Methods for additive manufacturing of minimal surface structures

Abstract

A method for additively manufacturing a minimum surface structure (63) of a three-dimensional article is described, the method comprising a computer (10) performing the following steps: recording an envelope of the three-dimensional article in the computer (10); generating a density field across the volume surrounded by the envelope, wherein the density of the density field corresponds to a local required value of at least one physical parameter at a corresponding location of the three-dimensional article; generating an adaptive Voronoi distribution of the volume using the density field; generating a first skeleton map associated with the adaptive Voronoi distribution; generating a second skeleton map associated with the first skeleton map; generating a digital minimum surface model (5) based on the first skeleton map and the second skeleton map; wherein the method further comprises a 3D printer (30) additively manufacturing the minimum surface structure (63) based on the digital minimum surface model (5).

Description

Technical Field

[0001] The present invention relates to a method for additively manufacturing a minimal surface structure of a three-dimensional article and the minimal surface structure additively manufactured by said method. Background Technology

[0002] Additive manufacturing is a manufacturing technology in which an object is created based on a digital 3D model, typically by adding material layer by layer. Compared to traditional processes such as subtractive manufacturing, additive manufacturing offers significantly increased design freedom and allows for the production of highly complex shapes and geometries. The prerequisite for producing any 3D object via additive manufacturing is a digital 3D model or computer-aided design file, based on which the object can be additively manufactured using a 3D printer.

[0003] Current additive manufacturing processes rely on filling the interior of hollow objects onto tubular supports, or, in more complex cases, onto triple periodic minimum surfaces (TPMS) infill structures. Alan H. Schoen's NASA Technical Report, NASA TND-5541, describes the generation of non-self-intersecting triple periodic minimum surfaces using a pair of periodic skeleton diagrams. The non-self-intersecting triple periodic minimum surfaces generated from a pair of skeleton diagrams divide space into two non-intersecting maze regions. According to Schoen, triple periodic minimum surfaces can conceptually be described as being generated by simultaneously expanding tubular neighborhoods around the skeleton diagrams, where the triple periodic minimum surfaces are formed when the two expanded regions collide.

[0004] Minimal surfaces such as TPMS allow for favorable force flow and load distribution. However, in the case of conventional periodic minimal surfaces, the high symmetry caused by periodicity leads to preferred orientations in the structure, which, due to the preferred orientations given by symmetry, reduces the overall response to physical requirements such as stress or strain. Furthermore, conventional periodic minimal surfaces such as TPMS exhibit poor adaptability to boundary geometry or requirements such as specific boundary conditions. Summary of the Invention

[0005] Therefore, the object of the present invention is to provide a method for additively manufacturing a minimal surface structure of a three-dimensional article and a minimal surface structure additively manufactured by said method, which at least partially improves upon the prior art and avoids at least some of the disadvantages of the prior art.

[0006] According to the invention, this objective is achieved by the features of the independent claim. Furthermore, other advantageous embodiments can be derived from the dependent claims, the description, and the drawings.

[0007] According to one aspect of the invention, this objective is achieved, in particular, by a method for additively manufacturing a minimal surface structure of a three-dimensional article, the method comprising a computer performing the following steps: recording the envelope of the three-dimensional article in a computer; generating a density field across the volume enclosed by the envelope, wherein the density in the density field corresponds to a locally required value of at least one physical parameter at a corresponding location of the three-dimensional article; generating an adaptive Voronoi (Thieson polygon) distribution of the volume using the density field; generating a first skeleton map associated with the adaptive Voronoi distribution; generating a second skeleton map associated with the first skeleton map; generating a digital minimal surface model based on the first and second skeleton maps; wherein the method further comprises a 3D printer additively manufacturing the minimal surface structure based on the digital minimal surface model.

[0008] The envelope of a 3D object can be an object envelope representing the outer boundary of the object. To reduce processing power when generating a digital minimum surface model, a so-called density field envelope representing a simplified object envelope with a simplified geometry can be used as the envelope of the 3D object. Preferably, the object envelope is completely contained within the density field envelope. For example, a density field envelope of a polygonal prism shape that surrounds the object envelope of a cylindrical shape can be used. In other examples, a density field envelope of an n-sided prism shape that surrounds the object envelope of an m-sided prism shape can be used, where m > n.

[0009] The adaptive Voronoi distribution described in the context of this invention should be understood as a 3D Voronoi distribution using three-dimensional Voronoi units. The term "adaptive" indicates that the adaptive Voronoi distribution is suited to the properties of the density field, as described herein.

[0010] The first and second skeleton graphs are preferably interwined but not intersecting. In particular, the second skeleton graph can be a dual graph based on the first skeleton graph. Further, the second skeleton graph can be a dual distribution based on a Voronoi distribution, such as 3D-Delaunay triangulation or Delaunay tetrahedralization, as described further below. The second skeleton graph can therefore be substantially dual to the first skeleton graph. However, the second skeleton graph can have features of one or more corrected segments deviating from the dual graph of the first skeleton graph to adapt to local topological conditions described further below. Optionally, to adapt to local topological conditions, the first skeleton graph can have features of one or more corrected segments deviating from the duality of the second skeleton graph. By generating a digital minimal surface model using two skeleton graphs, two non-intersecting mazes can be generated, each maze originating from one skeleton graph, separated by walls of a minimal surface structure. Through the generation of the two mazes, two channels of a minimal surface structure can be obtained. These channels can be closed by closures on their peripheral openings or can remain open.

[0011] By generating a density field, a spatial mapping of the local required value of at least one physical parameter can be obtained, since the density in the density field at the corresponding location of the object corresponds to the local required value of that at least one physical parameter at that location. For example, the density field can represent a spatial mapping of load condition requirements, which is parameterized by physical parameters such as stress and / or strain across the body enclosed by an envelope. For an example of plotting the local required value of stress across a three-dimensional object, the density in the density field can be proportional to the stress.

[0012] Using a density field, an adaptive Voronoi distribution can be generated as the starting point for generating the skeleton diagram of the digital minimum surface model. This allows the spatial mapping of the local requirement values ​​of at least one physical parameter to the digital minimum surface model, and correspondingly to the additively manufactured minimum surface structure. Therefore, by using a density field and an adaptive Voronoi distribution adapted to the density field, requirement parameterization based on the local requirement values ​​of at least one physical parameter can be transformed into parameterization of the digital minimum surface model. In doing so, since the digital minimum surface model is generated using a density field, the additively manufactured minimum surface structure can be obtained by structurally adapting the design to the physical requirements and specific boundary conditions across the 3D object.

[0013] For example, a density field having a density proportional to the stress requirements across a three-dimensional object can be transformed into a denser skeleton map at the corresponding location of the three-dimensional object with an increased stress value, which in turn leads to a minimum surface structure that is structurally denser at said location in order to withstand the higher stress values ​​present at said location.

