theory is as follows: ,in Impedance gradient correction factor , Let the impedance be the wave impedance of the k-th layer. The impedance of the (k-1)th layer is... The intrinsic impedance of the material, Let be the complex propagation constant. Let be the thickness of the k-th layer, D be the fractal dimension of the configuration, D1 be the reference fractal dimension, α be the material constant ranging from 1 to 10, and p be the duty cycle of the k-th layer. If there is a reflective substrate... The value is 0; if there is no reflective liner, The value is 1.

[0023] The fractal damping model based on mechanical wave theory is as follows: For each layer of the configuration, the loss factor... Among them, the equivalent stiffness Damping coefficient ; in, For material stiffness, Let fractal dimension be the number of ... D1 is the duty cycle of the calculation layer, D1 is the baseline fractal dimension, and β is the material constant, with a value range of 0-1.

[0024] Based on Fresnel diffraction theory, a fractal light transmission model is constructed as follows: For each layer in the configuration, the transmittance... , The reference transmittance is 1-10 if the interface is in free space. Impedance gradient correction factor Where D1 is the reference fractal dimension, ε is a material constant ranging from 1 to 10, and the optical attenuation coefficient is... Where λ is the wavelength of light and the equivalent refractive index is... ,in , Where is the refractive index of the material and the porosity, and K is the extinction coefficient. d represents the duty cycle and thickness of the calculation layer.

[0025] The present invention further provides a three-dimensional structural unit cell configuration multiphysics field performance coupling control system, comprising: The preprocessing module calculates the fractal dimension of the overall configuration based on the initially given specific three-dimensional structural unit cell configuration, and determines the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; it determines whether the currently calculated fractal dimension is greater than or equal to 2.5. If it is, it continues subsequent processing; otherwise, it adjusts the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.5, triggering the optimization module. The optimization module constructs a unified parameterized model of multiple physics fields. Based on the pre-designed thickness, electromagnetic performance, mechanical performance and optical performance indicators as constraints, iteratively optimizes the common geometric characteristic parameters of the structure, namely fractal dimension, duty cycle of each layer and thickness of each layer, to obtain the optimal three-dimensional structural unit cell configuration that simultaneously satisfies the electromagnetic performance, mechanical performance and optical performance indicators.

[0026] Preferably, the unified parameterized model of multiple physics fields includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

[0027] The present invention further provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for coupling and controlling the multiphysics performance of a three-dimensional single-cell configuration.

[0028] The present invention further provides a computer software product, including: a processor and a storage device; Storage device for storing one or more programs. When the one or more programs are executed by one or more processors, the one or more processors implement the three-dimensional structural unit cell configuration multiphysics field performance coupling control method.

[0029] Example Establish multi-field performance equations: Electromagnetic field: Based on transmission line theory, reflection loss , where the input impedance For fractal correction coefficients; In the field of mechanics: loss factor Among them, the equivalent stiffness Damping coefficient ; In the field of optics: based on Fresnel theory, transmittance equivalent refractive index Optical attenuation coefficient .

[0030] Optimized design: The composite material with both electromagnetic wave absorption and vibration suppression functions was optimized and designed according to the method of the present invention, and the results are as follows: Parameter optimization: D=2.85 (balanced electromagnetic and mechanical response bandwidth), duty cycle p=[0.3,0.6], two-layer structure, thickness d=150μm, 3mm; Performance calculations: Electromagnetic field 10GHz reflection loss -18dB, mechanical field 500Hz loss factor 0.7; Simulation experiments verified that the reflection loss RL = -17.5dB, the loss factor η = 0.68, and the multi-field control deviation ≤ 3%.

[0031] Example 2 For radar stealth and vibration isolation requirements, the intrinsic parameters of the material ( ε m =12.5- j 1.8, μ m =4.2- j 0.9, c_s=1.8×10 7 According to the method of this invention, D=2.92 was obtained. The thickness gradient (0.8 / 1.2 / 3.0mm) and duty cycle gradient (0.25 / 0.50 / 0.70) of the three-layer structure achieved multi-field coordinated control of "radar stealth + vibration isolation". Electromagnetic field: 8-12GHz full-band RL≤-10dB, meeting radar stealth requirements; In the field of mechanics: η≥0.6 across the entire 200-600Hz frequency band, meeting the requirements for vibration isolation.

[0032] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for coupling and controlling the multiphysics properties of a three-dimensional single-cell structure, characterized in that... include: Based on the initially given specific three-dimensional structural unit cell configuration, calculate the fractal dimension of the overall configuration and determine the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; determine whether the currently calculated fractal dimension is greater than or equal to 2.

