Method for lightweighting and / or design of an article for additive manufacturing

Abstract

The invention relates to a method for lightweighting and / or design of an additively manufactured article. The invention also relates to a computer program product suitable for carrying out the method of the invention and to an additively manufactured article obtainable by all methods according to the invention following the lead of the independent claim. The method comprises the step(s) of filling and / or building with quasicrystalline structures each of one or more constituent article parts. The additively manufactured article obtainable by carrying out the method comprises quasicrystalline structures and / or quasiperiodic minimal surface fillers and / or quasiperiodic minimal surface design structures and / or non-periodic minimal surface design structures and / or non-periodic minimal surface fillers. The invention also relates to the use of skeleton graphs for pre-processing in an additive manufacturing process.

Description

TECHNICAL FIELD

[0001] The present invention relates to a method for lightweighting and / or design of an additively manufactured article. The present invention also relates to a computer program product suitable for carrying out the method of the present invention and to an additively manufactured article obtainable by all methods according to the present invention following the lead of the independent claim. BACKGROUND

[0002] The way in which space-filling, periodic lattices can be organized is limited to 213 general symmetry constructions called space groups, which describe the overall combinatorial solution to the problem of repeating points in space using a series of replication operations like translations, rotations and reflections. However, there is an exception to this rule: infinite, non-periodic structures called quasicrystals. Like a lattice represented by one of the periodic space groups, a quasicystal is formed from one or more, but not an infinite number of types of basic unit cells. Because the repetition of these unit cells preserves a similar (or even identical) arrangement at small scales that never repeats at large scales, quasicrystals exhibit a characteristic called <quasi-periodicity> (rather than non-periodicity). Quasicrystals can fill (《tile》) space without repeating. Two-dimensional quasicrystals tile (like the well-known Penrose tiling) consist of two or more types of rhombi, while three-dimensional quasicrystals are formed from two or more rhombohedral unit cells.

[0003] Two methods are commonly used to create quasicrystals: the projection method, in which a pattern in six or more dimensions is projected into three-dimensional space; and De Bruijn's grid method, in which three or more vectors in space create a series of families of planes, which in turn give rise to the specifications of the quasicrystal.

[0004] Minimal surfaces are curved, two-dimensional, space-occupying mathematical constructs that satisfy the requirement that the average of two perpendicular measures of curvature at every point sums to zero. Thus, each point is defined such that if the surface is bent in a certain direction by a certain amount, the curvature measured perpendicular to that direction is the negative of the first curvature. Since minimal surfaces are the least curved surfaces connecting a particular set of points, they constitute the ideal geometry that allows the most efficient force conduit other than spheres and catenoids (which are themselves minimal surfaces). This makes minimal surfaces ideal for distributing forces and loads inside the structure of, for example, a 3D-printed part (and indeed, every load-bearing structure). Minimal surfaces are called <triple-periodic minimal surfaces> (TPMS), whose basic unit cells are constructed in such a way that these basic unit cells can be repeated in all directions (thus tiling infinite space).

[0005] Additive Manufacturing (AM), 3D printing, rapid prototyping, is an encompassing term that covers a wide range of computer-controlled production processes that allow the physical shaping of objects made of a variety of materials. For the scope of the present invention, Additive Manufacturing is to be understood as also including the robotic assembly of parts.

[0006] Before a 3D printable object can be printed, it has to be defined in the form of a virtual computer model (CAD model, 3D model), in which its geometry is represented as a mathematical function (CAD surface), describing the space enclosed by the 3D model by the coordinates of its vertices, edges, faces and their mutual relationships, or as a matrix of 3D voxels (<voxel> is a portmanteau of <volume> and <pixel>). In most standardized 3D model exchange formats, the object geometry is represented as a polygonal mesh consisting of triangular and / or quadrilateral faces (coordinates and mutual relationships of vertices, edges and faces forming a volume). While the polygonal mesh representation is highly flexible and can be used to (roughly) describe almost any shape without the need for a mathematical analysis of its geometry (as required when using a CAD surface representation), it is well known that it is error-prone and tends to produce large data volumes, and thus high network traffic and high computational load.

