Defective metamaterial and preparation method thereof
By constructing a triangular mesh and improving the genus level in the TPMS structure, a mirror-symmetric TPMS unit cell structure is generated, which solves the problems of mechanical property degradation at low density and resin residue during manufacturing, and achieves high mechanical properties and manufacturing feasibility.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-11
- Publication Date
- 2026-04-14
AI Technical Summary
Traditional TPMS structures exhibit a sharp decline in mechanical properties at low densities, and there are issues with the difficulty in removing resin or powder residues during the manufacturing process.
By constructing a triangulated mesh within a tetrahedral cell, introducing new vertices and adding boundary line segments to improve the genus level, and generating TPMS conjugate surfaces through energy criteria and Bonnet rotation, a mirror-symmetric TPMS single-cell structure is formed.
While maintaining zero average curvature and open-cell characteristics, it significantly improves specific stiffness and specific strength, improves stress distribution patterns, solves the problem of mechanical property degradation at low density, and simplifies the removal of resin or powder during additive manufacturing.
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Figure CN121862264A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of metamaterial manufacturing technology, specifically to the design and preparation methods of genus metamaterials, and particularly to methods for generating TPMS unit cell structures, methods for preparing genus metamaterials, and genus metamaterials themselves. Background Technology
[0002] Genus metamaterials are widely used in aerospace, medical implants, and energy absorption due to their advantages such as lightweight, breathability, and high designability. However, the deformation mechanism of traditional foam and lattice structures is mainly bending, which leads to a sharp decrease in their stiffness and strength as the relative density decreases, and there is a theoretical upper limit to their mechanical properties.
[0003] Triple Periodic Minimal Surface (TPMS) is a special type of open structure with zero mean curvature, defined by mathematical equations, which exhibits near-theoretical mechanical properties under hydrostatic loads. However, the relatively fixed topology of existing TPMS structures limits the improvement of their mechanical properties at low densities. Especially under uniaxial or non-uniform loads, traditional TPMS structures still exhibit predominantly local bending deformation, and their stiffness and strength decrease significantly with decreasing density, making it difficult to achieve high load-bearing capacity while maintaining lightweight design. Summary of the Invention
[0004] The embodiments of this application aim to solve one of the above-mentioned technical problems to a certain extent or at least provide a useful commercial option. In view of this, the embodiments of this application provide genus metamaterials and their preparation methods, which significantly improve the specific stiffness and specific strength of genus metamaterials at low densities, overcoming the industry problem that their mechanical properties decrease sharply with decreasing density.
[0005] In a first aspect, embodiments of this application provide a method for generating a TPMS unit cell structure. The method includes: constructing an initial triangulated mesh confined within a tetrahedron based on an initial TPMS structure, wherein the initial triangulated mesh is bounded by a predetermined number of line segments, the predetermined number being determined by the initial TPMS structure; obtaining a new initial triangulated mesh by introducing new vertices and adding boundary line segments within the initial triangulated mesh to improve the genus level of the initial triangulated mesh; wherein the new initial triangulated mesh is composed of multiple triangular faces formed by connecting original vertices and new vertices on triangular faces, the number of triangular faces being determined based on the number of newly added vertices, and the multiple triangular faces having no overlap or breakpoints; performing iterative evolution and Bonnet rotation on the initial triangulated mesh based on an energy criterion to obtain a TPMS conjugate surface confined within the tetrahedral cell; and generating the TPMS unit cell structure by performing mirror symmetry along the surface of a basic tetrahedron based on the TPMS conjugate surface, utilizing the symmetry of the initial TPMS structure.
[0006] In an exemplary embodiment, the initial TPMS structure has mirror symmetry; the initial TPMS structure is selected from FRD-A surface, SD surface, FRD-B surface, Batwing surface, Manta surface or SP surface.
[0007] In an exemplary embodiment, the vertices of the tetrahedral cell are determined based on the symmetry of the initial TPMS structure; for FRD-A, FRD-B, SD, or SP surfaces, the vertex coordinates of the tetrahedral cell are set to (0,0,0), (L / 2,0,0), (L / 2,L / 2,L / 2), and (L / 2,-L / 2,L / 2), respectively, where L is the structural side length of the cubic unit cell of the TPMS; for Batwing and Manta surfaces, the vertex coordinates of the basic tetrahedron are set to (0,0,0), (L,0,0), (L,-L,L / 2), and (L,-L,-L), respectively, where L is the structural side length of the cubic unit cell of the TPMS.
[0008] In an exemplary embodiment, for FRD-A, FRD-B, SD, or SP surfaces, the mirror face of the TPMS cubic unit cell formed by the triangular facets is the three (110) faces of the basic tetrahedron, and the number of mirror symmetries is 23 times; for Batwing or Manta surfaces, the TPMS cubic unit cell formed by the triangular facets is first mirrored 5 times along the two (110) faces of the basic tetrahedron to obtain an eighth of the cubic unit cell, and then mirrored 7 times along the two (100) faces.
[0009] In an exemplary embodiment, for an SP surface, a Bonnet rotation is performed on the initial triangulated mesh based on an energy criterion to obtain a conjugate surface confined within the tetrahedral cell; wherein the rotation angle is 90 degrees; for an FRD-A surface, SD surface, FRD-B surface, Batwing surface, or Manta surface, a surface evolution is performed on the initial triangulated mesh based on an energy criterion to obtain a conjugate surface confined within the tetrahedral cell.
