A design method for directional deformation hybrid TPMS structure based on additive manufacturing

Abstract

The present invention discloses a design method for a directional deformation hybrid TPMS structure based on additive manufacturing. The method first divides the initial lattice structure and separates it into multiple phase-complementary low-volume fraction substructures. By adopting a deformation strategy that tightly couples structural geometry with function modeling, the geometric form and topological characteristics of the substructures are consciously directional deformed and reconstructed, so that the substructures are intertwined and integrated with each other to form a new hybrid topological structure. The present invention expands the design space and maximizes the effective specific surface area while ensuring a certain volume fraction. At the same time, it has a controllable multi-level pore topology, which can finely control the size of the pores to achieve a rich and diverse pore structure. The present invention can independently control each discrete point on the isosurface by adjusting the design parameters and the offset function, and flexibly obtain different curved surface lattice structures to meet the specific needs of different implants and heat exchangers, etc., with extremely high designability and customization capabilities.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-aided design (CAD) and additive manufacturing (AM), and in particular to a design method for a directional deformation hybrid TPMS structure based on AM. Background Art

[0002] The design of traditional porous structures is severely limited by manufacturing technology. Due to their complex topology and internal pores, traditional cutting or milling methods cannot produce porous structures similar to those in nature. Although porous structures can be manufactured through methods such as salt leaching, gas foaming and phase separation, basic requirements such as pore shape, size and connectivity are difficult to control. Fortunately, revolutionary additive manufacturing technology provides a new solution for the manufacture of complex porous structures, greatly alleviating the limitations of topological complexity on manufacturing processes. However, how to design porous structures with controllable geometry and properties, reliable manufacturing quality and broad application prospects remains a key challenge.

[0003] In recent years, periodic porous materials, particularly triperiodic minimal surfaces (TPMS), have attracted considerable attention from researchers. TPMS can be arranged periodically along the three axes of a three-dimensional orthogonal Cartesian coordinate system. As a periodic implicit surface with zero mean curvature, TPMS offer two significant advantages over other structures: first, the entire structure can be precisely represented by a mathematical function, allowing direct control of performance parameters such as porosity and specific surface area by adjusting the equations; second, TPMS surfaces are smooth and their pores are highly interconnected. These unique advantages have led to their widespread application in tissue engineering, energy absorption, and heat dissipation, with particular promise in the biomedical field.

[0004] Biological bone is a complex, porous, curved structure with an irregular pore structure and uneven pore size and distribution. TPMS structures can precisely control pore parameters by adjusting equations, thereby adjusting the mechanical properties of the scaffold to more closely resemble the characteristics of human bone, optimizing interfacial resistance, and enhancing adhesion to bone tissue. Therefore, a properly designed multi-level pore structure can best mimic natural bone structure. Small pores facilitate tissue penetration and vascularization, while large pores facilitate seed cell penetration and rapid mineralization and growth of bone tissue within the implant. Furthermore, the varying pore shapes uniquely regulate fluid flow and ion exchange, helping to optimize the bioactivity of the implant. Ensuring overall structural continuity and mechanical integrity is a major challenge in constructing such a complex multi-level pore structure, placing extremely high demands on the structural design. However, the fixed mathematical function limits the design space of the TPMS structure, making it difficult to achieve novel structural forms through optimization, hindering breakthroughs in existing structural morphologies. Currently, the realization of multi-level pore structures primarily relies on gradient pore design. For example, invention patent CN117637076A discloses a method for preparing a TPMS gradient porous composite material. Based on the implicit surface equation, the changes in the shape of the three-dimensional structure are controlled, and the parametric design of the TPMS porous structure is carried out. Through finite element simulation and mechanical experiments, the mechanical behavior and heat transfer performance of the implicit surface porous structure are studied to obtain a structural form that meets certain mechanical and thermal load-bearing performance. Invention patent CN108096639A discloses a gradient porous material, in which the gradient of the porous material is graded according to the pore size of the pores in the gradient porous material body. The gradient porous material is a porous material formed by using the porous material of the smallest gradient level as the raw material to produce pores with larger pores. The pores of the porous materials of each gradient level that constitute the gradient porous material are interconnected. Although the above method can control the size of the pores, it cannot regulate the morphological structure of the pores, and has certain limitations.

[0005] Furthermore, the smooth inner surface and highly interconnected pores of the TPMS structure create an ideal microenvironment for cell attachment and growth. Numerous studies have shown that a higher specific surface area is more conducive to cell attachment, proliferation, and differentiation, which is crucial for successful bone implantation. However, there is an inherent antagonistic relationship between the specific surface area and volume fraction of the TPMS structure. As the volume fraction increases, the TPMS surface occupies more space, reducing the interface area with the external environment, thereby reducing the specific surface area, and vice versa. This antagonistic relationship limits further increases in the specific surface area for cell growth, as excessively low volume fractions can compromise the material's mechanical properties and structural integrity. Currently, multi-unit TPMS structural designs are widely used to increase the specific surface area. However, due to the independence and lack of connectivity of the individual unit structures, the overall structural integrity and bearing capacity are significantly reduced, making it unable to meet the mechanical performance requirements of applications such as bone implants.