[0014] Therefore, a so-called Adaptive Density Minimal Surface (ADMS) structure can be obtained through this method, which inherently and locally adapts to the input requirement parameters. The advantage of this method is that the local adaptation to the input requirement parameters can be included in a bottom-up manner, while parameterizing the digital minimum surface model itself, based on which the minimum surface structure is additively fabricated.

[0015] A three-dimensional object may include a shell, wherein a minimum surface structure forms an infill structure within the shell of the three-dimensional object. The shell may coincide with the object's envelope.

[0016] Alternatively, a minimal surface structure can form a three-dimensional object or part of a three-dimensional object without a shell.

[0017] In some embodiments, generating an adaptive Voronoi distribution includes: generating a set of scatter points corresponding to the distribution of density in a density field; randomly distributing the scatter points across the volume enclosed by the envelope; and using the randomly distributed scatter points as the generation points for Voronoi units to generate a plurality of Voronoi units of the adaptive Voronoi distribution.

[0018] By generating this set of scatter points, the number of Voronoi cells in the adaptive Voronoi distribution can be adapted to the density distribution to obtain a minimal surface structure with structural details corresponding to the density contrast in the density field. For example, for the physical parameters of stress across a three-dimensional object, the stress distribution can be recorded in a histogram stored in a computer, where the number of scatter points is proportional to the ratio of the sum of all stresses in the bars of the histogram to the product of the maximum stress and the number of bars. It will be apparent to those skilled in the art that other physical parameter values ​​can be correspondingly recorded in the histogram, which can be used to calculate the number of scatter points.

[0019] In some embodiments, randomly distributed scatter points are redistributed according to a density field, such that the distribution of the redistributed scatter points corresponds to the density field. These redistributed scatter points can then be used as initial generation points to generate Voronoi cells with an adaptive Voronoi distribution.

[0020] In some embodiments, generating an adaptive Voronoi distribution using a density field includes iteratively generating a plurality of Voronoi units of the distribution using a density field through weighted ticks.

[0021] By using weighted dot plots of the density field, a set of generation points can be generated for multiple Voronoi elements, where the positions of the generation points are determined by the density values ​​in the density field. In particular, using weighted dot plots of the density field typically results in regions with higher density values ​​containing more generation points than regions with lower density values, allowing the density field to weight the packets of Voronoi elements with an adaptive Voronoi distribution. Therefore, the advantage of weighting the packets of Voronoi elements by the density field is that the properties of the density field can be transferred to the structural properties of the minimal surface structure derived from the adaptive Voronoi distribution. Furthermore, iteratively generating Voronoi elements by weighted dot plots allows starting from an initial distribution (e.g., random distribution) of generation points for multiple Voronoi elements, and iteratively adapting the positions of the generation points or the packets of Voronoi elements to the density field by repeated weighted dot plots.

[0022] In some embodiments, the iterative generation of Voronoi cells via weighted point stacking begins with a randomly distributed or redistributed scatter point as described above. Therefore, the randomly distributed or redistributed scatter point can be used as the initial generation points for Voronoi cells with an adaptive Voronoi distribution.

[0023] In some embodiments, iteratively generating multiple Voronoi cells includes iterating through the following steps a) and b) until the calculated centroid matches the generation point of the Voronoi cell in step a): a) calculating the weighted centroid of each Voronoi cell using the density field and offsetting the generation point of the Voronoi cell to the corresponding centroid; b) generating new Voronoi cells with an adaptive Voronoi distribution using the offset generation point and replacing the Voronoi cell in step a) with the new Voronoi cell.

[0024] By iterating through steps a) and b) to iteratively generate multiple Voronoi elements, the density field-weighted 3D centroid Voronoi distribution can be implemented as an adaptive Voronoi distribution. The iterations of steps a) and b) preferably end when the calculated centroid coincides with the generation point of the Voronoi element in step a). However, in some embodiments, a tolerance is allowed such that the iterations of steps a) and b) end when the distance between the calculated centroid and the generation point of the Voronoi element in step a) is less than a predetermined tolerance value. For example, the tolerance value could be 10 times the minimum wall width of the minimum surface structure. -3 times.

[0025] In some embodiments, iteratively generating multiple Voronoi cells includes performing the following steps after step b) above: c) calculating cell weights for each Voronoi cell by integrating the density field over the respective Voronoi cell; d) recording a first weight threshold and a second weight threshold in a computer, wherein the first weight threshold is greater than the second weight threshold; e) segmenting Voronoi cells with cell weights above the first weight threshold and deleting Voronoi cells with cell weights below the second weight threshold.

[0026] By performing steps c)-e), the adaptive Voronoi distribution can be further adapted to the density field. Furthermore, the convergence of the adaptive Voronoi distribution to the centroid Voronoi distribution can be improved. Steps c)-e) advantageously allow for the creation of smaller Voronoi cells by partitioning and larger Voronoi cells by deleting or merging adjacent Voronoi cells, respectively, thereby adjusting the size of the Voronoi cells according to the density field.

[0027] The partitioning of a Voronoi cell can be achieved by randomly generating two generator points within the Voronoi cell and generating two new Voronoi cells from the two generator points.

[0028] Typically, Voronoi cells with cell weights between the first and second weight thresholds can remain unchanged.

[0029] In some embodiments, a first weight threshold is defined as the ratio of the integral of the density field over the volume surrounded by the envelope to the product of the number of centroids and the factor (1+a), and a second weight threshold is defined as the ratio of the integral of the density field over the volume surrounded by the envelope to the product of the number of centroids and the factor (1-a), wherein a is preferably between 0.3 and 0.7, more preferably a = 0.5.

[0030] Steps c)-e) can be performed until the cell weights of the Voronoi cells are between the first weight threshold and the second weight threshold and it is no longer necessary to split and / or merge the Voronoi cells.

[0031] In some embodiments, steps c)-e) are performed for the first 5-30% of iterations, preferably the first 10% of iterations, of steps a)-b).

[0032] Performing steps c)-e) after step b) provides the advantage that it can improve the convergence of the centroid Voronoi distribution.

[0033] In some embodiments, generating a density field includes: dividing the volume surrounded by the envelope into a plurality of primary voxels, preferably tetrahedral, and generating at least one local requirement value for each primary voxel.

[0034] Preferably, each primary voxel is assigned a local required value for a certain physical parameter. For example, each primary voxel may be assigned a stress value. In other examples, each primary voxel may be assigned both a stress value and a strain value.

[0035] The local requirement values ​​of primary voxels are preferably generated by FEM simulation. The local requirement values ​​of primary voxels generated by FEM simulation can be output to a histogram stored in a computer.

