Porous structure design method based on deformation three-period minimal curved surface and porous structure

Abstract

The invention discloses a porous structure design method based on a deformed three-period minimal curved surface and a porous structure. The design method comprises the following steps: designing a basic equation of a deformed three-period minimal curved surface in a three-dimensional space; designing a curved surface function of the Schwarz P curved surface by introducing periodic conditions and symmetry analysis; the curved surface function is substituted into the basic equation, then the gradient and the divergence of the gradient are calculated to determine the minimum curved surface condition, and finally the implicit equation of the Schwarz P curved surface is obtained according to the minimum curved surface condition; designing a control parameter containing at least two coordinate axis variables to replace a shape factor parameter in the implicit equation, and adjusting the control parameter according to a unidirectional gradient or a cyclic gradient; and designing hole units of the deformed three-period minimal curved surface to construct a porous structure. The anisotropy of the porous structure can be changed by adjusting control parameters according to needs, isotropy can be constructed, the weak part of the porous structure is increased, the wall thickness is increased, and the problem that the anisotropy of the porous structure is prone to fracture or failure is solved.

Description

Technical Field

[0001] The present invention relates to a method for designing a porous structure in the field of materials technology, and more particularly to a method for designing a porous structure based on a deformed triply periodic minimal surface, and also relates to a porous structure. Background Art

[0002] For a long time, most artificial materials have been completely dense, attempting to avoid and eliminate the formation of porous structures such as pores to endow the materials with better load-bearing capacity, but ignoring the excellent properties of the porous structures. With the development and progress of industry, science and technology, and information technology, people have gradually recognized and begun to prepare various porous structures to obtain materials with specific functions. Porous structures are ubiquitous in nature, such as spider webs, honeycombs, wood, bones, and sponges. In the fields of aerospace, national defense, automobiles, and medicine, lightweight porous structures have been widely used due to their remarkable high stiffness-to-mass ratio and approximate densification strain. The mechanical properties of these materials are mainly driven by the properties of their basic components and the geometric features they exhibit (such as lattice size, lattice topology, and relative density). In recent years, with the rapid development of additive manufacturing (AM) technology, a series of porous structures with complex geometries can be fabricated.

[0003] The currently studied porous structures include periodic porous structures, aperiodic structures, and composite porous structures, etc. Porous structures have been proven to be very reliable material structures and can be widely used in the fields of aviation, biology, medicine, environment, and agriculture. However, the limited control over their displayed morphology and inevitable process-related defects poses many challenges to their wide application, restricting the practical application of these porous structure materials.

[0004] Triply periodic minimal surfaces (TPMS) can be defined as surfaces with the same two principal curvatures but opposite signs at each point, that is, the mean curvature at all points is zero. Schwarz P surface is one of the triply periodic minimal surfaces (TPMS) and is periodic in the x, y, and z directions. "Minimal surface" does not refer to the smallest total area of a structure with a given unit size; TPMS structures can be mathematically modeled. They can be repeated in three directions perpendicular to the shape geometry. TPMS can be precisely designed and adapted to the structure by changing parameters. The internal structure of the porous structure of TPMS is smooth and tightly interconnected. Most of the existing porous structures are anisotropic and have different physical properties in different directions. In some special cases where uniform loading is required, the porous structure must have isotropic characteristics. In addition, anisotropy may be harmful to porous energy-absorbing materials. If an anisotropic porous energy-absorbing material is impacted from different directions, its weak parts may break or fail. Summary of the Invention

[0005] To solve the technical problem that the existing porous structure is anisotropic and prone to cracking or failure, the present invention provides a design method for a porous structure based on a deformed triply periodic minimal surface and a porous structure.

[0006] The present invention is implemented by the following technical solutions: A design method for a porous structure based on a deformed triply periodic minimal surface, which includes the following steps:

[0007] Design the basic equation of the deformed triply periodic minimal surface in three-dimensional space;

[0008] By introducing periodic conditions and symmetry analysis, design the surface function of the Schwarz P surface;

[0009] First, substitute the surface function into the basic equation, then calculate the gradient and the divergence of the gradient to determine the minimal surface condition, and finally obtain the implicit equation of the Schwarz P surface according to the minimal surface condition;

[0010] Design control parameters containing at least two coordinate axis variables to replace the shape factor parameter in the implicit equation, and adjust the control parameters according to the unidirectional gradient or cyclic gradient;

[0011] Design the pore unit of the deformed triply periodic minimal surface to construct a porous structure.