[0007] In most types of AM processes, the object is formed by the successive, layered application, or adhesion, or hardening or polymerization of one or more substances. The adhesion, hardening or polymerization process can be initiated either just after the application, or after the completion of each layer, or at the end of the build process, or in a completely separate process outside the actual printer machine. The 3D printing preparation of a 3D model thus involves the conversion ("preprocessing") of the spatial information contained in the 3D model into a <material / no material> information package for each layer (slice). In most cases, the slice is a simple bitmap image related to the desired print layer height, in which black represents <material> and white represents no <material>. On the one hand, each pixel in the slice corresponds to a minimum printing unit in a layer (depending on the characteristics of the printer machine; e.g. the minimum diameter of the laser spot, the laser path, etc.), and on the other hand, it represents a voxel in the printed object. In some cases, the slice contains additional control information related to the printer or object-specific parameters, such as laser energy or laser movement speed, which can be different for each layer or vary within a layer.

[0008] Other actions in the preprocessing include global parameter adjustments based on the characteristics of the printer machine and / or the printing process, and / or its simulation, as well as optimizations such as weight reduction (lightweighting).

[0009] AM allows the formation of highly complex objects that would be very difficult, if not impossible, to construct with classical production methods. Depending on the geometry of the object, the materials used and the printing method, external build support structures (build supports) are required to determine the correct and error-free production of the object. Some methods and / or materials do not require build supports, as they are stabilized by the medium itself when being formed. However, most methods for forming objects from metals such as steel, aluminum, titanium, etc. require build supports, not only for determining the error-free formation and correct geometry of the printout, but also to dissipate excess heat. Removing the build supports during post-processing is often laborious and, in the case of build supports that are difficult to access internally or due to the shape of the object, almost impossible or not possible at all without damaging the object.

[0010] Therefore, the better an object can be self-supporting (the less build support is required for the successful construction process), the better. In order to maximize strength while minimizing weight, and because complex, <bionically> or amorphous geometries can be produced in AM without increasing costs or effort, the shape of the object is often parameterized to tend towards a minimized material usage and optimized shape that meets the structural and geometric requirements of the object. Such optimized shapes often have holes, branches, protrusions and ribs compared to the initial design of the object, which in some cases is <classically> monolithic; the process that leads to such shapes is therefore called <topological optimization> because the topology of the object, the number of holes it has (its "genus"), is changed.

[0011] This optimization is often part of a CAE (Computer Aided Engineering) process, in which computer methods known as FEM (Finite Element Modeling) are often used to simulate geometric constraints, forces, stresses and movements. Some objects are designed and manufactured without or with the aid of FEM simulations, these are usually objects that do not need to be optimally optimized. On the other hand, FEM or similar methods are always used to plan objects in which the strength-to-weight ratio is crucial (such as in aerospace or industrial applications). Because forces tend to be transmitted along the surface of an object rather than through its interior, in principle an object can be reduced to a thin skin. Naturally, a certain material cross-section needs to be retained to conduct forces, determine geometric integrity and take into account material properties and stresses acting on the object.

[0012] In some cases, if the geometrical integrity of the article under stress and during the build process cannot be determined, adding internal structures to the sides of the connecting skin greatly improves the overall stability. However, while this hollowing out of both <classical> shaped articles or topologically optimized articles leads to reduced production time and costs, significant weight improvements, and sometimes even improved stability, most articles are still produced in solid form. This is partly due to the complexity of handling large polygonal meshes, which are notoriously error-prone, and because of the need to determine the shape and geometrical integrity of the article, which can easily deform during the build process, in use and / or under load if no coherent, well-designed and carefully planned internal structure is present.