[0010] In an exemplary embodiment, the genus level of the triangular facet is increased starting from an initial genus level 1, and then progressively increased in the order of genus levels 1, 2, 3, 4, and 5. Each time the genus level is increased, the number of boundary line segments is increased and new vertices are introduced according to predetermined rules. The predetermined rules are determined by the TPMS structure type to ensure that the triangular facets corresponding to each genus level have a stable topological structure and symmetry.
[0011] In an exemplary embodiment, the symmetry of the initial TPMS structure is utilized to generate the TPMS unit cell structure based on the conjugate surface. This includes performing four symmetry operations on each of the three 110 faces of the envelope tetrahedron of the smallest mirror unit of the TPMS basic surface to generate eight identical conjugate surfaces. A total of 24 conjugate surfaces are generated and seamlessly spliced along the boundary of the tetrahedral cell to finally form a complete cubic TPMS unit cell. The side length of the unit cell is equal to the longest side length of the tetrahedron.
[0012] Secondly, embodiments of this application provide a method for preparing genus metamaterials, the method comprising: generating a TPMS unit cell structure according to any example of the method in the first aspect; generating a three-dimensional solid model based on a model of the TPMS unit cell structure; generating instruction code for controlling additive manufacturing equipment based on the three-dimensional solid model; and preparing the genus metamaterial by means of photopolymerization technology or powder sintering technology based on the instruction code.
[0013] In an exemplary embodiment, generating a three-dimensional solid model based on the model of the TPMS unit cell structure includes: applying a uniform bias to the TPMS surface to impart a wall thickness t, the wall thickness t being determined based on the target relative density of the genus metamaterial, to obtain a solidified unit cell structure; and periodically arranging the solidified unit cells in a three-dimensional space at the same spacing to generate a three-dimensional solid model.
[0014] Thirdly, embodiments of this application provide a genus metamaterial, which is prepared by the method of any example in the second aspect.
[0015] In an exemplary embodiment, the relative density of the genus metamaterial is 0.04-0.12, the specific elastic modulus of the genus metamaterial is 0.16-0.94, and the Hashin-Shtrikman upper limit of the specific elastic modulus within the relative density range of the genus metamaterial is 0.51-0.53.
[0016] In an exemplary embodiment, the energy absorption range of the open-genus metamaterial is greater than 1.77 J / g.
[0017] In summary, the solution provided in this application involves constructing a triangulated mesh within a tetrahedral cell based on the initial TPMS structure. New vertices and additional boundary line segments are introduced into this triangulated mesh to improve the genus, transforming the topological characteristics of the TPMS structure from fixed to adjustable, thus achieving a systematic improvement in the structural genus. This process, while maintaining zero mean curvature and continuous opening characteristics, drives the TPMS geometry to undergo directional evolution, altering the Gaussian curvature distribution on its surface. Consequently, the generated TPMS unit cell structure can optimize the stress distribution pattern under load at low density, shifting the structural deformation mechanism from bending-dominated to tension / compression-dominated, thereby significantly improving the specific stiffness and specific strength of the structure. This effectively enhances the energy absorption capacity of the genus metamaterial, achieving high-efficiency load-bearing performance while maintaining lightweight design. It overcomes the problem of rapid mechanical property degradation in traditional genus metamaterials at low density and the difficulty in fabrication using additive manufacturing. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 This is a flowchart illustrating a method for generating a TPMS unit cell structure according to an embodiment of this application; Figure 2 This is a schematic flowchart of a method for preparing genus metamaterials according to an embodiment of this application; Figure 3 This is a schematic diagram of an FRD-A surface unit cell structure of different genus levels according to an embodiment of this application; Figure 4 According to one embodiment of this application Figure 3 The diagram shows the relationship between specific modulus and relative density for the series of results shown. Figure 5 This is a schematic diagram of SP surface unit cell structures of different genus levels according to an embodiment of this application; Figure 6 This is a schematic diagram showing the specific energy absorption (SEA) of an SP series structure according to an embodiment of this application as a function of genus. Detailed Implementation
[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in sequences other than those illustrated or described herein. In embodiments of this application, "B corresponding to A" means that B is associated with A. In one implementation, B can be determined based on A. However, it should also be understood that determining B based on A does not mean determining B solely based on A; B can also be determined based on A and / or other information. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or server that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or devices. In the description of this application, unless otherwise stated, "a plurality of" means two or more.
[0022] The technical problems to be solved and the inventive concept to be presented in the embodiments of this application will be described below: As mentioned earlier, traditional TPMS structures face the problem of a sharp decline in mechanical properties at low densities. Furthermore, traditional TPMS structures also face the dilemma of balancing open-cell structure with high performance. Specifically, closed-cell plate metamaterials can achieve the theoretical maximum modulus, but their closed-cavity structure presents significant challenges for additive manufacturing. During manufacturing, residual uncured resin or unmelted powder is difficult to remove, severely affecting the quality and performance stability of the finished product. To solve this problem, holes are usually created in the plate, but this introduces stress concentration, significantly weakening the structure's stiffness and strength, thus greatly diminishing its theoretical performance advantages. This results in the performance degradation of closed-cell plate metamaterials with excellent mechanical performance potential in actual manufacturing, while also increasing the complexity and cost of post-processing. Traditional methods cannot achieve near-theoretical mechanical properties while maintaining perfect open-cell characteristics (facilitating manufacturing).