[0036] In some embodiments, the following preprocessing steps are performed by a computer before generating the adaptive Voronoi distribution: dividing the volume enclosed by the envelope into multiple, preferably tetrahedral, primary voxels; generating a cuboid envelope BBB containing the envelope; calculating the volume env_vol enclosed by the envelope as the sum of the volumes of all primary voxels in the envelope, and calculating the volume bbb_vol enclosed by the cuboid envelope as the sum of the volumes of all voxels in the cuboid envelope; calculating the maximum grid size max_grid as 0.5 times the sum of the maximum channel diameter max_channel and the minimum wall width min_wall, where the maximum channel diameter max_channel represents the diameter of the maximum channel of the minimum surface structure. The minimum wall width, min_wall, represents the minimum wall width of the minimum surface structure. The number of points pts_bbb in the cuboid with the maximum grid size is calculated as follows: pts_bbb = (BBB_width / max_grid) × (BBB_depth / max_grid) × (BBB_height / max_grid), where BBB_width, BBB_depth, and BBB_height represent the width, depth, and height of the cuboid envelope BBB. The number of points pts_env in the envelope with the maximum grid size is calculated as follows: pts_env = pts_bbb × (env_vol / bbb_vol).

[0037] In some embodiments, the number of scatter points pts_use is calculated as: pts_use = pts_env × prop_hist, where prop_hist is the ratio of the sum of all values ​​of a physical parameter in the bars of a histogram that records the values ​​of a particular physical parameter to the product of the maximum value of that physical parameter and the number of bars.

[0038] In some embodiments, the primary voxels generated by the preprocessing steps described above are replaced by a plurality of secondary voxels, preferably cuboids. Typically, the number of secondary voxels is preferably one or more orders of magnitude larger than the number of primary voxels. The secondary voxels are preferably generated by interpolating the density field values ​​of the primary voxels.

[0039] In some embodiments, if the Voronoi unit contains fewer than 10 secondary voxels after iterations a)-b) (optionally including steps c)-e), the number of secondary voxels is increased, and the generation and iterations of the adaptive Voronoi distribution are restarted (a)-b) (optionally including steps c)-e).

[0040] In some embodiments, the first skeleton graph is formed by the edges of Voronoi cells with an adaptive Voronoi distribution.

[0041] In some embodiments, the second skeleton graph is generated by Delaunay tetrahedralizing the generated points of the adaptive Voronoi distribution.

[0042] Preferably, the first and second skeleton diagrams are generated after the adaptive Voronoi distribution has converged to the centroid Voronoi distribution according to the density field, as described above.

[0043] In particular, it is possible to realize two interwoven skeleton diagrams in order to generate a minimal surface structure without self-intersection.

[0044] Although the second skeleton graph is generated using Delaunay tetrahedronization, it may include one or more correction segments that do not coincide with the edges of the Delaunay tetrahedronization to adapt to topological conditions. For example, such topological conditions may require segments in the second skeleton graph that connect the generating points of adjacent Voronoi cells to travel only within those adjacent Voronoi cells. In cases where such segments need to travel through a third Voronoi cell, additional points can be inserted at planes adjacent to the adjacent Voronoi cell, allowing the segment to bypass these points and avoid intersecting the third Voronoi cell. Such correction segments may be applied alternatively or additionally to the first skeleton graph.

[0045] In some embodiments, from the segments of the first and / or second skeleton diagrams that pass through the envelope of the three-dimensional object, a first segment portion located outside the body surrounded by the envelope is removed and replaced with a segment portion obtained by mirroring a second segment portion located inside the body and adjacent to the first segment portion about the envelope at the location of the segment passing through the envelope in the first and / or second skeleton diagrams.

[0046] In doing so, the minimum surface structure can be made substantially perpendicularly adjacent to the envelope of the three-dimensional object. This is particularly advantageous for three-dimensional objects with a shell in which the minimum surface structure forms a filling structure, allowing the minimum surface structure to be substantially perpendicularly adjacent to the shell at the location where the load is applied.

[0047] In some embodiments, the ends of the first and / or second skeleton diagrams are modified to avoid the minimal surface structure resulting in overhangs that cannot be 3D printed without build supports. This can be achieved by modifying the ends of the first and / or second skeleton diagrams such that the segments at said ends are tilted toward the center of the 3D article. This is particularly advantageous for 3D articles without shells in which the minimal surface structure is designed to be 3D printed without build supports.

[0048] For a minimal surface structure modified at the boundary of a three-dimensional object as described herein, the zero mean curvature characteristic of a minimal surface may no longer be satisfied. However, a considerable portion of the minimal surface structure may still satisfy the zero mean curvature, and in the context of this invention, such a minimal surface structure should still be considered as being based on a minimal surface.

[0049] In some embodiments, Voronoi cells extending beyond the envelope of a three-dimensional object are trimmed at the envelope, and the centroid of the trimmed Voronoi cells is recalculated using a density field.

[0050] Alternatively, Voronoi units that extend beyond the envelope may be left untrimmed regardless of their extension beyond the envelope.

[0051] The maze or passage can be closed by closures on the outer openings of the passage. In some embodiments, the passage is closed by placing closures on the outer openings and applying smoothing using a conformal mean curvature flow algorithm. By doing so, the smoothness of the passage's internal space can be advantageously maximized. In some embodiments, the passage is closed by placing closures on the outer openings and applying smoothing using a conformal mean curvature flow algorithm while maintaining the center of the closure. By doing so, the internal volume of the passage can be advantageously maximized. In some embodiments, V-shaped or rounded V-shaped closures are used to close the outer openings of the passage. This can be achieved by increasing the wall width at the outer opening of the passage to more than half the local passage diameter. Rounding can be achieved using a conformal mean curvature flow algorithm. In some embodiments, the minimum surface structures engage with the envelope or shell at the locations where the minimum surface structures respectively connect to the envelope or shell, without applying separate closures or modifying the shape of the minimum surface structures, such that the envelope or shell closes the respective passages. Different closure schemes can be used for different outer openings of the passage. Alternatively, for all closure schemes, the original minimal surface structure (without closure) can be additionally retained to the envelope to enable ideal force transmission and ensure the integrability of the minimal surface structure in higher-level components.

[0052] Typically, two mazes can be non-intersecting and do not exhibit interconnection. However, in some embodiments, the walls with minimal surface structure can present one or more perforations, allowing the two mazes to interconnect. One or more perforations can be achieved by creating additional linking mazes between the two mazes.

[0053] In some embodiments, two mazes can be connected to each other through contact spaces at the envelope.

[0054] In some embodiments, a three-dimensional article may include one or more external conduit elements disposed outside the envelope, the one or more external conduit elements being interconnected with one or more peripheral openings of different channels or the same channel.

[0055] In some embodiments, all peripheral openings of each channel, except for the two outermost openings, are closed, allowing the unclosed openings to each form the fluid inlet and outlet of their respective channels. In doing so, two separate media flows (especially countercurrent flows) can be allowed through a minimal surface structure. This can be particularly advantageous for heat exchanger or heat balancer structures.