[0013] A commonly used hollowing technique is the application of a <filler>, which is a simple geometric mesh structure (<space mesh>) for filling the <interior> of the article. However, this technique has three main disadvantages: (1) the efficiency and effective structure impact of the filler has to be guessed if no FEM is used for the study, (2) the geometry of the filler itself needs to be very simple as it needs to be similar to the build support structure (which of course can always be built without additional build support), and (3) the filler structure greatly increases the number of polygons of the 3D model (and thus also the computational load and response time) as it is very small in scale compared to the 3D model itself, but still needs to be precisely defined. Because complex and / or delicate fillers can increase the number of polygons of the 3D model by one or several orders of magnitude, fillers are usually similar to build support structures: crude, shabby and thin, optimized for printability rather than for structural efficiency.

[0014] Therefore, there is a need for a method and an apparatus for providing a pre-processed additively manufactured article that overcomes at least one of the known limitations. SUMMARY

[0015] It is therefore an object of the present invention to provide a method, a computer program product and an additively manufactured article that overcomes at least one of the drawbacks of the current art. It is a particular object of the present invention to provide such a method, computer program product or article that is at least able to lightweight and / or design an article with superior properties with respect to its geometrical integrity and / or load bearing structure compared to the same article designed and / or lightweighted conventionally.

[0016] The present invention therefore relates to the manufacturing of an additively manufactured article and the pre-processing thereof, whereby the article can comprise one or more constituent article parts, each having an internal structure (a <filler>) providing stability improvements, weight reductions and production aids and / or build supports.

[0017] The object of the present invention is solved by the method, the computer program product and the additively manufactured article according to the features of the independent claims.

[0018] One aspect of the present invention is a method for lightweighting and / or designing of an additively manufactured article. The article comprises one or more constituent article components each having a structure. The method comprises at least the step of filling and / or building each of the one or more constituent article components with a quasicrystalline structure.

[0019] In a specific embodiment of the present invention, each of the one or more constituent article components or some of the constituent article components comprise an internal structure and the lightweighting involves a design of the internal structure such that stability, weight and production aids, respectively build supports during the additive manufacturing process are influenced by the method steps described herein.

[0020] In one specific embodiment, the article and / or one constituent component of the article essentially comprises the structure.

[0021] In the context of the present invention, the filling according to the above steps can be understood as the step of lightweighting according to the present invention, while the above building step can be considered as the step of designing the additively manufactured article according to the present invention. In the context of the present invention, filling can be understood as providing an internal structure which is at least partially, preferably essentially, hidden by the outer skin of the article in the finished product according to the present invention. By contrast, designing is the related method when the structure is “open” (i.e. the article is not covered by an outer skin). It is clear to the person skilled in the art that a combination of both method steps can be applied to a specific article, e.g. having multiple constituent article components and a finished product resulting from the method according to the present invention, which can consist of components with a skin covering the filler and components for article components with structures accessible from the outside.

[0022] In the context of the present invention, the quasicrystalline structure can be understood as an ordered but non-periodic structure as generally understood by the person skilled in the art.

[0023] In a specific embodiment of the present invention, the quasicrystalline structure is a three-dimensional quasicrystal made of two or more types of rhombohedral unit cells.

[0024] In an alternative embodiment, the quasicrystalline structure is a three-dimensional crystal, i.e. a regular repeating unit according to one of the 219 non-chiral space groups or 11 chiral space groups.

[0025] In the context of the present invention, such a rhombohedral unit cell can be understood as a three-dimensional body having six sides with parallelogram geometry.

[0026] In specific embodiments of the present application, the quasicrystal structure can be created by a projection method, for which a six-dimensional or higher-dimensional pattern is projected into three-dimensional space. Alternatively or additionally, the quasicrystal structure can be created by applying a tiling method, in which four or more vectors in space create a family of planes, which in turn give rise to the specification of the quasicrystal. The various methods for generating quasicrystal structures can be applied to the production of one item, for example for different item components, or even subsequently as a verification step.