[0023] To address the aforementioned problems in related technologies, the solution provided in this application constructs a triangulated mesh within a tetrahedral cell and systematically improves its genus level, guiding the morphological evolution of the minimal surface from a geometric and topological perspective. This enables the generated TPMS structure to maintain zero average curvature and fully open characteristics while achieving directional control over the Gaussian curvature distribution and stress transfer path.
[0024] Specifically, a triangular mesh is constructed within a tetrahedron based on the initial TPMS structure, allowing the surface generation process to take place within a confined space, thereby ensuring that the structural units maintain strict mirror symmetry and periodic extensibility in geometry.
[0025] Furthermore, by introducing new vertices and adding boundary line segments into the triangulated mesh, the genus level of the triangulated mesh is improved. This genus improvement essentially increases topological connectivity, introducing more connecting channels and openings within the same volume. This transforms the Gaussian curvature distribution on the structural surface from a state concentrated at finite curvature extrema to a more uniform and continuous distribution. This geometric change directly alters the energy distribution pattern of the material under stress, allowing stress to be transmitted along the entire surface rather than concentrated locally, thus improving flexural buckling instability at low densities. In other words, the complex topological structure formed after genus improvement can transition from a bending-dominated deformation mechanism to a tension / compression-dominated mechanism, enabling the structure to achieve higher specific strength and specific stiffness while maintaining lightweight and open-pore characteristics.
[0026] Furthermore, based on triangulation meshes and surface evolution and Bonnet rotation under energy criteria, the resulting conjugate surfaces possess both geometric continuity and physical stability. Ultimately, the TPMS unit cell formed after symmetric expansion not only maintains a perfect open-pore structure but also exhibits a more uniform mechanical response mode.
[0027] The technical solution of this application will be described in detail below: Figure 1 This is a flowchart illustrating a method for generating a TPMS unit cell structure according to an embodiment of this application. (Refer to...) Figure 1 The method may include: S110, based on the initial TPMS structure, construct a triangulated mesh confined within a tetrahedron, wherein the triangulated mesh is bounded by a predetermined number of straight line segments, the predetermined number being determined by the initial TPMS structure; In an exemplary embodiment, the initial TPMS structure exhibits mirror symmetry. This symmetry not only determines the geometric boundaries of the tetrahedral cell but also provides a stable topological basis for subsequent genus regulation. The aforementioned initial TPMS structure can be an FRD-A surface, an SD (Schwarz' D) surface, an FRD-B surface, a Batwing surface, a Manta surface, or an SP (Schwarz' P) surface, etc.
[0028] When constructing the triangulated mesh, its boundary consists of a predetermined number of straight line segments. This number is determined by the initial TPMS structure and is typically no less than 4, but can be 5, 6, 7, 8, 9, or 10, etc., to ensure that the formed surface accurately reflects the geometric features of the original TPMS structure while maintaining continuity and symmetry during topological evolution. This method, by confining the structure within a tetrahedral cell, allows the generated conjugate surfaces to be seamlessly spliced in subsequent mirroring operations, thereby forming a complete cubic unit cell structure.
[0029] S120, by introducing new vertices and adding boundary line segments within the initial triangulated mesh, a new initial triangulated mesh is obtained to improve the genus level of the initial triangulated mesh; wherein, the new initial triangulated mesh is composed of multiple triangular faces formed by connecting the original vertices and new vertices on the triangular faces, the number of the triangular faces is determined based on the number of newly added vertices, and there is no overlap or breakpoint between the multiple triangular faces; In an exemplary embodiment, the initial triangulated mesh consists of multiple triangular faces. Each triangular face is formed by connecting the original vertices and newly added vertices on a new triangular face. The faces are spatially continuous without overlap or breaks, thus ensuring the accuracy and stability of subsequent surface evolution and conjugate surface generation. The original number of vertices is 4, and the number of triangular faces increases by 1 for each new vertex added.
[0030] In an exemplary embodiment, to achieve precise control over the mechanical properties of the TPMS structure, after constructing an initial triangulated mesh, new vertices are systematically introduced into the triangulated mesh, and boundary line segments are added to obtain a new triangulated mesh, thereby gradually increasing its genus level. Specifically, the genus level is increased sequentially from the initial level 1 to level 5. Each genus increase strictly follows the rules predetermined by the TPMS structure type. These rules determine the method of adding boundary line segments and the location of introducing new vertices to ensure that the triangulated mesh at each level remains topologically stable and fully utilizes the mirror symmetry of the initial TPMS structure, making the structure geometrically highly continuous and topologically unbroken.
[0031] As the genus level increases, the Gaussian curvature distribution on the triangulated mesh changes significantly, gradually replacing local bending regions with tensile or compressive forces. This transforms the inefficient bending-dominated deformation mechanism of traditional TPMS structures into a more efficient tensile / compressive stress mode. This geometric evolution directly leads to a significant increase in specific stiffness and specific strength, especially under low relative density conditions, where the structure's load-bearing capacity is significantly superior to traditional fixed-topology TPMS or lattice structures. Furthermore, because the design of each genus level maintains mirror symmetry and topological stability, the newly formed triangulated mesh can be seamlessly spliced during subsequent triangulation and conjugate surface generation, ensuring the geometric consistency and fabrication feasibility of the complete unit cell structure.