[0056] In some embodiments, two passages or mazes are connected by one or more peripheral openings that interconnect different passages, wherein two peripheral openings remain open while the remaining peripheral openings are closed. The two peripheral openings that remain open are preferably arranged on opposite sides of the three-dimensional object. The two peripheral openings that remain open can serve as an inlet and an outlet. Such embodiments can be used, for example, in a collision-resistant fuel tank in a helicopter, or in a zero-gravity capability fuel tank in a spacecraft. The inlet can be used to fill the tank with fuel, wherein during operation of the tank, gas can be filled through the inlet to force the fuel to the outlet to exit the tank.

[0057] In some embodiments, the two labyrinths serve as storage compartments within the tank to store two components of the fuel, such as, for example, hydrogen and oxygen, which can be mixed upon exiting the tank. Such embodiments can be used, for example, in rockets. In some embodiments, the minimum surface structure may include additional labyrinths embedded within the walls of the minimum surface structure. For example, a single additional labyrinth may be embedded within the walls of the minimum surface structure, allowing for the formation of a three-chamber system. This can be particularly advantageous for heat exchanger structures with internal coolant circuits to accelerate initial heating and / or cooling. In other examples, two additional labyrinths may be embedded within the walls of the minimum surface structure, allowing for the formation of a four-chamber system. This can be particularly advantageous for heat exchanger structures with two counter-current circulating internal coolant circuits to accelerate initial heating and / or cooling.

[0058] In some embodiments of the three- or four-chamber system described above, the two chambers created by the original labyrinth are larger than one or both chambers embedded within the walls of the minimum surface structure. For cryogenic fuels, the larger chambers may include one or two fuel components, while the smaller chambers may include coolant circuits. Embodiments of such three- or four-chamber systems can be used as fuel tanks for rockets, which can also serve as the rocket's load-bearing structure. This load-bearing structure can be enclosed with an ultralight envelope or skin, which can be used to reduce aerodynamic drag during the rocket's ascent through the atmosphere.

[0059] In some embodiments, generating a digital minimum surface model based on a first skeleton diagram and a second skeleton diagram includes: generating a minimum surface precursor based on the first skeleton diagram and the second skeleton diagram; generating a minimum surface shape by smoothing the minimum surface precursor; assigning a wall width to the minimum surface shape; and generating a digital minimum surface model based on the minimum surface shape and the assigned wall width.

[0060] Preferably, the minimum surface precursor is generated as a surface equidistant from the first and second skeleton maps. In some embodiments, the minimum surface precursor is generated as a surface having a first distance d from the first skeleton map and a second distance s from the second skeleton map. In some embodiments, the first distance d and / or the second distance s varies along the first and / or second skeleton maps.

[0061] The wall width can be a global wall width with a global wall width value assigned to the minimum surface shape. Alternatively, the wall width can be a variable wall width that varies along the minimum surface shape when assigned, and correspondingly along the minimum surface structure generated based on the digital minimum surface model. Therefore, different local wall width values ​​can be assigned to the minimum surface shape at different locations. By generating a digital minimum surface model based on the minimum surface shape and the assigned wall widths, the digital minimum surface model can obtain the geometry defined by the minimum surface shape, and walls with the assigned wall widths, making it possible to 3D print the minimum surface structure based on the digital minimum surface model.

[0062] Local wall width values ​​can be inferred from the wall width density field. Alternatively, local wall width values ​​can be inferred from the density field by combining a set of rules that specify the wall width at different locations of the minimum surface structure or the 3D object, where the set of rules is defined by the requirements of the minimum surface structure or the 3D object.

[0063] For example, the local maximum wall width can be related to the minimum channel diameter of the minimum surface structure and defined as an upper bound on the local wall width in this set of rules to prevent walls from closing the channels in the minimum surface structure. In other examples, rules for local wall widths can be defined by relating the local wall width to the channel diameter to close one or more channels in the minimum surface structure. In other examples, rules for local wall widths can be defined by requiring the amount of printing material to remain constant at each cross-section of the minimum surface structure.

[0064] To generate the walls of a digital minimum surface model, a pair of equipotential surfaces can be generated. In some embodiments, this pair of equipotential surfaces is equidistant from the minimum surface shape in two directions away from the minimum surface shape. In some embodiments, this pair of equipotential surfaces is not equidistant from the minimum surface shape. In some embodiments, one or more distances from the equipotential surfaces to the minimum surface shape vary according to a local wall width assigned to the minimum surface shape, such that the walls generated by the digital minimum surface model exhibit a finite wall width depending on the assigned local wall width. This pair of equipotential surfaces can be joined together at their peripheral ends by generating end faces connecting the two equipotential surfaces.

[0065] After generating the digital minimum surface model, portions of the digital minimum surface model located outside the envelope can be removed by projecting these portions back into the envelope, where overlapping, self-intersecting, and / or zero-area surface portions and / or coincidence points are removed. Small surface portions with areas below a threshold area can be merged.

[0066] In some embodiments, generating a digital minimum surface model based on a first skeleton map and a second skeleton map includes: assigning a first charge to the first skeleton map; assigning a second charge to the second skeleton map, the second charge being equal in absolute value to the first charge but opposite in sign to the first charge; and generating a minimum surface precursor as an equipotential surface between the first skeleton map and the second skeleton map using a Coulomb force field calculated based on the first skeleton map, the second skeleton map, and their charges.

[0067] In doing so, a minimal surface precursor equidistant from the first and second skeleton diagrams can be achieved. Using a Coulomb force field to generate the minimal surface precursor as an equipotential surface between the first and second skeleton diagrams offers the advantage of an efficient and power-saving scheme for generating minimal surface precursors equidistant from the first and second skeleton diagrams and separating the two mazes defined by the skeleton diagrams.

[0068] Minimal surface shapes can be generated through smoothing, for example by using conformal average curvature flow algorithms, such as those described by K. Crane, U. Pinkall, P. This is described in ACM Transactions on Graphics, July 2013, article No. 61, “Robust fairing via conformal curvature flow.” The resulting minimum surface shape can be analyzed for zero mean curvature conditions, and the conformal mean curvature flow algorithm can be reapplied to optimize the minimum surface shape with respect to zero mean curvature conditions. Alternatively, the minimum surface shape can be generated from the minimum surface precursor by, for example, minimizing the square mean curvature of the minimum surface precursor, smoothing it using the Laplacian operator and / or LS3 loop subdivision.

[0069] Preferably, at least one physical parameter is selected from at least one of the following: mechanical load, stress value and / or distribution, maximum permissible stress, strain, local deformation margin, stiffness, flexibility, vibration, attenuation within a specified frequency range, amount of storable fluid, fluid flow rate, thermal transport, thermal transport along the minimum surface structure (inside the wall), thermal transport across the minimum surface structure (from the maze of the first skeleton diagram to the maze of the second skeleton diagram), mass budget, mass distribution, momentum distribution, article geometry (such as, for example, increased material density along the periphery of the article), minimum channel diameter of the minimum surface structure, and / or Maximum channel diameter, minimum and / or maximum wall width of minimum surface structure, forced cross-sectional area of ​​the channel or wall of minimum surface structure at a given cross-sectional location (globally equal or locally specified on the 3D article), 3D printability (such as, for example, increasing density below adjacent overhangs or horizontal shells), location of the centroid of the 3D article, geometry optimization for bone regeneration for implant applications, material absorption, permeability, volume ratio between mazes (which may vary due to asymmetric wall widths or asymmetric arrangement of minimum surface precursors with respect to the skeleton map), minimum and / or maximum voids in the maze.