5. If it is, continue the subsequent processing; otherwise, adjust the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.

5. A unified parameterized model of multiphysics is constructed. Based on the pre-designed thickness, electromagnetic properties, mechanical properties and optical properties as constraints, the common geometric characteristic parameters of the structure, namely fractal dimension, duty cycle of each layer and thickness of each layer, are iteratively optimized to obtain the optimal three-dimensional structural unit cell configuration that simultaneously satisfies the electromagnetic properties, mechanical properties and optical properties.

2. The method for coupling and controlling the multiphysics performance of a three-dimensional single-cell structure according to claim 1, characterized in that: The fractal dimension is calculated as follows: Construct a geometric model of a three-dimensional structural unit cell configuration, and use cubic meshes of different scales to contain the three-dimensional space occupied by the geometric model; Calculate the number of cubic meshes containing objects, Nr; right and In least squares regression analysis, the slope of the fitted line is the fractal dimension. Where r is the side length of the cubic grid, and r decreases by a factor of 10 to cover at least 3 orders of magnitude.

3. The method for coupling and controlling the multiphysics performance of a three-dimensional single-cell structure according to claim 1, characterized in that: The unified parameterized model of multiphysics includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

4. The method for coupling and controlling the multiphysics performance of a three-dimensional single-cell structure according to claim 1, characterized in that: The impedance transfer equation derived from transmission line theory is as follows: ,in Impedance gradient correction factor , Let the impedance be the wave impedance of the k-th layer. The impedance of the (k-1)th layer is... The intrinsic impedance of the material, Let be the complex propagation constant. Let be the thickness of the k-th layer, D be the fractal dimension of the configuration, D1 be the reference fractal dimension, α be the material constant with a value ranging from 1 to 10, and p be the duty cycle of the k-th layer.

5. The method for coupling and controlling the multiphysics performance of a three-dimensional single-cell structure according to claim 1, characterized in that: The fractal damping model based on mechanical wave theory is as follows: for each layer of the configuration, the loss factor... Among them, the equivalent stiffness Damping coefficient ; in, For material stiffness, Let fractal dimension be the number of ... D1 is the duty cycle of the calculation layer, D1 is the baseline fractal dimension, and β is the material constant, with a value range of 0-1.

6. The method for coupling and controlling the multiphysics performance of a three-dimensional single-cell structure according to claim 1, characterized in that: Based on Fresnel diffraction theory, a fractal light transmission model is constructed as follows: For each layer in the configuration, the transmittance... , The reference transmittance; Impedance gradient correction factor Where D1 is the reference fractal dimension, ε is a material constant ranging from 1 to 10; and the optical attenuation coefficient is... Where λ is the wavelength of light and the equivalent refractive index is... ,in , Where is the refractive index of the material and the porosity, and K is the extinction coefficient. d represents the duty cycle and thickness of the calculation layer.

7. A three-dimensional single-cell configuration multiphysics field performance coupling and control system, characterized in that... include: The preprocessing module calculates the fractal dimension of the overall configuration based on the initially given specific three-dimensional structural unit cell configuration, and determines the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration; it determines whether the currently calculated fractal dimension is greater than or equal to 2.

5. If it is, it continues the subsequent processing; otherwise, it adjusts the three-dimensional structural unit cell configuration until the fractal dimension is greater than or equal to 2.

5. The optimization module constructs a unified parameterized model of multiple physics fields. Based on the pre-designed thickness, electromagnetic performance, mechanical performance and optical performance indicators as constraints, iteratively optimizes the common geometric characteristic parameters of the structure, namely fractal dimension, duty cycle of each layer and thickness of each layer, to obtain the optimal three-dimensional structural unit cell configuration that simultaneously satisfies the electromagnetic performance, mechanical performance and optical performance indicators.

8. A three-dimensional structural unit cell configuration multiphysics field performance coupling and control system according to claim 1, characterized in that: The unified parameterized model of multiphysics includes the impedance transfer equation derived based on transmission line theory, the fractal damping model established based on mechanical wave theory, and the fractal optical transmission model constructed based on Fresnel diffraction theory.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the multiphysics performance coupling and control method for a three-dimensional structural unit cell configuration as described in any one of claims 1 to 6.

10. A computer software product, characterized in that... include: Processors and storage devices; Storage device for storing one or more programs. When the one or more programs are executed by one or more processors, the one or more processors implement the multiphysics performance coupling control method for a three-dimensional structural unit cell configuration as described in any one of claims 1 to 6.

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