[0032] In terms of application scenarios, the method of progressively increasing genus allows for the generation of multiple unit cell series with varying performance gradients for the same type of TPMS structure, providing customized options for different load environments or functional requirements. For example, in lightweight load-bearing structures, a medium genus level can be selected to balance stiffness and lightweight; in energy absorption or buffering scenarios, a high genus level structure can be used to fully utilize the tensile / compressive stress mechanism to enhance the specific energy absorption performance of the structure. In this way, this implementation not only solves the problem of stiffness decay that is traditionally prone to occur in low-density TPMS structures, but also maintains perfect open-cell characteristics, allowing resin or powder residues from the additive manufacturing process to be smoothly discharged, thereby achieving multiple optimizations in mechanical properties, manufacturing feasibility, and application flexibility.
[0033] S130, based on the energy criterion, iterative evolution and Bonnet rotation are performed on the initial triangulated mesh to obtain the TPMS conjugate surface confined within the tetrahedral cell. The energy criterion is used to control the geometric stability and topological rationality of the surface during its evolution. Its optimization objective is to minimize the total energy or geometric energy of the surface. Specifically, the energy criterion comprehensively considers factors such as surface area energy, curvature energy, and topological constraints: minimizing surface area energy ensures that the generated conjugate surfaces tend towards a minimum surface shape with zero mean curvature; curvature energy optimization balances the Gaussian curvature distribution on the surface, reducing local sharp or stress-concentrated areas, thereby improving surface smoothness and structural stability; topological constraints and mirror symmetry constraints ensure that the surface maintains topological continuity during iterative optimization, enabling seamless alignment of each conjugate surface when splicing tetrahedral cells. Through the above surface optimization based on the energy criterion, highly balanced and highly smooth conjugate surfaces can be obtained while ensuring geometric and topological stability.
[0034] In an exemplary preferred embodiment, for SP surfaces, the Bonnet rotation method is used to geometrically transform the initial triangulated mesh, with the rotation angle set to 90°. By maintaining zero mean curvature and mirror symmetry, the surface achieves continuous mapping between different parameter families, resulting in SP conjugate surfaces confined within tetrahedral cells. For FRD-A, SD, FRD-B, Batwing, and Manta surfaces, an energy-based surface evolution method is employed. This method iteratively adjusts the vertex positions of the triangulated mesh to minimize the overall structural energy, while maintaining topological continuity and symmetry constraints in each iteration. With adaptive optimization of vertex positions and gradual homogenization of curvature distribution, local high-curvature regions of the surface are smoothed, and existing high-stress concentration points are eliminated, thereby optimizing the stress path. This allows the conjugate surface to maintain high specific stiffness and specific strength even under low relative density conditions. Furthermore, the surfaces generated in this process are all open-cell structures with good continuity between channels, facilitating the full discharge of powder or resin during additive manufacturing.
[0035] By increasing the genus level of the triangulated mesh, the structural morphology of the metamaterial further evolves: the topological connectivity of the FRD-A and SD surface families gradually evolves towards a cubic foam structure as the genus level increases, with local nodes tending to form a near-cubic support framework; the FRD-B surface family expands along the octahedral symmetry direction, evolving into an octahedral foam structure, exhibiting higher isotropy and mechanical homogeneity; the Batwing and Manta surface families form a body-centered cubic (BCC) and TPMS composite structure, locally exhibiting the dual characteristics of continuous TPMS channels and BCC node connections, taking into account both high permeability and high energy absorption performance.
[0036] In this embodiment, the surface optimization method based on energy criteria used in this application can be found in the reference (Hsu, L., Kusner, R. and Sullivan, J., 1992. Minimizing the squared mean curvatureintegral for surfaces in space forms. Experimental Mathematics, 1(3), pp.191–207.). The reference is only used to illustrate the principle of energy minimization and does not constitute a limitation on the technical features of this application.
[0037] Furthermore, the implementation of the Bonnet rotation and surface evolution method can be found in the reference (Brakke, KA, 1992. The Surface Evolver. Experimental Mathematics, 1(2), pp.141–165.), which is used to assist in the numerical optimization and smoothing of surface energy.
[0038] S140, utilizing the symmetry of the initial TPMS structure, based on the TPMS conjugate surface, mirror symmetry is performed along the surface of the basic tetrahedron to generate the TPMS unit cell structure.
[0039] This step is used to generate a complete TPMS unit cell structure based on the generated TPMS conjugate surfaces and the symmetry of the initial TPMS structure. Specifically, the vertex coordinates of the tetrahedral cell are first determined to provide the spatial positioning basis for the conjugate surfaces within the unit cell. For FRD-A, FRD-B, SD, and SP surfaces, the vertex coordinates of their tetrahedral cells are set to (0,0,0), (L / 2,0,0), (L / 2,L / 2,L / 2), and (L / 2,-L / 2,L / 2), respectively, where L is the structural side length of the TPMS cubic unit cell. For Batwing and Manta surfaces, the vertex coordinates of the tetrahedral cells are set to (0,0,0), (L,0,0), (L,-L,L / 2), and (L,-L,-L) to ensure that the conjugate surfaces of different surface types can be correctly positioned within the unit cell and maintain the expected topology and symmetry. By precisely determining the vertex coordinates of the tetrahedral cell, it can be ensured that the generated conjugate surfaces do not overlap or break in space, and can be seamlessly spliced to form a complete cubic unit cell in subsequent mirroring operations.