[0027] In especially preferred embodiments, the tiling method is based on the diagonalization method according to de Bruijn (N. de Bruijn, Ned. Akad. Weten. Proc. Ser. A 43, 39 (1981); 43, 53 (1981)).

[0028] In specific embodiments of the present application, the filling and / or building of each of the one or more constituent item components is a filling and / or building with a quasiperiodic minimal surface filler and / or a quasiperiodic minimal surface design structure and / or a non-periodic minimal surface design structure and / or a non-periodic minimal surface filler.

[0029] In especially preferred embodiments, the resulting filler and / or design comprises a periodic surface, such as for example a three-dimensional crystal surface.

[0030] In the context of the present application, substantially zero can be understood as a curvature that is sufficient to practically show the properties of a minimal surface on the scale and form of the item design and / or its filler, even more specifically a deviation of the average of the two perpendicular measured curvatures from zero up to + / - 0.0005 on the surface.

[0031] In especially preferred embodiments, the resulting filler and / or design comprises a periodic surface, such as for example a three-dimensional crystal surface.

[0032] One of the advantages of the minimal surfaces according to the present application can be that they are ideal for distributing loads and forces within a structure or over the entire structure. Furthermore, these minimal surfaces can be ideally used to create objects with a large surface and / or a surface-to-volume ratio that is advantageous for them, such as item components with applications in the fields of architecture, catalysis, heat exchange, batteries, etc., or objects for which any other range of the surface-to-volume ratio is important. Without being bound by theory, the achieved structural advantages can be attributed to the fact that a minimal surface is the smallest curved surface that connects a specific set of points and thus allows for the formation of very efficient force conduits between these points.

[0033] In a particularly preferred embodiment, the method of the present application is performed with filling and / or building having quasi-periodic minimal surface fillings and / or quasi-periodic minimal surface design structures and / or aperiodic minimal surface design structures and / or aperiodic minimal surface fillings such that an efficient force conduit through the article is achieved.

[0034] In a particular embodiment of the present application, the method comprises the further step of using a quasicrystal structure as a framework to generate quasi-periodic minimal surface fillings and / or quasi-periodic minimal surface design structures. In the context of the present application, a framework can be a generated skeleton, for example to define the genus of the quasi-periodic minimal surface to be achieved. In an alternative or additional embodiment of the present application, the method comprises the further step of using a quasicrystal structure as a framework to generate aperiodic minimal surface fillings and / or aperiodic minimal surface design structures.

[0035] In a particular embodiment of the present application, the method further comprises the step of creating a geometry of a quasicrystal. This creation of a geometry of a quasicrystal can be performed, inter alia, by a first step of inputting at least three main vectors. In a further particular embodiment, the step is inputting 3 to 12 vectors. In the context of the present application, inputting can be understood as selecting and / or generating the respective specific parameters in a computer program product. Such inputting can be performed, for example, with a digital pre-processing and / or a configuration of the pre-processing associated with the additive manufacturing software and device.

[0036] In this particular embodiment, creating a geometry of a quasicrystal can inter alia comprise the further step of creating a plurality of parallel plane sets for each of the inputted main vectors. Each parallel plane set comprises at least three planes.

[0037] In this specific embodiment, the number of sets of parallel planes is only limited by the processing power and memory of the computer system used. Although it has been found that the number of sets of parallel planes is especially preferred in the range between 3 and 1000, and even more preferred in the range between 3 and 50. The user can select the number of sets of parallel planes and the number of planes in each set and define the "resolution" of the quasi-crystal. In the context of the present invention, the resolution can be understood as the number of unit cells in a certain predetermined volume of the item. Without being bound by theory, the number of planes selected by the user is left to the discretion of the user, but can be influenced by or required to be within certain thresholds of certain goals or applications. For example, a certain number of planes can be set as required for achieving a desired stability, or because of requirements set by size limitations of the item. As mentioned, there is theoretically no upper limit to the number of planes selected, although in practice it can be limited by the computational power of the computer used for the method. Although it is conceivable that a computer powerful enough can handle up to 100’000 planes.