[0012] The present invention derives the implicit equation of the Schwarz P surface in the deformed triply periodic minimal surface, and uses control parameters containing at least two coordinate axis variables to replace the shape factor parameter, improves the mechanical properties of the porous structure in a certain direction, and at the same time can adjust the coefficient in the control parameters as needed to change the anisotropy of the porous structure, can construct isotropy, increase the weak parts of the porous structure in the prior art, increase the wall thickness, solves the technical problem that the porous structure is anisotropic and prone to cracking or failure, can adjust the parameters according to actual needs, and meets the actual isotropic requirements.

[0013] As a further improvement of the above solution, the implicit equation is:

[0014]

[0015] Wherein, x, y, and z are coordinate axis variables, k is the unit size, and c is the shape factor.

[0016] Further, for the unidirectional gradient, the expression of the control parameter is:

[0017] R = K(x + z)

[0018] For the cyclic gradient, the expression of the control parameter is:

[0019] R = K|x + z|

[0020] Among them, R is the control parameter.

[0021] As a further improvement of the above solution, the basic equation is:

[0022] (1 + f y 2 )f xx - 2f x f y f xy +(1 + f x 2 )f yy = 0

[0023] Among them, f (x，y) is the surface function, f x , f y are partial derivatives, f xx , f yy are second-order partial derivatives.

[0024] As a further improvement of the above solution, the periodic condition is:

[0025] f(x + a, y + b, z + c) = f(x, y, z)

[0026] Among them, a, b, c are periods, x, y, z are coordinate axis variables, and f(x, y, z) is the surface function.

[0027] As a further improvement of the above solution, the expression for symmetry analysis is:

[0028] f(x, y, z) = cos(x) + cos(y) + cos(z)

[0029] Among them, f(x, y, z) is the surface function.

[0030] As a further improvement of the above solution, the calculation formula for the gradient is:

[0031]

[0032] Among them, x, y, z are coordinate axis variables, is the gradient of the surface function.

[0033] As a further improvement of the above solution, the calculation formula for the divergence of the gradient is:

[0034]

[0035] Among them, is the gradient of the surface function.

[0036] Further, K is 0.15 and k is 0.5.

[0037] The present invention also provides a porous structure, which is designed by any one of the above-mentioned design methods of the porous structure based on the deformed triply periodic minimal surface.

[0038] Compared with the existing porous structures and their design methods, the design method of the porous structure based on the deformed triply periodic minimal surface and the porous structure of the present invention have the following beneficial effects:

[0039] 1. For the design method of the porous structure based on the deformed triply periodic minimal surface, by deriving the implicit equation of the Schwarz P surface in the deformed triply periodic minimal surface and using the control parameters containing at least two coordinate axis variables to replace the shape factor parameters, the mechanical properties of the porous structure in a certain direction are improved. At the same time, the anisotropy of the porous structure can be adjusted according to needs by adjusting the coefficients in the control parameters, isotropicity can be constructed, the weak parts of the porous structure in the prior art are increased, and the wall thickness is increased, solving the technical problem that the anisotropy of the porous structure is prone to cracking or failure. The parameters can be adjusted according to actual needs, meeting the actual isotropic requirements.

[0040] 2. For the porous structure, after being designed by the design method of the porous structure based on the deformed triply periodic minimal surface, through the optimization of each direction by the control parameters, the mechanical properties of the porous structure in a certain direction are improved. By controlling the unit size and shape factor, precise control of the pore characteristics of the structure can be achieved, a composite porous structure can be realized, solving the characteristics that some single pore structures cannot change by themselves, and greatly improving the performance. Description of the Drawings

[0041] Figure 1 It is a flowchart of the design method of the porous structure based on the deformed triply periodic minimal surface in Embodiment 1 of the present invention;

[0042] Figure 2 It is a partial structure comparison diagram of the Schwarz surface in Embodiment 1;

[0043] Figure 3 It is an original surface model diagram of the porous structure in Embodiment 2 of the present invention;