[0006] Therefore, in view of the differences in the characteristics of implant bone tissue and the existing problems, it is necessary to design a device that can freely regulate the specific surface area and multi-level pore structure of the implant to meet the requirements of the characteristics of different implant bone tissues. Summary of the Invention

[0007] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to provide a design method for a directional deformation hybrid TPMS structure based on additive manufacturing to solve the problems of the existing TPMS structure such as the contradiction between the specific surface area and volume fraction, and the single and uncontrollable pore structure.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solution: a design method of a directional deformation hybrid TPMS structure based on additive manufacturing, comprising the following steps:

[0009] 1) Generate an initial lattice structure using the three-periodic minimal surface equation;

[0010] 2) Dividing the initial lattice structure generated in step 1) into a plurality of phase-complementary low-volume-fraction substructures; phase-complementary substructures are different substructures that can be embedded and complemented with each other to form a "negative cavity positive carving" relationship.

[0011] 3) applying appropriate translation vectors to the multiple low volume fraction substructures obtained in step 2) on the isosurface to separate the substructures and generate void regions between them, thereby forming a new composite structure, namely a multilayer lattice structure;

[0012] 4) Each point on the multiple phase contour surfaces of the multilayer lattice structure obtained in step 3) can be independently moved and adjusted to perform directional transformations, thereby achieving structural interlaced fusion, that is, obtaining an interlaced hybrid multilayer TPMS lattice structure. The crystal units in this structure partially overlap and fuse, forming an interconnected overall network topology, significantly improving its load-bearing performance.

[0013] Preferably, the three-periodic minimal surface equation in step 1) includes a Gyroid surface implicit function, a Diamond surface implicit function or a Primitive surface implicit function.

[0014] The implicit function of the Gyroid surface is expressed as follows:

[0015] φ G (x,y,z)=sin(X)cos(Y)+sin(Z)cos(X)+sin(Y)cos(Z)

[0016] Where, a is a constant related to the unit cell size.

[0017] Preferably, the volume fraction of the initial lattice structure in step 1) can be controlled by an equivalent constant c, which can be expressed as:

[0018] -c≤φ G ≤c

[0019] Where c is used to determine the volume fraction of the region separated by the isosurface.

[0020] Preferably, the initial lattice structure in step 2) is divided into a plurality of phase-complementary low volume fraction substructures. In order to keep the volume fraction unchanged, the formula can be expressed as:

[0021]

[0022] Preferably, applying the translation vector in step 3) means translating the generated slice-based substructure along the normal direction or the reverse normal direction of the minimum surface, which can be expressed as:

[0023]

[0024] Where n is the mixing coefficient, representing the number of segmented structures, and t represents the distance of the isosurface translation.

[0025] Preferably, the directional transformation in step 4) refers to accurately controlling the offset of each point on the isosurface of the TPMS structure in each direction of the Cartesian coordinate system through the offset function f(x, y, z). The optimization formula can be expressed as:

[0026]

[0027] Where n is the mixing coefficient, representing the number of segmented structures, f(x), f(y), and f(z) are continuous offset functions with independent variables x, y, and z, respectively, which are used to describe the offset of points on the isosurface along the x, y, and z axes of the Cartesian coordinate system.

[0028] By adjusting the form and parameters of the offset function, each point on the isosurface can be assigned a precise offset along a certain direction, achieving complex deformations such as twisting and fusion of the structure. This method of finely controlling the isosurface morphology through mathematical functions enables the precise design of multi-level pore structures.

[0029] Preferably, the offset function is a continuous function equation, including a linear function, a tangent function or an odd-exponent power function.

[0030] Preferably, the formula of the offset function is as follows:

[0031] Where δ represents the maximum offset and determines the slope of the offset function curve, and a is a constant related to the unit cell size.

[0032] Another object of the present invention is to provide a metal product manufactured according to the above method.

[0033] Another object of the present invention is to provide applications of the above-mentioned product in bone implants or heat exchangers for electronic products.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. The present invention provides a novel design method for a TPMS porous structure. The method first divides the initial lattice structure and separates it into multiple phase-complementary low-volume fraction substructures. Then, an offset function is used to independently adjust the displacement of any discrete sampling point on the isosurface of the TPMS substructure to deform the structure in a direction, thereby achieving structural mixing and overlapping, and thus obtaining an interlaced fusion hybrid structure. The TPMS lattice structure designed by the present invention is constructed based on implicit mathematical equations, combining traditional TPMS mathematical equations with adjustable offset functions, breaking the limitation of TPMS structural design being constrained by fixed functions and expanding the design space. By changing the function, this method can adjust the position of discrete points in the structure to meet the personalized needs of different application scenarios, greatly improving design flexibility and speed, providing a new approach to the regulation of TPMS structures, and solving the problem that previous methods could only adjust the entire isosurface.