[0040] Based on the spatial positioning of conjugate surfaces and tetrahedral cells, mirroring operations are performed to generate complete TPMS unit cells. For FRD-A, FRD-B, SD, and SP surfaces, the mirror faces of the triangular facets forming the TPMS cubic unit cell are the three (110) faces of the basic tetrahedron. Four mirroring operations are performed on these faces, for a total of 23 mirroring operations, ultimately forming a complete cubic unit cell seamlessly spliced from 24 identical conjugate surfaces. For Batwing and Manta surfaces, the two (110) faces of the basic tetrahedron are mirrored five times to obtain one-eighth of the cubic unit cell, and then the remaining unit cells are spliced seven times along the two (100) faces, ultimately obtaining a complete cubic TPMS unit cell. Through mirroring and splicing operations, the generated unit cell structure not only ensures topological continuity and structural integrity but also retains open-pore permeability, allowing residual resin or powder to be smoothly discharged during additive manufacturing, greatly improving manufacturing feasibility and post-processing efficiency.
[0041] The TPMS unit cell generated by the above method possesses both high stability and high tunability. By utilizing the initial TPMS structural symmetry and precise control of tetrahedral cell positioning, conjugate surfaces of different genus levels can be rationally distributed within the unit cell, further optimizing stress distribution under load. This shifts the dominant deformation mechanism from inefficient bending to efficient tension / compression, resulting in a significant improvement in specific stiffness and specific strength at low relative density. Simultaneously, the unit cell maintains a perfectly open structure, providing an ideal structural basis for various applications such as fluid permeation, heat conduction, energy absorption, and bioimplantation. This implementation method achieves complete assembly and topology optimization of the TPMS unit cell while ensuring an organic combination of lightweight, high performance, and manufacturing feasibility, effectively overcoming the technical bottleneck of easy degradation of mechanical properties in traditional TPMS structures at low densities.
[0042] Figure 2 This is a flowchart illustrating a method for preparing genus metamaterials according to an embodiment of this application, with reference to... Figure 2 The method may include: S210, Generate a TPMS unit cell structure according to the method of any example of the first aspect; This step is used to generate a TPMS unit cell structure according to the method described in any embodiment of the first aspect. Detailed description is provided above and will not be repeated here.
[0043] S220, Based on the model of the TPMS unit cell structure, generate a three-dimensional solid model; In an exemplary embodiment, generating a three-dimensional solid model based on the TPMS unit cell structure model includes: performing a uniform bias operation on the TPMS surface to impart a wall thickness t, thereby transforming the idealized zero-thickness mathematical surface into a manufacturable solid structure. The wall thickness t is determined based on the relative density of the target metamaterial and can be parameterized by establishing a wall thickness-density mapping relationship, for example: ρ= Equation 1); in, ρ S represents relative density; Area L is the surface area, L is the unit cell size, and t is the wall thickness.
[0044] In engineering implementation, S Area It can be accurately determined using computational geometry software from the initial triangulated mesh or the mesh evolved from the surface. p The selection is based on the target application and mechanical / permeability requirements (e.g., for lightweight load-bearing or energy-absorbing structures). ρA range of 0.04-0.12 can be selected to balance strength and lightweight. When using the above formula for parametric design, a set of wall thickness-relative density mapping curves can be generated by scanning the value of t, thereby allowing for the rapid selection of t values that meet the requirements of strength, stiffness, and porosity during the design phase.
[0045] When biasing a mathematical surface into a solid, attention should be paid to the consistency of the bias direction and the bias amount to maintain topological invariance. Equidistant biasing both inside and outside is preferred to form a closed thick shell. For larger t values, it is necessary to check whether self-intersection or locally closed cavities are introduced after biasing. If necessary, Boolean correction or local trimming should be performed on the geometry after biasing to avoid manufacturing defects. Furthermore, in actual manufacturing, the influence of process factors on the final wall thickness must be considered, such as the curing shrinkage of the photocurable material and printing resolution. Therefore, it is recommended to introduce an adjustment factor γ (e.g., γ = 1 + δ, where δ is an empirical correction term, typically ranging from 0.02 to 0.10, depending on the material and equipment) based on the calculated t. design =γ t is used to compensate for shrinkage and processing errors; while ensuring t design The thickness should not be less than the minimum printable wall thickness (equipment resolution) of the additive manufacturing equipment used to avoid manufacturing failures or wall oxidation / brittle fracture. If thin-walled channels with insufficient thickness appear locally after offsetting, they can be corrected during the modeling stage by local thickening or topology fine-tuning to balance transparency and mechanical safety.
[0046] Solidified unit cells are periodically arrayed in three-dimensional space at equal intervals (usually L is taken as the interval) to form a periodic array of three-dimensional solid models. Due to the adoption of a seamless stitching strategy based on the natural periodicity of TPMS, the interface weakening caused by traditional Boolean stitching can be avoided, thereby maintaining the global topological continuity and uniform stress distribution of the unit cell array.