[0038] In specific embodiments, the number of sets of parallel planes corresponds to the number of input vectors. In especially preferred embodiments, the direction of the planes is defined by the vectors. Even more preferably, the direction of the planes is perpendicular to the selected vectors. In other words, each vector can be associated with a set of parallel planes that are at a 90° angle with respect to the vector.

[0039] In specific embodiments of the present invention, the planes in one specific set of parallel planes are evenly spaced. In this context, evenly spaced shall mean the distance of the planes in one specific set, i.e. the group of at least three planes, with respect to each other. In especially preferred embodiments, all planes of this one specific set are evenly spaced. This can be understood as all planes in this specific set having the same distance with respect to the preceding and the subsequent adjacent plane in the direction of the normal to the plane.

[0040] In specific embodiments of the present invention, the planes in one specific set of parallel planes are randomly spaced. More specifically, all planes in this one specific set are randomly spaced. The random spacing can be defined at the point in time of the generation of the vectors. By inputting the vectors, a plurality of planes can be created that are arranged randomly perpendicular to the vectors, e.g. each plane having a random distance with respect to the other planes in the same set.

[0041] In specific embodiments of the present invention, the planes in one specific set of parallel planes are spaced according to a predetermined pattern. Especially preferably, all planes in this one specific set are then arranged in this predetermined pattern. In specific embodiments, the spacing can be determined by the results of a specific FEM, i.e. a finite element method applied to design and / or fill the item with respect to a desired property.

[0042] In specific embodiments of the present invention, at least some of the planes in a particular set of parallel planes are evenly spaced and / or some of the planes are randomly spaced and / or some of the planes are spaced according to a predetermined pattern. As mentioned before, the number of planes can be chosen as a measure for the resolution of the resulting geometry of the quasicrystal. In further specific embodiments, a set of planes can be created with certain predetermined rules. In the context of this example, the predetermined rules can for instance define that if ten planes are created in a particular set, for instance an input vector must have ten parallel planes perpendicular to said vector, in other words an angle of 90° is enclosed between the planes and the vector; out of these ten planes, three planes are defined to be randomly spaced along the extension of the vector, four planes are arranged with equidistant arrangement relative to each other, i.e. following a certain regular distance is the consecutive plane out of the four planes after each plane, and the remaining three planes in this set are arranged according to a pattern which for instance can be 1 :3, which means that the second plane follows the first plane with a first distance, and the third plane follows the second plane with a second distance, the second distance being three times as long as the first distance. It will be clear to the person skilled in the art that these variables can be subject to rules which are interdependent, wherein for instance a certain predetermined pattern is combined with equidistantly arranged planes, such that all three requirements, i.e. random, predetermined and equidistant, can be combined in the creation of the geometry of a particular quasicrystal according to the present invention.

[0043] In specific embodiments of the present invention, the method further comprises the step of bisecting the rhombohedral unit cell, such that the faces resulting from the bisecting have a hexagonal form. In the context of the present invention, the bisecting thus results in an intersection which is in the shape of a hexagon.

[0044] In specific embodiments, bisecting the rhombohedral unit cell results in two equal monotriatruncated tetrahedra outside the unit cell.

[0045] A truncated tetrahedron is a regular tetrahedron in which the four corners are cut off. For the context of the present invention, a monotriatruncated tetrahedron is a new term defined for the purpose of illustrating the present invention, and can be understood as a tetrahedron in which only three of the four corners are cut off. In comparison to a truncated tetrahedron, a monotriatruncated tetrahedron has seven faces instead of eight (in Greek, mono is 1 and tria is 3)

[0046] In specific embodiments of the present invention, the center of gravity of the rhombohedral unit cell is within the intersection plane resulting from the bisecting of the rhombohedral unit cell. This plane is in the form of a hexagon, as mentioned above.