[0036] 2. The products prepared by the present invention optimize the contradiction between specific surface area and volume fraction in existing TPMS structures by precisely controlling the directional deformation and staggered fusion of substructures, thereby maximizing the effective specific surface area while ensuring a certain volume fraction (i.e., structural mechanical properties); at the same time, the structure has a controllable multi-level pore structure, and each discrete point on the isosurface can be independently regulated by adjusting the offset function. This not only enables fine-tuning of the pore size, but also enables a rich variety of pore shapes and topological structures, optimizing biological performance and providing new degrees of freedom for optimizing biological activity.

[0037] 3. The present invention can be designed to generate a variety of porous structures with different structural characteristics according to different application environments, and is suitable for engineering problems that require personalized design. By adjusting the design parameters, isotropic mechanical properties can be achieved to meet the requirements for material uniformity. Compared with the traditional TPMS structure, at an equivalent volume fraction, it can significantly increase the specific surface area, provide a larger active area for cell growth, and promote cell proliferation and adhesion; compared with the multi-unit TPMS structure, it retains the topological characteristics of the TPMS structure and maintains good mechanical properties and structural integrity to a certain extent; the present invention optimizes biological performance and has a wider range of uses, and can be widely used in implanted stents, heat exchangers and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the computer-aided design process of the present invention.

[0039] Figure 2 The influence of the offset function on the geometric morphology and internal structure of the TPMS structure (a) Offset function curve design, (b) The effect of changing δ on the staggered hybrid lattice structure, (c) Different cross-sectional changes in the Z direction of the staggered hybrid lattice.

[0040] Figure 3 is the relationship between the number of divisions of the initial lattice structure and the unit cell.

[0041] Figure 4 Schematic diagram of the structure constructed for different forms of offset functions.

[0042] Figure 5 OM images of the cross sections of the printed supports of the structures of Example 4 and Comparative Example 1.

[0043] Figure 6 Specific surface area growth rate of the printing supports of Examples 4-5 and Comparative Examples 1-2.

[0044] Figure 7 The anisotropy of SDG and SDD is evaluated by the numerical homogenization method; A is the three-dimensional surface diagram of the elastic modulus of SDD and SDG structures in different directions, and B is the influence of different parameters c and δ on the anisotropy of SDG and SDD structures.

[0045] Figure 8 The relationship between the relative mechanical properties and volume fraction of the printed scaffolds fitted by the Gibson-Ashby model.

[0046] Figure 9 The mechanical properties of the printed supports of Example 4 and Comparative Example 1 are shown.

[0047] Figure 10This is the co-culture of cells of Example 4, Comparative Example 1 and blank control structure scaffolds; a is a schematic diagram of the operation process, b is a comparison of cell concentrations after 1 day and 3 days of cell culture, and c is an optical electron microscopy image of cells after 1 day and 3 days of cell culture. DETAILED DESCRIPTION

[0048] The present invention will be further described in detail below with reference to the examples. It should be understood that the specific examples described herein are intended only to illustrate the present invention and are not intended to limit the present invention. In the following examples, where specific conditions are not specified, the procedures were carried out under conventional conditions or conditions recommended by the manufacturer. Raw materials, equipment, or instruments used, where the manufacturer is not specified, are all commercially available conventional products.

[0049] 1. A design method for a directional deformation hybrid TPMS structure based on additive manufacturing

[0050] Specific implementation, such as Figure 1 As shown in Figure 1, the core concept of this method is to consider the design object as a composite system formed by the fusion of two homogeneous traditional TPMS topologies. First, the generated initial lattice structure is divided into multiple phase-complementary, low-volume-fraction substructures. Opposing translation vectors are applied to the isosurfaces of these two substructures, reconstructing their surfaces in three-dimensional space and generating a new surface space. Subsequently, by introducing an offset function into the implicit surface equation, the offset of each isosurface point is controlled, resulting in a graded offset along the longitudinal dimension of the isosurface. Because the translation vectors of the two substructures are in opposite directions, the crystal units in this structure partially overlap and fuse, forming an interconnected overall network topology that significantly improves its load-bearing performance. The computer-aided design steps are as follows: 1) isosurface sampling is performed on the original double-layer Gyroid structure (DG) to obtain discrete point cloud data on the two-phase isosurfaces. 2) A 3D offset function is defined to control the offset of each sampling point in each Cartesian coordinate system. 3) The offset function is applied to each sampling point on the isosurface, independently adjusting the displacement to achieve local deformation and reconstruction. 4) The two sets of offset point clouds are fused so that they partially overlap and intersect in space. 5) Based on the fused point cloud data, a new closed isosurface is generated to obtain an interlaced hybrid double-layer TPMS lattice structure (SDG).

[0051] The specific steps include:

[0052] (1) Generate an initial lattice structure using the three-periodic minimal surface equation.

[0053] The three-periodic minimal surface equations include but are not limited to Gyroid surface implicit functions, Diamond surface implicit functions or Primitive surface implicit functions. The empty-solid boundary of the lattice structure can be designed by defining the isosurface (φ=0) equation.