[0047] S230, Based on the three-dimensional solid model, generate instruction code for controlling the additive manufacturing equipment; In an exemplary embodiment, the process of generating instruction code for controlling additive manufacturing equipment based on the three-dimensional solid model includes: exporting the three-dimensional solid model as a Standard Template Library (STL) file format, and performing necessary preprocessing and quality verification on the exported mesh file. Preprocessing steps include, but are not limited to, unit calibration, ensuring the mesh is a watertight mesh, normal consistency correction, deleting isolated faces and overlapping triangles, and, if necessary, resampling or subdivision to meet equipment resolution requirements. For self-intersections or locally closed cavities that may appear after offsetting, Boolean patching or local geometric adjustments are also required at this stage to avoid slicing failures or printing defects. After mesh verification, the STL model is sliced in slicing software. Slicing parameters include layer height, exposure time or light intensity per layer, layer-by-layer lifting / lowering speed, platform lifting / lowering strategy, support structure generation strategy and minimum contact surface, and component orientation and arrangement during slicing. During slicing, the orientation of the pore openings should be prioritized to facilitate cleaning and resin drainage, minimizing contact between supports and those within the pores to maintain the unobstructed pore network and reduce post-processing complexity. Simultaneously, forming simulations (such as calculating layer-by-layer curing volume and thermal / shrinkage effects) can be performed during the slicing stage to predict and compensate for deformation, thereby improving the geometric accuracy and mechanical consistency of the finished product. After slicing, the slicing software outputs instruction codes for the additive manufacturing equipment (which may be equipment-specific print files or universal control path codes depending on the equipment). These instructions include layer-by-layer path information, exposure / energy parameters, support and curing strategies, and necessary pre- and post-printing processing instructions. This process not only reliably transforms mathematical models into executable manufacturing instructions, but also helps ensure the practical feasibility of wall thickness, pore size, and pore connectivity at the manufacturing end through mesh quality control, slicing parameter optimization, and printing simulation. This reduces printing defects and improves the geometric and mechanical consistency of printed parts, thereby ensuring that the genus metamaterials prepared meet design performance and have good batch manufacturing stability and repeatability in different application scenarios that require high permeability (such as fluid mass transfer or biological scaffolds), high specific stiffness (such as aerospace load-bearing components), or high energy absorption (such as buffers / protective components).
[0048] S240, based on the instruction code, the genus metamaterial is prepared by photopolymerization technology or powder sintering technology.
[0049] In an exemplary embodiment, the genus metamaterial is prepared based on the instruction code using photopolymer additive manufacturing technology or powder sintering technology. The additive manufacturing preferably employs photopolymerization (such as SLA or DLP) equipment, and the material used is a photosensitive resin with ABS-like mechanical properties to ensure that the finished product's elongation at break, impact toughness, and tensile strength are close to the mechanical performance of engineering plastic ABS, thereby meeting the engineering application requirements such as lightweight load-bearing and energy absorption. To ensure geometric accuracy and mechanical consistency, the printing resolution and layer height should meet a printing accuracy requirement of not less than 0.01 mm. In parameter settings, the layer-by-layer exposure energy and curing time should be reasonably controlled to avoid channel shrinkage or surface roughening caused by over-curing. Simultaneously, appropriate energy compensation strategies should be adopted when necessary to counteract material curing shrinkage. During the manufacturing process, the part placement direction and slicing strategy should be designed and selected preferentially, so that the main channels of the open network are oriented in a direction favorable to the gravity and fluid outflow of uncured resin and cleaning fluid, minimizing the formation of support structures or contact areas between supports and the hole walls inside the channels, so that residual resin can be quickly and thoroughly removed after printing by means of solvent rinsing, ultrasonication, and vacuum extraction. After printing, it is recommended to first clean with solvent (such as isopropanol) combined with ultrasonic treatment or fluid flushing to remove residues inside the pores. Then, perform necessary drying and secondary UV curing to stabilize material properties and complete the final cross-linking reaction. This combination of open-pore design and cleaning process not only effectively avoids the problem of difficult-to-remove residual resin in traditional closed-pore plate structures, but also significantly improves the dimensional accuracy, surface quality, and mechanical stability of the product by reducing internal cavity residue and avoiding localized stress concentration, thereby reducing post-processing costs and improving the consistency of batch manufacturing.
[0050] The above method not only achieves high-precision conversion from TPMS theoretical surfaces to manufacturable entities, but also realizes an adjustable balance between porosity, specific strength and permeability under parametric control, making the metamaterial of this application have excellent application potential in various engineering scenarios such as aerospace, energy absorption, biological scaffolds, fluid permeation and acoustic control.
[0051] This application also provides a genus metamaterial, which is prepared by the method of the second aspect.
[0052] In exemplary embodiments, the genus metamaterials prepared by the aforementioned method exhibit significant advantages in mechanical properties, and their performance parameters have been verified in both theoretical and experimental results. The relative density ρ of the metamaterial is in the range of 0.04 to 0.12, which can be achieved by controlling the bias thickness t to ensure a balance between lightweighting and load-bearing capacity. Within this range, the specific elastic modulus of the prepared metamaterial can reach 0.16-0.94, while the theoretical upper limit of the specific elastic modulus according to the Hashin-Shtrikman theory is 0.51-0.53, indicating that the genus-controlled TPMS structure of this application has broken through the performance boundary predicted by traditional continuous medium theory in terms of topology optimization. Furthermore, experimental results show that when the structural genus is gradually increased from level 1 to level 5 at the same relative density, the elastic modulus of the metamaterial is significantly improved compared to Young's modulus, with the FRD-A structure showing an improvement of approximately 52.4% in multiple sets of repeated tests. This performance enhancement stems from the increased topological complexity of the structure after the genus is increased, the number of load transfer paths inside the microstructure is significantly increased, and the bending elements in the curved surface are transformed into continuous tensile / compressive main load-bearing elements, making the stress distribution more uniform, thereby achieving a nonlinear increase in the macroscopic modulus.