[0070] According to another aspect, the present invention also relates to a minimal surface structure additively manufactured by the method according to the invention.

[0071] In an embodiment of the minimum surface structure, the minimum surface structure is a quasi-periodic structure.

[0072] In an embodiment of the minimum surface structure, the minimum surface structure is an amorphous structure.

[0073] According to another aspect, the present invention also relates to a non-transitory computer-readable medium having stored thereon computer-executable instructions adapted to cause a 3D printer to additively manufacture a minimum surface structure based on a digital minimum surface model as described herein, the computer-executable instructions comprising causing a processor to perform the following steps: recording an envelope of a three-dimensional object in a computer; generating a density field across the volume surrounded by the envelope, wherein the density in the density field corresponds to a locally required value of at least one physical parameter at a corresponding location of the three-dimensional object; generating an adaptive Voronoi distribution of the volume using the density field; generating a first skeleton map associated with the adaptive Voronoi distribution; generating a second skeleton map associated with the first skeleton map; and generating a digital minimum surface model based on the first and second skeleton maps.

[0074] According to another aspect, the present invention also relates to a computer implementation method for generating a digital minimum surface model, applicable to additively manufacturing a minimum surface structure based on the digital minimum surface model by a 3D printer as described herein. This computer implementation method includes a processor performing the following steps: recording the envelope of a three-dimensional object in a computer; generating a density field across the envelope of the volume, wherein the density in the density field corresponds to a locally required value of at least one physical parameter at a corresponding location of the three-dimensional object; generating an adaptive Voronoi distribution of the volume using the density field; generating a first skeleton map associated with the adaptive Voronoi distribution; generating a second skeleton map associated with the first skeleton map; generating the digital minimum surface model based on the first and second skeleton maps; and storing the digital minimum surface model on a computer-readable medium.

[0075] Computer-readable media can be non-transitory computer-readable media or data signals embodied as carrier waves.

[0076] According to another aspect, the present invention also relates to a computer program product comprising computer program code, configured to control a computer so that the computer performs the steps of the computer implementation method according to the present invention. Attached Figure Description

[0077] The invention will be explained in more detail by way of exemplary embodiments with reference to the schematic diagrams, wherein:

[0078] Figure 1 A perspective view showing the envelope of the object and the envelope of the density field is shown;

[0079] Figure 2 It shows Figure 1 Perspective views of the density field envelope and the cuboid envelope;

[0080] Figure 3 A perspective view showing the density field envelope and the object envelope of a closed volume subdivided by a tetrahedral voxel field;

[0081] Figure 4 The calculated density field with the density field envelope is shown. Figure 3 A perspective view of the density field envelope;

[0082] Figure 5 A perspective view showing a group of randomly distributed scatter points across the envelope of an article;

[0083] Figure 6 The adaptive Voronoi distribution and its use are shown. Figure 5 A perspective view of the first skeleton diagram generated by the scatter points based on the adaptive Voronoi distribution of the volume enclosed by the density field envelope;

[0084] Figure 7 It shows that according to Figure 6 A perspective view of the second skeleton diagram generated by the Delaunay tetrahedralization of the adaptive Voronoi distribution;

[0085] Figure 8 It shows Figure 6 First skeleton diagram and Figure 7 A perspective view of the second skeleton diagram;

[0086] Figure 9 A perspective view of the minimum surface precursor generated from the first and second skeleton diagrams and protruding outside the article envelope is shown.

[0087] Figure 10 It shows from such as Figure 9 A perspective view of the minimum surface shape of an item envelope is obtained and trimmed to the minimum surface shape of the minimum surface precursor, such as the minimum surface precursor.

[0088] Figure 11 It shows things like Figure 10 Minimum surface shape, such as the minimum surface shape, and perspective view of the skeleton diagram;

[0089] Figure 12 It shows from Figure 11 A perspective view of the digital minimum surface model obtained from the minimum surface shape;

[0090] Figure 13 It shows Figure 12 A perspective view of the digital minimum surface and an additional second skeleton diagram shown;

[0091] Figure 14 A perspective view of a satellite chassis having a heat exchanger or thermal equalizer as an embodiment of a three-dimensional article including a minimal surface structure is shown;

[0092] Figure 15 A perspective view of a spinal retainer, which is an embodiment of a three-dimensional article formed by a minimal surface structure, is shown.

[0093] Figure 16 a- Figure 16 Figure c illustrates a series of steps involved in correcting the edges of the Delaunay tetrahedron to adapt to topological conditions;

[0094] Figure 17 A flowchart illustrating an embodiment of a method for additively manufacturing a three-dimensional article with a minimum surface structure is shown;

[0095] Figure 18 A block diagram illustrating an embodiment of the method according to the present invention is shown;

[0096] Figure 19 An example of processing a fragment of a skeleton diagram that passes through the envelope of a 3D object is shown. Detailed Implementation

[0097] Figure 1 A perspective view of an item envelope 11 and a density field envelope 12 surrounding a 3D object to be additively manufactured is shown. The item envelope 11 has a cylindrical shape and represents the boundary of the cylindrical 3D object. The density field envelope 12 is a heptagonal prism, which provides simplification to the item envelope 11 to reduce the processing power of computer-generated digital minimum surface models.

[0098] Figure 2 It shows Figure 1 A perspective view of the density field envelope 12 and the cuboid envelope 13 (BBB) ​​surrounding the density field envelope 12. Using the cuboid envelope 13 and subdividing the volumetric area enclosed by the density field envelope 12 and the cuboid envelope 13 into voxels, the number of points pts_bbb at bbb_vol under the maximum grid size max_grid can be calculated as: pts_bbb = (BBB_width / max_grid) × (BBB_depth / max_grid) × (BBB_height / max_grid), where BBB_width, BBB_depth, and BBB_height represent the width, depth, and height of the cuboid envelope BBB. The maximum grid size max_grid is calculated as 0.5 times the sum of the maximum channel diameter max_channel and the minimum wall width min_wall, where the maximum channel diameter max_channel represents the diameter of the maximum channel of the minimum surface structure, and the minimum wall width min_wall represents the minimum wall width of the minimum surface structure to be 3D printed. Therefore, the number of points pts_env in the density field envelope at the maximum grid size can be calculated as: pts_env = pts_bbb × (env_vol / bbb_vol).

[0099] Figure 3 A perspective view of a density field envelope 12 is shown, which has a closed volume 121 subdivided by a tetrahedral voxel field having tetrahedral primary voxels 122. Additional views are shown... Figure 1 The object envelope 11. A computer performs a FEM (finite element method) simulation to generate local required values ​​for physical parameters such as strain of the three-dimensional object for each primary voxel 122.