[0054] The implicit function of the Gyroid surface is expressed as follows:

[0055] φ G (x,y,z)=sin(X)cos(Y)+sin(Z)cos(X)+sin(Y)cos(Z) (1)

[0056] in, a is a constant related to the unit cell size.

[0057] Specifically, by solving Equation (3), the spatial nodes bounded by the two isosurfaces constitute a solid domain, which represents a patch-based lattice derived from the minimum surface, and the parameter c is used to determine the volume portion of the region separated by the isosurfaces.

[0058] -c≤φ G ≤c (2)

[0059] (2) Split the initial lattice structure generated in step 1) into two phase-complementary low volume fraction substructures. That is, split the original Gyroid isosurface Φ(x, y, z) = 0 into two complementary sub-isosurfaces and The two substructures are embedded and complemented with each other to form a "negative cavity and positive carving" relationship, thus achieving the segmentation of the initial single Gyroid.

[0060] Specifically, the isosurface will occupy the part of the Boolean union of the two structures in space, namely φS urface1 ∪φ Surface2 Therefore, the simple case of a mixed lattice consisting of two of the same type can be described as follows:

[0061] φ hybrid =φ Surface1 ·φ Surface2

[0062] Among them, φ Surface1 and φ Surface2 For the same type of lattice. At the same time, in order to keep the volume fraction unchanged, the expression formula is as follows:

[0063] -c≤2φ G1 φ G2 ≤c (3)

[0064] (3) Appropriate translation vectors are applied to the isosurfaces of the two low volume fraction substructures so that there are gap regions between the substructures, thereby achieving the separation of the substructures and forming a new composite structure named double-layer lattice structure (Double, D).

[0065] Based on the fact that the two lattice structures can be offset in opposite directions along the normal direction or the reverse normal direction of the minimum surface, a new pore area is generated, which is expressed as follows:

[0066] -c≤2(φ G1 +t1)(φ G2 -t2)≤c (4)

[0067] Where t represents the offset distance of the isosurface. New gap areas will only be generated if t>c is satisfied.

[0068] (4) Directional transformation is performed on the two phases in the double-layer lattice structure obtained in step 3) to achieve structural staggered fusion, that is, a staggered hybrid double-layer TPMS lattice structure (Staggered hybrid double, SD) is obtained.

[0069] The offset function f(z) is used to precisely control the offset of any point on the TPMS structural isosurface. The optimization formula can be expressed as Equation (5):

[0070] -c≤2(φ G1 +f(x,y,z))(φ G2 -f(x,y,z))≤c (5)

[0071] Where f(z) is a continuous function with the independent variable z, which is used to describe the offset of a point on the isosurface along the z-axis of the Cartesian coordinate system. It can also be replaced by f(x) and f(y), which are used to describe the offset of a point on the isosurface along the x-axis and y-axis of the Cartesian coordinate system, respectively.

[0072] Furthermore, the formula of the offset function is as follows:

[0073]

[0074] Where δ represents the offset rate, which is numerically equivalent to the maximum offset, and a is a constant related to the unit cell size.

[0075] Example 1

[0076] (1) Generate an initial lattice structure using the three-periodic minimal surface equation.

[0077] The void-solid boundary of the lattice structure can be designed by defining the equation of the isosurface (φ=0), the Gyroid surface implicit function, and its expression formula is as follows:

[0078] φ G (x,y,z)=sin(X)cos(Y)+sin(Z)cos(X)+sin(Y)cos(Z) (1)

[0079] in, a is a constant related to the unit cell size.

[0080] By solving Equation (3), the spatial nodes bounded by the two isosurfaces constitute a solid domain that represents a patch-based lattice derived from the minimal surface. The parameter c is used to determine the volume fraction of the region separated by the isosurfaces.

[0081] -c≤φ G ≤c (2)

[0082] (2) The initial lattice structure generated in step 1) is divided into two phase-complementary low volume fraction substructures. Specifically, the isosurface will occupy part of the Boolean union of the two structures in space, i.e., φ Surface1 ∪φ Surface2 Therefore, the simple case of a mixed lattice consisting of two of the same type can be described as follows:

[0083] φ hybrid =φ Surface1 ·φ Surface2

[0084] Among them, φ Surface1 and φ Surface2 is the same type of lattice. At the same time, in order to keep the volume fraction unchanged, its expression formula is as follows:

[0085] -c≤2φ G1 φ G2 ≤c (3)

[0086] (3) An appropriate translation vector (offset) is applied to the two low volume fraction substructure isosurfaces so that there are gaps between the substructures, forming a new composite structure named double-layer lattice structure (Double, D).

[0087] The original double-layer Gyroid structure (DG) is sampled to obtain discrete point cloud data on the two-phase isosurface. The offset operation is performed in opposite directions along the normal direction or the reverse normal direction of the minimum surface, thereby generating a new pore area. The expression formula is as follows:

[0088] -c≤2*φ G1 +t1)(φ G2 -t2)≤c (4)

[0089] Where t represents the offset distance of the isosurface.