[0053] In a preferred embodiment, a directional genus control strategy is employed for the SP surface, increasing the boundary straight line segments along the load direction while maintaining mirror symmetry along the principal axis. This design increases the structure's stiffness under uniaxial loads to over 90% of that of traditional honeycomb structures, demonstrating extremely high structural efficiency and material utilization. This result demonstrates that by directionally introducing topological genus, a significant improvement in mechanical performance is achieved without substantially increasing material consumption.
[0054] In terms of energy absorption performance, the specific energy absorbed (SEA) of the genus metamaterial increases significantly with increasing genus level. Experimental tests show that as the genus level increases, the specific energy absorption range of the genus metamaterial can increase from 1.77 J / g to 6.93 J / g, an increase of nearly three times. The mechanism of this improvement lies in the presence of more high-curvature nodes and branch surfaces in high-genus structures, which form multi-stage collapse behavior under compressive buckling, enabling a more stable energy dissipation process. At the same time, the interconnected pore network within the structure makes stress transmission between collapse regions smoother, avoiding excessive local damage, thus resulting in a broad plateau characteristic in the energy absorption curve. In summary, the high-genus TPMS metamaterial can simultaneously achieve high specific stiffness and high specific energy absorption performance under low density and light mass conditions, making it suitable for applications with extremely high requirements for lightweight and energy absorption performance, such as aerospace, automotive cushioning, protective equipment, and biomedical implants.
[0055] The embodiments of this application are described in detail below. It should be noted that the embodiments described below are exemplary and are only used to explain this application, and should not be construed as limiting this application.
[0056] Example 1: Preparation of genus metamaterials Model design: The Schoen FRD (FRD-A) surface was selected as the initial structure. For example... Figure 3 As shown, five unit cell models with genus levels from 1 to 5 are generated by progressively increasing the number of vertices on the boundaries of their triangular faces (e.g., from the initial path ----, adding 1 to 4 new vertices in sequence).
[0057] Solidification: Relative density is a key parameter for evaluating the mechanical properties of TPMS structures. To systematically explore the relationship between TPMS design parameters and relative density, this embodiment selects five relative density values of 4%, 6%, 8%, 10%, and 12% for systematic analysis. For each TPMS structure, five different offset wall thicknesses are set for comparison. Taking the FRD-A structure as an example, the thickening operation process in the construction of the TPMS metamaterial solid representative volume element is specifically demonstrated: First, the smallest symmetric element of the TPMS is generated using SurfaceEvolver, and then solidification modeling and assembly are completed in AutoCAD through offset and mirror operations. In this process, the level set formula is used to characterize the FRD surface features, and the offset parameter t is determined by the target relative density ρ. The surface is offset using CAD software to generate a solid model.
[0058] Additive Manufacturing: A stereolithography 3D printer (Form 3+) was used with rigid photosensitive resin material to manufacture the above model into a standard mechanical test specimen. In this example, Tough 2000 resin material was selected as the raw material, with an elastic modulus of 1.3 GPa and a Poisson's ratio of 0.3, exhibiting good mechanical properties. The photopolymerization printing process mainly employs a layer-by-layer stacking strategy to form the component. The semi-open topology of the structure ensures convenient and quick removal of residual resin material from the structural cavity. The specific values of the structure's macroscopic dimensions, unit cell size, plate thickness, and aperture are closely related to the process parameters such as the size of the photopolymerization equipment table and the forming accuracy. Here, the printed structure has dimensions L=W=H=40 mm, where L is the unit cell length, W is the unit cell width, and H is the unit cell height; the relative density is fixed at 12%, and the printed structure is an FRD-A structure with a genus of 1-5.
[0059] Finite element analysis and mechanical testing: Finite element analysis was performed on these five models to calculate the specific modulus. The results show that the specific modulus of the metamaterials increases significantly with increasing genus, reaching a maximum performance point of 125% of the upper limit of HS (Hyper- ... Figure 4 ).
[0060] Example 2: High Energy Absorption SP Metamaterial Model Design: Based on the Schwarz' P(SP) surface, a metamaterial unit cell with anisotropic mechanical properties is generated by non-uniformly controlling the genus in specific directions (such as the Z-axis). Figure 5 ).
[0061] Additive manufacturing: A stereolithography 3D printer (Form 3+) was used, employing rigid photosensitive resin materials. Tough2000 resin was selected as the raw material, with an elastic modulus of 1.3 GPa and a Poisson's ratio of 0.3, exhibiting excellent mechanical properties. The printed structure dimensions were L = W = H = 40 mm, where L is the unit cell length, W is the unit cell width, and H is the unit cell height; the relative density was fixed at 12%, and SP structures with genus levels of 1-5 were printed.
[0062] Finite element analysis and mechanical testing: Finite element analysis shows that the stiffness of the structure is specifically enhanced in the Z-axis direction. The SP structure with directional genus control can achieve 90% of the stiffness of honeycomb materials under uniaxial load. The stress-strain curve was measured through quasi-static compression tests, and the energy absorption capacity was calculated. Results are as follows: Figure 6 As shown, the specific energy absorption (SEA) of the high-genus SP structure prepared by 3D printing reaches 6.93 J / g, which is much higher than that of the low-genus structure (1.77 J / g).