[0100] Figure 4 A density field 2, generated based on local required values ​​within volume 121 enclosed by a density field envelope 12, is shown. In this example of strain, the density in density field 2 is proportional to the local strain values ​​in primary voxels 122. Therefore, density field 2 represents a spatial mapping of local strain within the density field envelope 12. Accordingly, the density varies across volume 121. For example, Figure 4 The density of the lower central region (white area / voxel) of medium body 121 is higher than that of the adjacent region. Figure 4 The top of body 121 (black area / voxel) indicates that stress decreases from the bottom to the top of body 121. From Figure 4 It can also be recognized that the density is higher towards the front of volume 121 compared to the voxels on the two adjacent left and right faces (as shown in...). Figure 4 (In the direction shown), as indicated by the brighter voxel on the front of the heptagonal prism of body 121.

[0101] Figure 5 This shows the results after the random distribution of volume 121 enclosed by the article envelope, according to... Figure 4 A perspective view of a set of scatter points 21 redistributed from the density field 2. Density field characteristics are further included in the calculation of the number of scatter points 21 (pts_use), which is pts_use = pts_env × are_prop, where are_prop = area_histo / area_full. area_histo and area_full are obtained through a histogram, which records all stress or density values ​​obtained from the FEM simulation. area_histo is the sum of all stresses or densities in the histogram bars, and area_full is the product of the maximum stress in the histogram and the number of bars in the histogram. pts_env is the number of points in the density field envelope at the maximum mesh size, as described above. Scatter points 21 are used as the initial generation points for Voronoi cells with an adaptive Voronoi distribution.

[0102] Figure 6 A perspective view of the adaptive Voronoi distribution VO and the first skeleton diagram A derived from the adaptive Voronoi distribution VO of volume 121 surrounded by the density field envelope is shown, where the data has been generated from the initial generation point. Figure 5 Starting with scatter point 21, and subsequently using... Figure 3The density field iteratively generates Voronoi cells of an adaptive Voronoi distribution VO by performing the weighted point steps as described above, thereby generating the adaptive Voronoi distribution VO and obtaining the weighted centroid Voronoi distribution VO according to the density field. The skeleton diagram A travels along the edges of the Voronoi cells of the adaptive Voronoi distribution VO. For the skeleton diagram A, iterative steps a) and b) as described above, using the density field to offset the generation points 21 of the Voronoi cells to the centroids of the Voronoi cells, have been performed. Further, iterative steps c)-e) as described above, using the cell weights of the Voronoi cells to segment and / or merge Voronoi cells, have also been performed. Therefore, the skeleton diagram A has been generated according to the density field from the weighted centroid Voronoi distribution VO of the density field with adapted dimensions of Voronoi cells.

[0103] Figure 7 It shows that according to Figure 6 A perspective view of the second skeleton diagram B generated by the Delaunay tetrahedralization of the centroid Voronoi distribution VO. Also shown is... Figure 6 The centroid C of the Voronoi element. The second skeleton diagram B is essentially dual to the first skeleton diagram A. The two skeleton diagrams A and B are interwoven but do not cross each other.

[0104] Figure 8 It shows Figure 6 and Figure 7 A perspective view of the interwoven first and second skeleton diagrams.

[0105] Figure 9 A perspective view of the minimum surface precursor 3 is shown, which is based on... Figures 6-8 The first and second skeleton diagrams shown are generated and protrude beyond the article envelope 11. The minimum surface precursor 3 is a surface equidistant from the first and second skeleton diagrams. As described above, the minimum surface precursor 3 is generated as an equipotential surface using a Coulomb force field, which is calculated using the positive and negative charges assigned to the first and second skeleton diagrams.

[0106] Figure 10 It shows that according to such Figure 9 The minimum surface precursor, such as the minimum surface precursor, is obtained by smoothing the minimum surface shape 4. The minimum surface shape 4 is generated by using a conformal mean curvature flow algorithm, in which the boundaries of the minimum surface precursor are preserved to prevent the minimum surface precursor from shrinking when the conformal mean curvature flow algorithm is executed. Figure 8 The first and second skeleton diagrams, and the corresponding protrusions from the object envelope. Figure 9The minimum surface precursor 3 ensures that the conformal average curvature flow algorithm also has optimized performance at the position of the object envelope when smoothing the minimum surface precursor 3 to obtain the minimum surface shape 4.

[0107] Figure 11 It shows things like Figure 10 A perspective view of the minimum surface shape 3, such as the minimum surface shape. Additionally, a perspective view of the minimum surface shape 3 is shown. Figure 7 The second skeleton diagram B is for illustrative purposes. The first skeleton diagram has been omitted for improved representation.

[0108] Figure 12 It shows from Figure 11 A perspective view of the digital minimum surface model 5 obtained from the minimum surface shape 3. The digital minimum surface model 5 includes a wall 51, which is generated as... Figure 10 The minimum surface shape is generated by a pair of equidistant equilateral surfaces 52.1 and 52.2, which are equidistant from each other. The distance between equilateral surfaces 52.1 and 52.2 is equal to the distance assigned to the minimum surface shape. Figure 10 The wall width of the minimum surface shape 3 is such that wall 51 exhibits the stated wall width. In this example, a constant global wall width is applied. Equilateral surfaces 52.1 and 52.2 are connected by end face 53. It will be apparent to those skilled in the art that the illustration of the additively manufactured minimum surface structure based on the digital minimum surface model 5 will be similar to... Figure 12 The representations of the digital minimum surface model 5 shown are substantially the same. The minimum surface structure 3D printed based on the digital minimum surface model 5 can constitute a three-dimensional article. Alternatively, the three-dimensional article may include a shell disposed at the boundary of the minimum surface structure 3D printed based on the digital minimum surface model 5. The shell may enclose the channel 54. In some embodiments, the channel 54 may be enclosed by one of the methods described above.

[0109] Figure 13 It shows Figure 12 The perspective view of the smallest surface 5, with a second skeleton diagram B additionally shown for illustrative purposes. The first skeleton diagram has been omitted for improved representation.

[0110] Figure 14A perspective view of a satellite chassis 100 with a heat exchanger or thermal equalizer as an embodiment of a three-dimensional article including a minimum surface structure 61 manufactured according to the invention is shown. The minimum surface structure 61 of the satellite chassis 100 serves as a heat exchanger having a first heat transfer medium FA and a second heat transfer medium FB, the first heat transfer medium FA flowing through a black pipe and a first labyrinth associated with a first skeleton diagram of the minimum surface structure 61, and the second heat transfer medium FB flowing through a white pipe and a second labyrinth associated with a second skeleton diagram of the minimum surface structure 61. The media FA and FB flow in opposite directions, thereby providing temperature balance across the satellite chassis 100 (between sunlit and shaded areas), which allows for reduced stress and deformation of the chassis 100 due to temperature differences.