[0044] Figure 4 It is a schematic diagram of the porous structure with a unidirectional gradient in Embodiment 2 of the present invention;

[0045] Figure 5 It is a schematic diagram of the porous structure with a combination of unidirectional gradient and cyclic gradient in Embodiment 2 of the present invention;

[0046] Figure 6 It is a stress-strain schematic diagram of the porous structure in Embodiment 2 of the present invention and the control group before annealing;

[0047] Figure 7 Schematic diagram of stress-strain of the porous structure of Embodiment 2 of the present invention and the control group after annealing;

[0048] Figure 8 Schematic diagram of stress-strain of the porous structure of Embodiment 2 of the present invention without annealing during simulation;

[0049] Figure 9 Schematic diagram of stress-strain of the porous structure of Embodiment 2 of the present invention after annealing during simulation;

[0050] Figure 10 Variation diagram of the original surface model of the porous structure of Embodiment 2 of the present invention without annealing during simulation;

[0051] Figure 11 Variation diagram of the unidirectional gradient model of the porous structure of Embodiment 2 of the present invention without annealing during simulation;

[0052] Figure 12 Variation diagram of the mixed gradient model of the porous structure of Embodiment 2 of the present invention without annealing during simulation;

[0053] Figure 13 Variation diagram of the original surface model of the porous structure of Embodiment 2 of the present invention after annealing during simulation;

[0054] Figure 14 Variation diagram of the unidirectional gradient model of the porous structure of Embodiment 2 of the present invention after annealing during simulation;

[0055] Figure 15 Variation diagram of the mixed gradient model of the porous structure of Embodiment 2 of the present invention after annealing during simulation. Detailed implementation manners

[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0057] Embodiment 1

[0058] Please refer to Figure 1 and Figure 2 , this embodiment provides a design method for a porous structure based on a deformed triply periodic minimal surface. This design method is used to design a porous structure and can be used in anisotropic control methods and isotropic porous construction methods. In this embodiment, the design method designs a porous structure based on a deformed triply periodic minimal surface, and the designed porous structure can be used in fields such as impact protection and energy absorption components of aerospace vehicles.

[0059] In this embodiment, the Primitive Surface in Triply Periodic Minimal Surfaces (TPMS) is a classical TPMS, which has significant differences from other TPMSs (such as the Diamond Surface, the Gyroid Surface, etc.) in terms of geometric structure, symmetry, topological properties, and application performance. For specific references, see Table 1.

[0060] Table 1 Comparison Table of the Characteristics of Each Surface in Triply Periodic Minimal Surfaces

[0061] Characteristic P surface D surface G surface Geometric structure Simple cubic arrangement Tetrahedral arrangement Helical arrangement Symmetry Cubic symmetry Diamond symmetry Chiral symmetry Curvature distribution Uniform Complex Chiral feature Topological property Simply connected region Complex connected region Chiral connected region Mechanical property Uniform stress High strength and high stiffness Unique mechanical property Fluid property Good Poor Excellent Manufacturing difficulty Simple Relatively complex Relatively complex

[0062] To sum up, under the condition that all conditions are the same, the mechanical properties of the Primitive Surface are poor. The composite porous structure generally combines two or more pore structures, and can well solve the problems of some characteristics that cannot be changed by a single pore structure itself. In addition, the composite porous structure can perform topological optimization on the pore structure to improve the structural performance. Many pore structures are inspired by nature, such as the structure of tree stem cells, the lotus root structure, the honeycomb structure, and ceramics. In this embodiment, the Schwarz Primitive Surface is designed and optimized to improve the mechanical properties.

[0063] Specifically, the design method of the porous structure based on the deformed triply periodic minimal surface mainly includes the following steps.

[0064] (1) Design the basic equation of the deformed triply periodic minimal surface in three-dimensional space. The minimal surface is a surface with zero mean curvature everywhere, so the basic equation is:

[0065] (1 + f y 2 )f xx - 2f x f y f xy + (1 + f x 2 )f yy = 0

[0066] where f (x，y) is the surface function, f x , f y are partial derivatives, and f xx , f yy are second-order partial derivatives.

[0067] For a surface in three-dimensional space, the condition for a minimal surface is:

[0068]

[0069] Among them, is the gradient of the surface function.