[0047] In specific embodiments of the invention, the halving is performed through the six edges of the rhombic unit cell in question, preferably in the middle of the six segment lines in question.

[0048] In specific embodiments of the invention, the method comprises the further step of assigning each single triakisdodecahedron to one of two groups, such that two labyrinths are formed from the two groups of single triakisdodecahedrons. In specific embodiments, each of the single triakisdodecahedrons resulting from the halving of the rhombic unit cell is assigned to either one of the two groups, i.e. to a first group of single triakisdodecahedrons, or to a second group of single triakisdodecahedrons. The first group forms a first labyrinth and the second group forms a second labyrinth. Preferably, the first labyrinth and the second labyrinth extend through the entire internal structure of the article and / or of the constituent article parts.

[0049] In specific embodiments, the method of the invention comprises the further step of inserting a skeleton graph into each type of rhombic unit cell, in particular one skeleton graph into each single triakisdodecahedron, such that two interlaced skeleton graphs are created that span the entire quasicrystal without being interconnected at any point. The skeleton graphs each extend through one of the two labyrinths formed by assigning each single triakisdodecahedron to one of the two groups, as described above. The skeleton graphs can be arranged inside the single triakisdodecahedrons in such a way that they extend through the faces of the tetrahedrons into adjacent tetrahedrons of the same group, such that all skeleton graphs within a particular group of single triakisdodecahedrons are connected to each other. In other words, a first skeleton graph extends through the first group of single triakisdodecahedrons, and a second skeleton graph extends through the second group of single triakisdodecahedrons.

[0050] In specific embodiments of the invention, the step of selecting the number of planes is performed separately for articles having more than one constituent article part, each having a structure. One of the benefits of doing so is to make it possible to create areas of increased "resolution".

[0051] In specific embodiments involving constituent article parts having an internal structure, the skeleton graphs can be scaled up and / or down to create locally denser skeleton graphs and / or locally less dense skeleton graphs. The scaling up and / or down can be performed dependent on a set of parameters, such as parameters selected from the group comprising: the three-dimensional geometry of the article, the printer parameter(s), finite element simulation, etc.

[0052] In the context of the invention, the skeleton graphs may, for example, be formed by a plurality of trees, each tree representing a small-scale graph that fills one single triakisdodecahedron and comprises a plurality of segments. In particular, each tree has a mirror twin tree that is rotated by 60 degrees along the diagonal axis of the rhombic unit cell of the respective single triakisdodecahedron.

[0053] In a specific embodiment, scaling up and / or down can result in empty areas in the constituent article part with internal structures. Accordingly, the method can further comprise the step of filling the empty areas in the constituent article part with internal structures resulting from the scaling up and / or down of the skeleton graph. This can be achieved, for example, by extending the open ends of the skeleton graph with more trees.

[0054] By being able to dynamically and locally adapt the geometry, density and scale of the skeleton graph, it becomes possible to create customizable and adaptive infill and / or designs. If printing parameters are also taken into account, it can further become possible to make articles printable without the need for previously required printing support structures for handling, and / or to print high-strength articles. A further characteristic of these objects is to have the maximum interface surface within a given space, and to achieve this with the least amount of material. Possible applications can be as building blocks or as structures for heat exchangers, air conditioners, batteries, dialysis machines, other medical devices, filters, implants, nanoscale materials metamaterials, microscale materials and metamaterials, etc. Since the labyrinths create two interleaved but separate continuous internal volumes, they can be used as anti-collision tanks for powder, granular, liquid and / or gaseous substances, which has a particular advantage in applications where the two components are stored separately (i.e. before being mixed together at the time of use). Further advantageously, the resulting articles are useful as containers for systems in which two components are stored separately and subsequently used together, such as fuel, glue or construction materials. This is just an exemplary number of possible applications of the resulting articles.