[0090] (4) Applying an offset function to each sampling point on the two-phase isosurface in the double-layer lattice structure obtained in step 3) to perform independent displacement adjustment to achieve local deformation and reconstruction. The two groups of point clouds after offset are fused so that they partially overlap and intersect in space. Based on the fused point cloud data, a new closed isosurface is generated to obtain an interlaced mixed double-layer TPMS lattice structure (SDG).

[0091] Specifically, f(z) is used to accurately control the offset of any point on any isosurface of the TPMS structure. The optimization formula can be expressed as Equation (5):

[0092] -c≤2(φ G1 +f(x,y,z))(φ G2 -f(x,y,z))≤c (5)

[0093] Where f(z) is a continuous offset function with the independent variable z, which is used to describe the graded offset of points on the isosurface along the z-axis of the Cartesian coordinate system.

[0094] Furthermore, the formula of the offset function is as follows:

[0095]

[0096] Where a is a constant related to the unit cell size, δ represents the offset rate, which is numerically equivalent to the maximum offset, and δ takes values ​​of 0.1, 0.2, 0.3, 0.4, and 0.5, respectively; z is the vertical height, which takes values ​​of 0, -0.5 mm, -1 mm, -1.5 mm, -2 mm, and -2.5 mm, respectively. The results are shown in Figure 2 shown.

[0097] As can be seen from the figure, this embodiment sets 5 different offset function curves, which describe the linear variation of the offset t of each point on the isosurface from A to B with the z coordinate. Along the height change of the z axis of the Cartesian coordinate system, the value of t changes linearly from -δ to δ. The offset of the 5 isosurfaces from A1 to A5 follows Figure 2 By changing the offset function f(z), the offset of each point on the A to B isosurface along the z-axis can be precisely controlled, thereby effectively adjusting the geometric shape of the structure ( Figure 2 a, b). It should be noted that although a linear offset function is used for exploration, the mathematical form of the offset function is not unique. In fact, any continuous function can be used as an offset function, including but not limited to a sine function, a tangent function, and an odd-exponential power function, so as to implement precise control of the TPMS structure. And through different longitudinal offsets, the staggered hybrid lattice SDG obtained contains a large number of different multi-level pore structures distributed longitudinally ( Figure 2c) not only provides a wide variety of pore shapes and sizes, but also boasts a larger surface area, which facilitates cell adhesion and proliferation within the porous structure. Furthermore, the interlaced hybrid structure exhibits a continuous topological feature of interlaced fusion, which offers advantages in maintaining excellent mechanical properties.

[0098] Example 2

[0099] The initial lattice structure is divided into 1, 2, 4, and 6 phase-complementary low volume fraction substructures, respectively. The other steps are the same as in Example 1. The results are as follows: Figure 3 shown.

[0100] As can be seen from the figure, different unit cells can be obtained by varying the number of divisions. The greater the number of divisions, the more unit cells there are. The structural morphology gradually evolves from a simple single topology to a complex, leaf-like structure, significantly increasing its surface area. This high specific surface area characteristic offers potential applications for TPMS structures in improving cell attachment and regeneration, optimizing heat conduction, and chemical reaction efficiency.

[0101] Example 3

[0102] The offset function is set as a one-variable linear function, a three-variable linear function, an odd-exponential power function or a tangent function. The other steps are the same as in Example 1. The results are as follows: Figure 4 shown.

[0103] As can be seen from the figure, the offset function is set as a univariate linear function ( Figure 4 a), ternary linear function ( Figure 4 b), odd exponential power function ( Figure 4 c) or tangent function ( Figure 4 d) The obtained structural model has great variations in pore size, shape, and specific surface area, indicating that the present invention can flexibly obtain different surface lattice structures by changing the form of the offset function, and can independently control each discrete point on the isosurface, thereby presenting different interlaced and fused continuous topological features.

[0104] Example 4

[0105] The structure of this embodiment was designed as 3×3×3 units with a structural dimension of 15mm×15mm×15mm. After completing the structural design and establishing a three-dimensional gradient structure model, the staggered hybrid Gyroid minimal surface structure bracket was prepared using LPBF additive manufacturing technology on a commercial BLT S210 system. The optimal parameters used in the preparation were: laser power 80W, scanning speed 800mm / s, layer thickness 20μm, and hatch spacing 70μm. The material used for the matrix of the structural bracket was commercial WE43 magnesium alloy powder (Mg-3.77Y-2.46Nd-1.23Gd-0.4Zr-0.21Zn). The structure was produced using the following steps:

[0106] (1) Generate an initial lattice structure using the three-periodic minimal surface equation.