[0063] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0064] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.
Claims
1. A method for generating TPMS unit cell structures, characterized in that, include: Based on the initial TPMS structure, an initial triangulated mesh is constructed within a tetrahedron. The initial triangulated mesh is bounded by a predetermined number of straight line segments, which is determined by the initial TPMS structure. By introducing new vertices and adding boundary line segments within the initial triangulated mesh, a new initial triangulated mesh is obtained to improve the genus level of the initial triangulated mesh; wherein, the new initial triangulated mesh is composed of multiple triangular faces formed by connecting the original vertices and new vertices on the triangular faces, the number of triangular faces is determined based on the number of newly added vertices, and there is no overlap or breakpoint between the multiple triangular faces; Based on the energy criterion, iterative evolution and Bonnet rotation are performed on the initial triangulated mesh to obtain the TPMS conjugate surface confined within the tetrahedral cell. Utilizing the symmetry of the initial TPMS structure, and based on the TPMS conjugate surface, mirror symmetry is performed along the surface of the basic tetrahedron to generate the TPMS unit cell structure.
2. The method according to claim 1, characterized in that, The initial TPMS structure has mirror symmetry; The initial TPMS structure is selected from FRD-A surface, SD surface, FRD-B surface, Batwing surface, Manta surface or SP surface.
3. The method according to claim 2, characterized in that, The vertices of the tetrahedral cell are determined based on the symmetry of the initial TPMS structure; For FRD-A, FRD-B, SD, or SP surfaces, the vertex coordinates of the tetrahedral cell are set to (0,0,0), (L / 2,0,0), (L / 2,L / 2,L / 2), and (L / 2,-L / 2,L / 2), respectively, where L is the structural side length of the cubic unit cell of the TPMS. For Batwing and Manta surfaces, the vertex coordinates of the basic tetrahedron are set as (0,0,0), (L,0,0), (L,-L,L / 2), and (L,-L,-L), respectively, where L is the structural side length of the cubic unit cell of the TPMS.
4. The method according to claim 3, characterized in that, For FRD-A, FRD-B, SD or SP surfaces, the mirror face of the TPMS cubic unit cell formed by the triangular facets is the three (110) faces of the basic tetrahedron, and the number of mirror symmetries is 23. For Batwing or Manta surfaces, the TPMS cubic unit cell is formed from the triangular facets. First, the 1 / 8 cubic unit cell is obtained by mirroring the two (110) faces of the basic tetrahedron five times, and then mirroring it seven times along the two (100) faces.
5. The method according to claim 3, characterized in that, For the SP surface, based on the energy criterion, a Bonnet rotation is performed on the initial triangulated mesh to obtain a conjugate surface confined within the tetrahedral cell; wherein the rotation angle is 90 degrees. For FRD-A, SD, FRD-B, Batwing, or Manta surfaces, surface evolution is performed on the initial triangulated mesh based on the energy criterion to obtain conjugate surfaces confined within the tetrahedral cell.
6. The method according to any one of claims 1-5, characterized in that, The genus level of the triangular facets is increased starting from the initial genus level 1, and then gradually increased in the order of genus level 1, 2, 3, 4 and 5. Each time the genus level is increased, the number of boundary line segments is increased and new vertices are introduced according to predetermined rules. The predetermined rules are determined by the TPMS structure type to ensure that the triangular facets corresponding to each genus level have a stable topological structure and symmetry.
7. The method according to any one of claims 1-5, characterized in that, Utilizing the symmetry of the initial TPMS structure, the TPMS unit cell structure is generated based on the conjugate surface, including: Four symmetry operations are performed on each of the three 110 faces of the envelope tetrahedron of the smallest mirror unit of the TPMS basic surface to generate eight identical conjugate surfaces. A total of 24 conjugate surfaces are generated and seamlessly spliced along the boundary of the tetrahedral cell to finally form a complete cubic TPMS unit cell. The side length of the unit cell is equal to the longest side length of the tetrahedron.
8. A method for preparing genus metamaterials, characterized in that, include: The method according to any one of claims 1 to 7 generates a TPMS single-cell structure; Based on the model of the TPMS single-cell structure, a three-dimensional solid model is generated. Based on the three-dimensional solid model, instruction code for controlling the additive manufacturing equipment is generated. Based on the instruction code, the genus metamaterial is prepared using photopolymerization technology or powder sintering technology.
9. The method according to claim 8, characterized in that, Based on the model of the TPMS unit cell structure, the generation of a three-dimensional solid model includes: A uniform bias is applied to the TPMS surface to impart a wall thickness t, which is determined based on the target relative density of the genus metamaterial, to obtain a solidified unit cell structure. The solidified unit cells are periodically arrayed at the same intervals in three-dimensional space to generate a three-dimensional solid model.
10. A genus metamaterial, characterized in that, Prepared by the method described in claim 8 or 9.
11. The genus metamaterial according to claim 10, characterized in that, The relative density of the genus metamaterial is 0.04-0.12, the specific elastic modulus of the genus metamaterial is 0.16-0.94, and the Hashin-Shtrikman upper limit of the specific elastic modulus within the relative density range of the genus metamaterial is 0.51-0.
53.
12. The genus metamaterial according to claim 10 or 11, characterized in that, The energy absorption range of the genus metamaterial is higher than 1.77 J / g.