[0055] In a specific embodiment of the invention, which can be an alternative or a complement to the scaling of the skeleton graph described above, a voxel-based 3D pre-processing is performed, in which the internal structure is optimized based on stress and automatically generated. In this embodiment, a pair of skeleton graphs can be generated as described before at an un-scaled density, preferably the un-scaled density corresponds to the highest density required for a specific job depending on stress / strain and article shape. In a further specific embodiment, the voxel-based 3D pre-processing comprises a FEM simulation. In a still further specific embodiment, the article shape is fitted into the skeleton graph at a uniform density. Based on stress / strain analysis and / or build parameters and / or article shape, the skeleton graph is thinned by removing individual segments and / or trunks from the skeleton graph, thereby creating locally denser and less dense regions.

[0056] In the context of the present invention, a skeleton graph of unscaled density can be provided by the method of the present invention as described above: starting from a rhombic unit cell, halving the unit cell into single tri-aktrahedra and creating a skeleton graph to extend through both sets of single tri-aktrahedra, all as explained above and encompassing the different variations and alternatives as described above. Alternatively, the skeleton graph provided by the method of the present embodiment can be provided from a pre-existing skeleton graph, e.g. from a triply periodic minimal surface known in the art.

[0057] Another advantage of the present invention can be to provide a fill system that can be automated by performing the method according to the present invention. All this taking into account the FEM simulation, the desired resistance, the geometry, the dimensions, the weight, the material and the equipment parameters freely decided upon according to the respective print job.

[0058] In a specific embodiment of the present invention, the skeleton graph is used to construct a surface equidistant to both graphs and globally separates the two labyrinths defined by the skeleton graph.

[0059] In a further specific embodiment, a voxel-based Voronoi analysis is used to create a first approximation of a surface equidistant to both graphs.

[0060] In a still further embodiment, a minimal surface can be created as detailed above by minimizing the squared mean curvature of the surface. Alternatively and / or additionally, the smoothing of the surface can be performed by a method selected from the group comprising: smoothing by using a Laplacian operator, LS3 Loop subdivision and a curvature flow algorithm, or combinations thereof. In an alternative or additional embodiment, a non-periodic minimal surface can be created as detailed above by minimizing the squared mean curvature of the surface.

[0061] In a still further embodiment, the smoothing of the surface equidistant to both graphs obtained by the voxel-based Voronoi analysis can be performed by repeatedly applying the following operations: (1) one iteration of weighted LS3 Loop subdivision to enhance regularity, (2) one to ten iterations of smoothing by a Laplacian operator using cotangent weighting, preferably three iterations, and (3) reducing the mesh resolution by at most 50% using a quadric edge collapse simplification algorithm, or reducing the mesh resolution to 50%, or to 25%, or to 12.5%, or to 6.25%, or to 3.125%. Preferably, the operations are performed such that any triangle at the edge(s) of the surface remains unaltered.

[0062] It is possible to approximate the minimal surface with greater accuracy by increasing the number of iterations. This results in a smoother surface. The number of repetitions can depend on the computer performance, the desired accuracy, and the available computation time, preferably two to three repetitions are performed.