[0107] The void-solid boundary of the lattice structure can be designed by defining the equation of the isosurface (φ=0), the Gyroid surface implicit function, and its expression formula is as follows:

[0108] φ G (x,y,z)=sin(X)cos(Y)+sin(Z)cos(X)+sin(Y)cos(Z) (1)

[0109] in, a is a constant related to the unit cell size. By solving Equation (3), the spatial nodes bounded by the two isosurfaces constitute a solid domain that represents the sheet-based lattice derived from the minimum surface. The parameter c is used to determine the volume fraction of the region separated by the isosurfaces.

[0110]

[0111] (2) Split the initial lattice structure generated in step 1) into two phase-complementary low volume fraction substructures. Specifically, the isosurface will occupy the part of the Boolean union of the two structures in space, i.e., φ Surface1 ∪φ Surface2 Therefore, the simple case of a mixed lattice consisting of two of the same type can be described as follows:

[0112] φ hubrid =φ Surface1 ·φ Surface2

[0113] Among them, φ Surface1 and φ Surface2 For the same type of lattice. At the same time, in order to keep the volume fraction unchanged, the expression formula is as follows:

[0114] -c≤2φ G1 φ G2 ≤c (3)

[0115] (3) Appropriate translation vectors are applied to the two low volume fraction substructure isosurfaces so that there are gaps between the substructures, forming a new composite structure named double-layer lattice structure (Double, D).

[0116] The two lattice structures are offset in opposite directions along the normal direction or the reverse normal direction of the minimum surface, thereby generating a new pore area, which is expressed as formula (4):

[0117] -c≤2(φ G1 +t1)(φ G2 -t2)≤c (4)

[0118] Where t1=t2, t represents the distance of the isosurface offset.

[0119] (4) Directional structural transformation is performed on the two phases in the double-layer lattice structure obtained in step 3) to achieve structural staggered fusion, that is, to obtain a staggered hybrid double-layer TPMS lattice structure (SD).

[0120] Specifically, f(z) is used to accurately control the offset of any point on any isosurface of the TPMS structure. The optimization formula can be expressed as Equation (5):

[0121] -c≤2(φ G1 +f(x,y,z))(φ G2 -f(x,y,z))≤c (5)

[0122] Where f(z) is a continuous offset function with the independent variable z, which is used to describe the graded offset of points on the isosurface along the z-axis of the Cartesian coordinate system.

[0123] Furthermore, the formula of the offset function is as follows (6):

[0124]

[0125] Where a is a constant related to the unit cell size, δ represents the maximum offset and also determines the slope of the offset function curve. The values ​​of δ are 0.1, 0.2, 0.3, 0.4, and 0.5, respectively.

[0126] Example 5

[0127] The only difference from Example 4 is that the Diamond surface implicit function replaces the Gyroid surface implicit function, and its expression formula is as shown in formula (7):

[0128] φ D(x,y,z)=sin(X)sin(Y)sin(Z)+sin(X)cos(Y)cos(Z)+cos(X)sin(Y)cos(Z)+cos(X)cos(Y)sin(Z) (7)

[0129] in, a is a constant related to the unit cell size.

[0130] Comparative Example 1

[0131] The difference from Example 4 is that no offset is applied, namely step 3) and step 4), which is a traditional single Gyroid structure.

[0132] Comparative Example 2

[0133] The difference from Example 5 is that no offset is applied, namely step 3) and step 4), which belongs to the traditional single Diamond structure.

[0134] 2. Performance Verification

[0135] 1. Obtain the cross-section of the printed stents of Example 4 and Comparative Example 1 and observe their microscopic morphologies under an optical microscope. The results are as follows: Figure 5 shown.

[0136] As can be seen from the figure, compared with Comparative Example 1, there are a large number of longitudinal multi-level fine channels inside the SDG structure. These micropores can simulate the function of bone canaliculi (Volkmann's canals). At the same time, the axial channels composed of large pores on the periphery are similar to central blood vessels (Haversian canals), simulating the microcirculation structure of the Haversian system (Haversian system). This bionic design containing a longitudinal multi-level pore structure inside the SDG lattice can not only provide efficient transmission of nutrients, but also promote cell activity and metabolism, providing an ideal growth microenvironment for tissue engineering bone repair.

[0137] 2. The specific surface areas of the printed supports of Examples 4 and 5 and Comparative Examples 1 and 2 were compared by numerical calculation and nitrogen adsorption / desorption experiments. Examples 4 and 5 were compared with Comparative Examples 1 and 2 respectively. Figure 6 shown.

[0138] As can be seen from the figure, compared with the comparative example, at the equivalent volume fraction, the specific surface areas of the staggered mixed lattice structures SDD and SDG of the present invention can be increased by 50.32% and 51.19% respectively ( Figure 6a). For the fabricated samples, the surface area per unit mass of the SDG structure maintained an increase of about 24% relative to the Gyroid structure, while the SDD structure increased by about 20% relative to the Diamond structure ( Figure 6 b) This is because the staggered hybrid topology with a larger surface area exhibits more significant manufacturing deviations, increasing the volume fraction. If the actual volume fraction is kept consistent, the improvement will be more significant.