[0070] In some embodiments, the minimal surface can be represented by the Weierstrass representation, that is:

[0071]

[0072] Among them, the Cartesian coordinates of each point on the surface are represented by the real part Re of the contour integral. The types of TPMS that can be expressed by this method are limited. In some embodiments, TPMS is represented by an equation defined by a Fourier series:

[0073]

[0074] Among them, F(k) is the amplitude factor, k is the lattice vector, and α(k) is the phase shift.

[0075] By truncating the high-frequency terms in the Fourier series, an approximate expression composed of trigonometric functions can be obtained. When the right side of the expression is a constant C, Ψ(x, y, z) = C defines a level set, and the surface structure represented is also called a triply periodic minimal surface. Some of these surfaces are very close to the known minimal surfaces. In particular, the P, D, and G minimal surfaces and their corresponding level sets are often expressed by the same name.

[0076] (2) By introducing periodic conditions and symmetry analysis, design the surface function of the Schwarz P surface. The Schwarz P surface is a type of triply periodic minimal surface (TPMS) and is periodic in the x, y, and z directions. Among them, the periodic condition is:

[0077] f(x + a, y + b, z + c) = f(x, y, z)

[0078] Among them, a, b, and c are the periods, x, y, and z are the coordinate axis variables, and f(x, y, z) is the surface function.

[0079] The Schwarz P surface has a high degree of symmetry, especially symmetric in the x, y, and z directions. Therefore, the expression for symmetry analysis is:

[0080] f(x, y, z) = cos(x) + cos(y) + cos(z)

[0081] Among them, f(x, y, z) is the surface function.

[0082] (3) First, substitute the surface function into the basic equation, then calculate the gradient and the divergence of the gradient to determine the minimal surface condition, and finally obtain the implicit equation of the Schwarz P surface according to the minimal surface condition. In this embodiment, substitute f(x, y, z) = cos(x) + cos(y) + cos(z) into the minimal surface equation to verify whether it satisfies the condition that the mean curvature is zero.

[0083] The calculation formula for the gradient is:

[0084]

[0085] where x, y, and z are the coordinate axis variables, is the gradient of the surface function.

[0086] The calculation formula for the divergence of the gradient is:

[0087]

[0088] where, is the gradient of the surface function.

[0089] It can be known through calculation that when cos(x) + cos(y) + cos(z) = 0, the above condition holds. Therefore, cos(x) + cos(y) + cos(z) = 0 describes a minimal surface.

[0090] In order to obtain the implicit equation of the Schwarz P surface, let f(x, y, z) = cos(x) + cos(y) + cos(z) be 0, that is, cos(x) + cos(y) + cos(z) = 0. This equation describes the geometric shape of the Schwarz P surface in three-dimensional space. Further, the implicit equation can be obtained as:

[0091]

[0092] where x, y, and z are the coordinate axis variables, k is the cell size, and c is the shape factor.

[0093] As Figure 2 shown, in the implicit equation, by changing the size of k, the size of the Schwarz P cell changes, and the pore size of the Schwarz P surface structure changes. By changing the size of c, the offset value of the Schwarz P surface changes, and the shape of the Schwarz P surface structure changes. Therefore, controlling the sizes of k and c can achieve precise control of the pore characteristics of the Schwarz P structure.

[0094] Among them, there is a threshold for the size of c. When the size of c reaches a certain value, the connecting line between the upper and lower layers of the Schwarz P structure is too thin, resulting in a pinching phenomenon, which makes the Schwarz P structure discontinuous. Therefore, it is necessary to limit the size of c. In this embodiment, the size of c shall not be greater than 1.

[0095] (4) Design control parameters containing at least two axis variables to replace the shape factor parameters in the implicit equation, and adjust the control parameters according to the unidirectional gradient or cyclic gradient.

[0096] For the unidirectional gradient, the expression of the control parameter is:

[0097] R = K(x + z)

[0098] For the cyclic gradient, the expression of the control parameter is:

[0099] R = K|x + z|

[0100] Among them, R is the control parameter.

[0101] In this embodiment, K is 0.15 and k is 0.5, ensuring that the pore structure characteristics of the unidirectional gradient and the cyclic gradient are consistent.