[0111] Figure 15 A perspective view of a spinal retainer 200, formed as an embodiment of a minimal surface structure 62 manufactured additively according to the present invention, is shown. The scale bar is 1 cm. Small peripheral channels 621 of the minimal surface structure 62 are optimized for ideal bone ingrowth. Larger channels 622 are used to improve stability. The wall width of the minimal surface structure is 0.4 mm or less, depending on the capabilities of the 3D printer. For the illustrated example of the spinal retainer 200, bone ingrowth characteristics provide a set of locally required values ​​for the density field. Bone ingrowth is typically supported by inserting one's own, a donor's, or artificial bone marrow into the spinal retainer 200 prior to implantation surgery. In the case of reabsorbable implants made of magnesium or bioceramics (such as bTCP or HA), reabsorption curves related to mechanical load-bearing capacity provide a set of locally required values ​​for the density field. For example, the peripheral region of the minimal surface structure 62 where bone contact occurs needs to exhibit a channel diameter between 0.8 and 1.2 mm to optimize bone ingrowth. Furthermore, for the spinal retainer 200 shown, which may be made of magnesium or bioceramics, the walls in the central region of the minimum surface structure 62 need to exhibit sufficient wall width to ensure adequate load-bearing capacity (in the case of bioceramics) and to ensure that, on the timescale of bone ingrowth, bioresorption removes only a certain amount of material in which the load-bearing capacity of the minimum surface structure 62 is guaranteed.

[0112] Figure 16 (a)- Figure 16 (c) illustrates a series of steps in which the edges of the Delaunay tetrahedral are corrected to adapt to a topological condition that requires the segments of the second skeleton graph associated with the Delaunay tetrahedral, connecting the generation points of adjacent Voronoi cells, to travel only within said adjacent Voronoi cells. For illustrative purposes, Figure 16 (a)- Figure 16(c) is shown as a two-dimensional construction. Those skilled in the art will recognize that the correction scheme shown can be correspondingly transformed into a three-dimensional case. Figure 16 (a) shows an adaptive Voronoi distribution with generating points and points showing the midpoints and corners of the edges of marked Voronoi units, where Voronoi units are defined by dotted lines. Figure 16 (b) illustrates the Delaunay triangulation of the generated points of the Voronoi elements connected by solid lines. Edge E represents the edge of the Delaunay triangulation that does not satisfy the topological conditions and must be corrected according to the dashed curve. Figure 16 (c) shows the corrected Delaunay triangulation, where Figure 16 (b) The edge E has been based on Figure 16 (b) The dashed curve is bypassed and proceeds in parallel, replacing the edge of the midpoint of the edge of the adjacent Voronoi cell, thus satisfying the topological condition. The second skeleton graph obtained from the corrected Delaunay triangulation is essentially dual to the first skeleton graph obtained from the adaptive Voronoi distribution.

[0113] Figure 17 A flowchart illustrating an embodiment of a method for additively manufacturing a minimal surface structure of a three-dimensional article according to the present invention is shown. In step S1, the computer records the envelope of the three-dimensional article in the computer. In step S2, the computer generates a density field across the volume surrounded by the envelope, wherein the density in the density field corresponds to a locally required value of at least one physical parameter at a corresponding location on the three-dimensional article. In step S3, the computer generates an adaptive Voronoi distribution of the volume using the density field. In step S4, the computer generates a first skeleton map associated with the adaptive Voronoi distribution. In step S5, the computer generates a second skeleton map associated with the first skeleton map. In step S6, the computer generates a digital minimal surface model based on the first and second skeleton maps. In step S7, a 3D printer additively manufactures the minimal surface structure based on the digital minimal surface model.

[0114] Figure 18 A block diagram illustrating an embodiment of the method according to the present invention is shown. First, a method having computer-executable instructions stored thereon for performing, such as... Figure 17 The method shown uses a computer 10 on a non-transitory computer-readable medium 101 (such as memory) to generate a digital minimum surface model 5. The digital minimum surface model 5 is stored as a CAD file on a non-transitory computer-readable medium 20 (such as memory). Using this CAD file, a 3D printer 30 prints a minimum surface structure 63 based on the digital minimum surface model 5.

[0115] Figure 19An example of processing a segment of a skeleton diagram that passes through the envelope of a 3D object is shown, wherein a first segment portion located outside the body surrounded by the envelope, from the segments of the first and / or second skeleton diagrams that pass through the envelope of the 3D object, is removed and replaced with a segment portion obtained by mirroring a second segment portion located inside the body and adjacent to the first segment portion about the envelope at the segment location of the first and / or second skeleton diagrams that passes through the envelope. As in Figure 19 As can be seen, the open-end segment A”'(x) (i.e., the segment that does not connect to any other segment and terminates in the gap) has been removed. Further, from the outermost segment(s) (i.e., the segment that will pass through the outer skin 25 of the article), the portion A”'(o) outside the outer skin is removed and replaced with a mirror image A”'(m) of the segment portion A”'(i) inside the article, thus the mirror image being the reflection of the portion located inside the article with respect to the outer skin 25 where the segment passes. This determines that the resulting minimal surface structure contacts the envelope 25 in a substantially perpendicular direction, thereby providing an ideal load-bearing conduit.

Claims

1. A method for additively manufacturing a minimum surface structure (61, 62, 63) of a three-dimensional article (100, 200), the method comprising a computer (10) performing the following steps: Record the envelopes (11, 12) of the three-dimensional objects (100, 200) in the computer (10); Generate a density field (2) across the volume (121) surrounded by the envelope (12), wherein the density in the density field (2) corresponds to a local required value of at least one physical parameter at the corresponding location of the three-dimensional object (100, 200); Adaptive Voronoi distribution generated by density field (2) for volume (121); Generate the first skeleton graph (A) associated with the adaptive Voronoi distribution; Generate a second skeleton diagram (B) associated with the first skeleton diagram (A); A digital minimum surface model (5) is generated based on the first skeleton diagram (A) and the second skeleton diagram (B); in, The method also includes a 3D printer (30) additively manufacturing a minimum surface structure (61, 62, 63) based on a digital minimum surface model (5). The generation of the adaptive Voronoi distribution includes: Generate a set of scatter points (21) corresponding to the density distribution in the density field (2). Scattered points (21) are randomly distributed across the volume (121) enclosed by the envelope (12). Using randomly distributed scatter points (21) as the generation points of Voronoi units, multiple Voronoi units with an adaptive Voronoi distribution are generated.

2. The method according to claim 1, characterized in that, Using density field (2) to generate an adaptive Voronoi distribution involves using density field (2) to iteratively generate multiple Voronoi units of the adaptive Voronoi distribution by weighted point truncation.

3. The method according to claim 2, characterized in that, Iteratively generating the plurality of Voronoi elements involves iteratively performing the following steps a) and b) until the calculated centroid (C) matches the generation point of the Voronoi element in step a): a) Calculate the weighted centroid (C) of each Voronoi cell using the density field (2) and offset the generation point of the Voronoi cell to the corresponding centroid (C); b) Generate new Voronoi cells with an adaptive Voronoi distribution using the offset generation points, and replace the Voronoi cells in step a) with the new Voronoi cells.