[0139] 3. The anisotropy of Examples 4 and 5 was evaluated using the numerical homogenization method. The basic unit of the TPMS system was selected as the representative volume element (RVE). Different load directions were applied to the unit cell of the TPMS structure. The material model was simulated using the linear elastic model. The material parameters were elastic modulus of 44.8 GPa, Poisson's ratio of 0.35, and density of 1.8 g / cm 3 The results are as follows Figure 7 shown.

[0140] As can be seen from the figure, the Zener anisotropy index of the SDG structure remains essentially constant at around 1.15, showing little sensitivity to changes in δ, and therefore can be considered an isotropic material. In contrast, the Zener anisotropy index of the SDD structure is significantly dependent on the parameter c, generally increasing with increasing c. However, regardless of the value of c, the Zener anisotropy index of the SDD structure approaches 1 as δ increases. This demonstrates that the present invention can achieve isotropic mechanical properties by adjusting design parameters.

[0141] 4. The relationship between relative mechanical properties and volume fraction was fitted by the Gibson-Ashby model for the stents of Example 4, Example 5 and Comparative Examples 1-2. The results are as follows: Figure 8 shown.

[0142] As can be seen from the figure, for the four structures of Gyroid, SDG, Diamond and SDD, the determination coefficient R 2They are all higher than 0.98, and the fitting parameter C value is within the Gibson-Ashby recommended range of 0.1 to 4, indicating that the model fitting effect is good. It should be pointed out that the n values ​​of the four structures are 1.37, 1.48, 1.32 and 1.41, respectively. According to the experimental research of Gibson and Ashby, when n≈1, it means that the material exhibits a "stretching encryption" or "bending" mechanism; and when n≈2, it is dominated by "squeezing / buckling of cell edges or unit rods." It can be seen that the SDG structure and SDD structure are consistent with their basic topological structures (Gyroid and Diamond) in deformation behavior, and both use bending deformation as the dominant mechanism, which further verifies the inheritance of the staggered hybrid topology optimization structure in deformation mechanism. The mechanical properties of the staggered hybrid lattice structure of the present invention are comparable to those of the traditional structure, and the deformation mode under uniaxial compression load is the same.

[0143] 5. The printing brackets of Example 4 and Comparative Example 1 were tested using a quasi-static testing machine. The loading speed of the quasi-static compression of the various structures was 1.5 mm / min. Figure 9 shown.

[0144] As can be seen from the figure, the stress-strain curve shows four different regions. First, the stress increases linearly with the applied strain, which indicates that the slope of the linear curve represents the elastic region of Young's modulus. When the stress-strain curve deviates from the linear response and enters the nonlinear state, the stress continues to increase until it reaches a peak representing the maximum stress. After reaching the peak stress, the sample begins to show signs of significant deformation, followed by a sharp drop in the stress-strain curve. After that, deformation continues until all units in the structure fail. It can be seen that at the same volume fraction, the staggered mixed lattice structure maintains good mechanical properties.

[0145] 6. If Figure 10As shown in a, all completed scaffolds for cell culture were first electrochemically polished and then cleaned in anhydrous ethanol three times for 5 minutes each time by an ultrasonic cleaner to remove residual powder in the pores and semi-melted powder on the surface. All samples were then placed in a 24-well plate. The different scaffold structures prepared in Example 4, Comparative Example 1 and the blank control were sequentially soaked in 75% ethanol for sterilization for 2 hours, irradiated with ultraviolet light for 2 hours, and washed three times with phosphate buffered saline (PBS). They were then placed in the plate. Bone marrow mesenchymal stem cells were then seeded into the plate and incubated in a high-glucose liquid medium (DMEM) containing 10% fetal bovine serum and 1% penicillin / streptomycin sulfate at 37°C and a CO2 content of 5%. To maintain pH stability, the culture medium was renewed once a day. After 3 days of co-culture, the scaffold was removed and the cells on the scaffold were digested with trypsin. To ensure that all cells were separated from the scaffold surface and fell into the solution, 1 mL of fresh culture medium was added to each well to wash the sample. All solutions in each well were collected and centrifuged at 3000 rpm for 5 minutes to remove the supernatant. The digested cells were collected in a plate, stained with calcein / PI and incubated for another 30 minutes. Afterwards, the labeled cells were rinsed three times with PBS. Finally, the cells were examined under a fluorescence microscope. Figure 10 c; At the same time, CCK-8 assay was used to quantitatively detect cell proliferation behavior. After 1 and 3 days of culture, the cells on the scaffold were trypsinized and then fixed with 4% paraformaldehyde in PBS for 15 minutes. The CCK-8 solution was diluted 1:10 with the culture medium, and the cells were cultured in a 37°C incubator for 2 hours. After that, the culture medium of each well was collected using a multifunctional microplate scanner, and the OD value was measured at 450nm. The results are shown in Figure 10 As shown in b.