[0102] (5) Design the pore units of the deformed triply periodic minimal surface and construct a porous structure.

[0103] This embodiment of the porous structure design method based on the deformed triply periodic minimal surface has the following advantages compared with the existing porous structure design methods:

[0104] This porous structure design method based on the deformed triply periodic minimal surface derives the implicit equation of the Schwarz P surface in the deformed triply periodic minimal surface, and uses control parameters containing at least two axis variables to replace the shape factor parameters, improving the mechanical properties of the porous structure in a certain direction. At the same time, the coefficient in the control parameter can be adjusted as needed to change the anisotropy of the porous structure, and it is possible to construct isotropic directions, strengthen the weak parts of the porous structure in the prior art, increase the wall thickness, solve the technical problem of easy cracking or failure of the anisotropic porous structure, and can adjust the parameters according to actual needs, meeting the actual isotropic requirements.

[0105] Embodiment 2

[0106] Please refer to Figures 3 to 15 , this embodiment provides a porous structure, which is designed by the porous structure design method based on the deformed triply periodic minimal surface in Embodiment 1. Please refer to Figure 3 、 Figure 4 and Figure 5 , this embodiment conducts tests by printing samples, such as Figure 6and Figure 7 As shown, the porosity before annealing is the same, all 95%, but the mechanical properties are not ideal. Annealing is adopted and the wall thickness is increased at the same time, but the porosity is also the same, all 80%, and the annealing conditions are a heating rate of 5°C, rising to 800°C and holding for 4 hours, followed by slow cooling in the furnace. The porous structure in this embodiment has an increased wall thickness and significantly improved performance. Continuing to refer to Figures 8 to 15 , in this embodiment, the porous structure is simulated. In Figure 8 , the curves from top to bottom are the mixed gradient, the unidirectional gradient, and the original curve in turn. In Figure 9 , the curves from top to bottom are the mixed gradient, the unidirectional gradient, and the original curve in turn. It can be seen that the characteristics of the porous structure in this embodiment are significantly improved.

[0107] The static compression properties of the TPMS structure can be obtained from the nominal stress-nominal strain curve of the quasi-static compression experiment. The nominal stress-nominal strain curve of the TPMS structure under quasi-static compression is as shown in Figure 6 , 7 , 8, and 9. Similar to conventional porous materials, the compression curve of the TPMS structure includes an elastic stage, a plateau stage, and a compaction stage. In the elastic stage, the TPMS structure undergoes small deformations and the stress increases linearly. After reaching the plateau stage, the stress remains basically unchanged, and at this time the strain increases rapidly. In the compaction stage, the internal holes of the TPMS structure are squeezed, and at this time the stress increases rapidly. In terms of the compression deformation mode, in the vast majority of TPMS structures, the deformation of each layer of unit cells is the same, that is, it shows uniform deformation. Different types of unit cell structures also exhibit different deformation modes. In the P-type structure, the thin-walled structure inside is prone to instability, resulting in softening in the plateau stage during compression, and this phenomenon is not obvious in the compression curve of the multi-cell structure.

[0108] In the elastic stage, the elastic modulus of the Ti6Al4V block is 110 GPa and the Poisson's ratio is 0.35. In the finite element analysis, the plastic behavior of the material under study is described by the Johnson-Cook model. This model comprehensively considers the effects of strain hardening, strain rate effect, and temperature softening on the dynamic mechanical response of the material. Therefore, the Johnson-Cook model is widely used in simulations under static loading conditions. According to the Johnson-Cook model, the yield stress of the material is:

[0109]

[0110] In the formula, A and B represent the yield strength and the hardening constant respectively, ε e is the equivalent plastic strain, n is the hardening index, C is the strain rate constant, ε p is the equivalent plastic strain rate, ε θ$\dot{\bar{\varepsilon}}_{eq}^*$ is the reference equivalent plastic strain rate, $T^*$ is the melting temperature, and $m$ is the softening exponent.