4. The method according to claim 3, characterized in that, Iteratively generating the plurality of Voronoi units includes performing the following steps after step b) of claim 3: c) Calculate the element weights for each Voronoi element by integrating the density field (2) over the corresponding Voronoi element; d) Record the first weight threshold and the second weight threshold in the computer, wherein the first weight threshold is greater than the second weight threshold; e) Segment Voronoi cells with cell weights above a first weight threshold, and delete Voronoi cells with cell weights below a second weight threshold.

5. The method according to claim 4, characterized in that, For the first 10-30% of the iterations of steps a)-b) of claim 3, perform steps c)-e).

6. The method according to claim 5, characterized in that, For the first 20% of iterations of steps a)-b) of claim 3, perform steps c)-e).

7. The method according to claim 1, characterized in that, The generation density field (2) includes: The volume (121) surrounded by the envelope (12) is divided into multiple voxels (122), and at least one local requirement value is generated for each voxel (122).

8. The method according to claim 7, characterized in that, The voxel (122) is a tetrahedron.

9. The method according to claim 1, characterized in that, The first skeleton graph (A) is formed by the edges of Voronoi units with an adaptive Voronoi distribution.

10. The method according to claim 1, characterized in that, The second skeleton graph (B) is generated by Delaunay tetrahedronizing the generating points of the adaptive Voronoi distribution.

11. The method according to claim 1, characterized in that, From the segment in the first skeleton diagram (A) that passes through the envelope of the three-dimensional object, the first segment portion located outside the body (121) surrounded by the envelope (12) is removed and replaced with a segment portion obtained by mirroring a second segment portion located inside the body and adjacent to the first segment portion about the envelope (12) at the location in the first skeleton diagram where the segment passes through the envelope (12), and / or From the segment of the second skeleton diagram (B) that passes through the envelope of the three-dimensional object, the third segment portion located outside the body (121) surrounded by the envelope (12) is removed and replaced with a segment portion obtained by mirroring the fourth segment portion located inside the body and adjacent to the third segment portion about the envelope (12) at the location where the segment of the second skeleton diagram passes through the envelope (12).

12. The method according to claim 1, characterized in that, The Voronoi elements extending beyond the envelope (12) of the three-dimensional objects (100, 200) are trimmed at the envelope, and the centroid of the trimmed Voronoi elements is recalculated using the density field.

13. The method according to claim 1, characterized in that, The generation of the digital minimum surface model (5) based on the first skeleton diagram (A) and the second skeleton diagram (B) includes: Generate the minimum surface precursor based on the first and second skeleton diagrams (3); Minimum surface shape (4) is generated by smoothing the minimum surface precursor (3); Assign the wall width to the smallest surface shape (4); A digital minimum surface model (5) is generated based on the minimum surface shape (4) and the assigned wall width.

14. The method according to claim 13, characterized in that, The generation of the digital minimum surface model (5) based on the first skeleton diagram (A) and the second skeleton diagram (B) includes: The first charge is assigned to the first skeleton diagram (A); The second charge is assigned to the second skeleton diagram (B), which is equal in absolute value to the first charge but opposite in sign; Using the Coulomb force field calculated based on the first skeleton diagram (A) and the second skeleton diagram (B) and the charges of the first skeleton diagram (A) and the second skeleton diagram (B), a minimal surface precursor (3) is generated as an equipotential surface between the first skeleton diagram (A) and the second skeleton diagram (B).

15. The method according to claim 1, characterized in that, The at least one physical parameter is selected from at least one of the following: mechanical load, stiffness, amount of storable fluid, fluid flow rate, and heat transport capacity.

16. A minimum surface structure (61, 62, 63) said minimum surface structure (61, 62, 63) is additively manufactured by the method according to any one of claims 1-15.

17. The minimum surface structure (61, 62, 63) according to claim 16, characterized in that, The minimum surface structures (61, 62, 63) are quasi-periodic structures.

18. The minimum surface structure (61, 62, 63) according to claim 16, characterized in that, The minimum surface structures (61, 62, 63) are amorphous structures.

19. A non-transitory computer-readable medium (101) storing computer-executable instructions adapted to cause a 3D printer (30) to additively manufacture a minimum surface structure (61, 62, 63) of a three-dimensional article (100, 200) based on a digital minimum surface model (5), the computer-executable instructions comprising a computer (10) performing the following steps: Record the envelopes (11, 12) of the three-dimensional objects (100, 200) in the computer (10); Generate a density field (2) across the volume (121) surrounded by the envelope (12), wherein the density in the density field (2) corresponds to a local required value of at least one physical parameter at the corresponding location of the three-dimensional object (100, 200); Adaptive Voronoi distribution generated by density field (2) for volume (121); Generate the first skeleton graph (A) associated with the adaptive Voronoi distribution; Generate a second skeleton diagram (B) associated with the first skeleton diagram (A); A digital minimum surface model (5) is generated based on the first skeleton diagram (A) and the second skeleton diagram (B). in, Generating an adaptive Voronoi distribution includes: Generate a set of scatter points (21) corresponding to the density distribution in the density field (2). Scattered points (21) are randomly distributed across the volume (121) enclosed by the envelope (12). Using randomly distributed scatter points (21) as the generation points of Voronoi units, multiple Voronoi units with an adaptive Voronoi distribution are generated.

20. A computer implementation method for generating a digital minimum surface model (5), suitable for additively manufacturing three-dimensional articles (100, 200) by a 3D printer (30) based on the digital minimum surface model (5) with minimum surface structures (61, 62, 63), the computer implementation method comprising a computer (10) performing the following steps: Record the envelopes (11, 12) of the three-dimensional objects (100, 200) in the computer (10); Generate a density field (2) across the volume (121) surrounded by the envelope (12), wherein the density in the density field (2) corresponds to a local required value of at least one physical parameter at the corresponding location of the three-dimensional object (100, 200); Adaptive Voronoi distribution generated by density field (2) for volume (121); Generate the first skeleton graph (A) associated with the adaptive Voronoi distribution; Generate a second skeleton diagram (B) associated with the first skeleton diagram (A); A digital minimum surface model (5) is generated based on the first skeleton diagram (A) and the second skeleton diagram (B); The digital minimum surface model (5) is stored on a computer-readable medium (20). in, Generating an adaptive Voronoi distribution includes: Generate a set of scatter points (21) corresponding to the density distribution in the density field (2). Scattered points (21) are randomly distributed across the volume (121) enclosed by the envelope (12). Using randomly distributed scatter points (21) as the generation points of Voronoi units, multiple Voronoi units with an adaptive Voronoi distribution are generated.

21. A computer program product comprising computer program code configured to control a computer (10) to cause the computer (10) to perform the steps of the method according to claim 20.

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