[0146] As can be seen from the figure, compared with Comparative Example 1 and the blank control, the cell proliferation rate on the staggered hybrid lattice structure (SDG) of the present invention is the fastest and the largest in number, indicating that the staggered hybrid lattice structure promotes the growth and proliferation of bone mesenchymal stem cells. This is due to the unique geometric topological characteristics of the staggered hybrid TPMS structure, which contains a large number of internal multi-level pores and curved surface areas, giving it a large specific surface area, which is conducive to promoting the adhesion and proliferation of cells in the porous structure, thereby improving the internal growth ability of bone tissue. At the same time, the staggered hybrid structure can also maintain a certain degree of continuous topological characteristics, ensuring its good structural integrity and mechanical properties, and meeting the basic requirements of bone implants for rigidity and strength. In addition, by adjusting the structural parameters and offset functions, it is possible to achieve optimized control of key parameters such as the elastic modulus, porosity, and specific surface area of ​​the implant, so that its comprehensive performance reaches the best state. For example, when the volume fraction of the implant is in the range of 20%-35%, relatively balanced mechanical properties and bioactivity can be obtained, providing a potential design solution for bone defect repair. In summary, the staggered hybrid TPMS structure brings a new multifunctional additive manufacturing method to the field of bone implants, which is expected to promote the development of bone defect repair and regenerative medicine.

[0147] Furthermore, the staggered hybrid TPMS structure also has broad application prospects in the field of thermal management of electronic products. This type of structure has a large specific surface area and a rich internal piping structure, which is conducive to improving heat conduction and heat dissipation efficiency. Due to its enhanced topological characteristics, the specific surface area is further improved, making its thermal management performance even better. At the same time, the staggered hybrid TPMS structure can still maintain good structural integrity and continuity, which makes it less prone to phase change and stiffness degradation problems, and can withstand higher temperatures and heat flows, thereby maintaining excellent heat exchange performance under relatively harsh heat dissipation conditions, meeting the stringent requirements for the use of electronic products. In addition, the staggered hybrid TPMS structure can also achieve regulation of heat transfer characteristics by adjusting design parameters and offset functions, so that it can better adapt to different heat dissipation needs.

[0148] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A design method for a directional deformation hybrid TPMS structure based on additive manufacturing, characterized in that: The following steps are involved: 1) Generate an initial lattice structure using the three-periodic minimal surface equation; 2) dividing the initial lattice structure generated in step 1) into a plurality of phase-complementary low volume fraction substructures; 3) applying appropriate translation vectors to the multiple low volume fraction substructures obtained in step 2) on the isosurface to separate the substructures and generate void regions between them, thereby forming a new composite structure, namely a multilayer lattice structure; Applying a translation vector means translating the generated patch-based substructure along the normal direction or the anti-normal direction of the minimum surface; 4) Each point on the multiple phase isosurfaces in the multilayer lattice structure obtained in step 3) can be independently moved and adjusted to perform directional transformation, so as to achieve structural interlaced fusion, that is, to obtain an interlaced hybrid multilayer TPMS lattice structure; the directional transformation refers to the precise control of the offset of each point on the isosurface in each direction of the TPMS structure along the Cartesian coordinate system through the offset function f(x, y, z), so that the crystal substructures partially overlap and fuse.

2. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 1 is characterized in that: The three-periodic minimal surface equation in step 1) includes a Gyroid surface implicit function, a Diamond surface implicit function, or a Primitive surface implicit function; The implicit function of the Gyroid surface is expressed as follows: ； Where, , , , is a constant related to the unit cell size.

3. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 1 is characterized in that: The volume fraction of the initial lattice structure in step 1) can be controlled by the equivalent constant c, which can be expressed as follows: ； Where c is used to determine the volume fraction of the region separated by the isosurface.

4. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 3 is characterized in that The initial lattice structure described in step 2) is divided into multiple phase-complementary low volume fraction substructures. In order to keep the volume fraction unchanged, the formula is expressed as: ； Where n is the mixing coefficient, which represents the number of segmented structures.

5. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 4 is characterized in that: The formula of the translation vector in step 3) is expressed as: ； Where n is the mixing coefficient, which represents the number of segmented structures. t Indicates the distance the isosurface is shifted.

6. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 5 is characterized in that: The formula for the directional transformation in step 4) is expressed as: ； Where n is the mixing coefficient, representing the number of segmented structures, f(x), f(y), and f(z) are continuous offset functions with independent variables x, y, and z, respectively, which are used to describe the offset of points on the isosurface along the x, y, and z axes of the Cartesian coordinate system.

7. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 6 is characterized in that: The offset function is a continuous function equation, including a linear function, a sine function, a tangent function or an odd-exponent power function.

8. The design method of the directional deformation hybrid TPMS structure based on additive manufacturing according to claim 6 is characterized in that: The formula of the offset function is as follows: ； Where δ represents the maximum offset and determines the slope of the offset function curve. a is a constant related to the unit cell size.

9. A metal product, characterized in that: Prepared according to the method according to any one of claims 1 to 8.

10. Use of the product according to claim 9 in bone implants or heat exchangers for electronic products.

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