[0111] In order to accurately evaluate the fracture characteristics of the lattice structure, the Johnson-Cook damage model is adopted in this embodiment:

[0112]

[0113] In the formula, $\varepsilon_f$ represents the fracture strain; $D_1$, $D_2$ and $D_3$ are damage constants, which determine the relationship between the failure strain rate and temperature; $D_4$ and $D_5$ are constants determined by the strain rate and temperature respectively. In addition, $\sigma^*$ represents the stress triaxiality, which is defined as the ratio of the hydrostatic stress to the equivalent stress. Given that the experiment is carried out at a constant loading rate under room temperature conditions, the parameters $C$, $m$, $D_4$ and $D_5$ in the Johnson-Cook model are ignored in this embodiment.

[0114] For this porous structure, after being designed by the method based on the triply periodic minimal surface porous structure of deformation, through the optimization of each direction by controlling parameters, the mechanical properties of the porous structure in a certain direction are improved. By regulating the unit size and shape factor, precise control of the pore characteristics of the structure can be achieved, and a composite porous structure can be realized, solving some characteristics that cannot be changed by the single pore structure itself, and greatly improving the performance. By introducing the design of a gradient-changing wall thickness in the Primitive structure, the deformation mode changes from the original oblique shear band to layer-by-layer collapse, and the energy absorption characteristics are greatly improved.

[0115] Example 3

[0116] This embodiment provides a computer terminal, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps of the method based on the triply periodic minimal surface porous structure design method in Example 1.

[0117] When the method in Example 1 is applied, it can be applied in the form of software, such as designed as an independently running program and installed on a computer terminal. The computer terminal can be a computer, a smart phone, a control system, and other Internet of Things devices, etc. The method in Example 1 can also be designed as an embedded running program and installed on a computer terminal, such as installed on a single-chip microcomputer.

[0118] Example 4

[0119] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps of the method based on the triply periodic minimal surface porous structure design method in Example 1.

[0120] When the method of Embodiment 1 is applied, it can be applied in the form of software, such as being designed as an independently running program on a computer-readable storage medium. The computer-readable storage medium can be a USB flash drive, designed as a USB key, and the program for starting the entire method by external trigger is designed through the USB flash drive.

[0121] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for designing porous structures based on deformed three-periodic minimal surfaces, characterized in that: It includes the following steps: Designing basic equations of the deformed three-periodic minimal surface in three-dimensional space; By introducing periodic conditions and symmetry analysis, the surface function of Schwarz P surface is designed; First, the surface function is substituted into the basic equation, then the gradient and the divergence of the gradient are calculated to determine the minimum surface condition, and finally the implicit equation of the Schwarz P surface is obtained according to the minimum surface condition; Designing a control parameter containing at least two coordinate axis variables to replace the shape factor parameter in the implicit equation, and adjusting the control parameter according to a unidirectional gradient or a cyclic gradient; The pore units of the deformed three-periodic minimal surface are designed to construct a porous structure.

2. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The implicit equation is: Among them, x, y, z are coordinate axis variables, k is the unit size, and c is the shape factor.

3. The method for designing porous structures based on deformed three-periodic minimal surfaces as claimed in claim 2, characterized in that: For a unidirectional gradient, the expression of the control parameter is: R=K(x+z) For the cycle gradient, the expression of the control parameter is: R=K|x+z| Wherein, R is the control parameter.

4. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The basic equation is: (1+f y 2 )f xx -2f x in y in xy +(1+f x 2 )f yy =0 Among them, f (x，y) is the surface function, f x 、f y is the partial derivative, f xx 、f yy is the second-order partial derivative.

5. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The periodic conditions are: f(x+a,y+b,z+c)=f(x,y,z) Among them, a, b, c are periods, x, y, z are coordinate axis variables, and f(x, y, z) is the surface function.

6. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The expression for symmetry analysis is: f(x,y,z)=cos(x)+cos(y)+cos(z) Among them, f(x,y,z) is the surface function.

7. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The gradient is calculated as: Among them, x, y, and z are coordinate axis variables. is the gradient of the surface function.

8. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 1, characterized in that: The calculation formula for the gradient divergence is: in, is the gradient of the surface function.

9. The method for designing porous structures based on deformed three-periodic minimal surfaces according to claim 3, characterized in that: K is 0.15 and k is 0.

5.

10. A porous structure, characterized in that: The porous structure is designed by a method for designing a porous structure based on a three-periodic minimal surface according to any one of claims 1 to 9.

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