[0063] In specific embodiments of the invention, the skeleton graph creates a triply periodic minimal surface from a group comprising: Brakke complex square-wedge surfaces of genus 31, 35, 43, 51, 55, and 67, Brakke hexagonal surfaces of genus 6, 12, 18, 24, and 30, Brakke starfish surfaces of genus 31, 43, 47, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 99, 103, 115, Brakke trihedral surfaces of genus 3, 9, 15, 21, 27, 33, Fisher-Koch's S, C(S), Y, and C(Y) surfaces, Lord-Mackay's P3a surface, Neovius' surface, and Schoen's complementary P surfaces of genus 15, 21, 27, 33, 39, and 45, Schoen's batwing surfaces of genus 25, 41, and 57, and Brakke's pseudo-batwing surfaces, Schoen's F-RD, F-RD(r), P, F-RD, S'-S"|P, and S-S" surfaces, Schoen's GW, I-WP, I-WP(r), and O, C-TO surfaces, Schoen's gyroid icositopes surfaces, Schoen's H'-T, H"-R, T'-R', H'-T|H"-R, T'-R'|H'-T, and H"-R|T'-R' surfaces, Schoen's hybrid surfaces S-S", S'-S"|P, H'-T, H"-R, T'-R', H'-T|H"-R, T'-R'|H'-T, and H"-R|T'-R', Schoen's manta surfaces of genus 19, 35, and 51, Schoen's RII, RIII, I-6, I-8, and I-9 surfaces, Schoen / Brakke's N14, N26, and N38 surfaces, Schwarz's P, D, H, CLP surfaces, Schoen's complementary D surfaces, and all derivatives thereof.

[0064] Especially preferably, the skeleton graph, after minimizing the squared mean curvature of the isometric surface, or after smoothing by any of the other ways described above, creates a triply periodic minimal surface selected from the group comprising: Schwarz P surface type, Schwarz D surface type, Schoen G surface type, Fischer-Koch S surface type, Fischer-Koch CY surface type, Schoen's GW surface type, and / or Lord-Mackay's P3a surface type.

[0065] The person skilled in the art understands from the teaching of the present application that the application of the methods described herein can result in a design and / or infill having a quasi-periodic and / or aperiodic minimal surface that has not been characterized as given in any of the groups above before.

[0066] In a specific embodiment of the present application, the local adaptation of the skeleton graph as described above, i.e. the local adaptation by scaling up and / or scaling down and / or removing segments, results in a unique minimal surface that is optimized for the specific item.

[0067] One aspect of the present application is the application of the described methods in a pre-processing step of the design and light-weighting of an item to be printed. The parameters for the local adaptation and hyperbolic scaling of the skeleton graph are then determined by the person skilled in the art based on the item geometry, finite element simulation of the load case, printing method parameters, etc. as required for the specific printing job.

[0068] Another aspect of the present application is a computer program product for pre-processing an item for additive manufacturing, wherein the item comprises one or more item components each having a structure, especially wherein one of the structures is an internal structure. When executed on a computer, the computer program product is adapted to perform a method according to the present application.

[0069] Another aspect of the present application is an item for additive manufacturing obtainable by performing the method of the present application. The item comprises a quasi-crystal and / or a quasi-periodic minimal surface infill and / or a quasi-periodic minimal surface design structure and / or an aperiodic minimal surface infill and / or an aperiodic minimal surface design structure.

[0070] In a specific embodiment of the present application, the item for additive manufacturing obtainable by the method described above comprises a skin defining the shape of the item and an infill. The infill comprises a substantially quasi-periodic minimal surface. In the context of the present application, the substantially quasi-periodic minimal surface can be an approximation of a minimal surface by performing a smoothing as described in the method embodiments above.

[0071] In a further embodiment, the additively manufactured article has a minimal surface infill contacting the skin in a substantially perpendicular direction. In this context, substantially perpendicular can be understood as tolerating a potential deviation from the 90 degree angle between 0.1 and 5 degrees, which provides an ideal load conduit from the article skin to the infill. In an embodiment, the minimal surface is aperiodic.

[0072] In an embodiment of the invention, the additively manufactured article consists of metal, even more preferably of a metal used for selective laser melting.

[0073] With the present invention, a general method for the creation, specification and dimensioning of adapted and optimized structures of additively manufactured articles is proposed, which is able to construct and infill these articles with tailored structures as specific to the geometry of the article, the structure and the printer specific requirements as the skilled person would define.

[0074] The invention is illustrated below by means of the attached drawings and specific embodiments, but is not limited thereto. Nevertheless, the person skilled in the art will be able to derive further advantageous embodiments and implementations of the invention by studying the corresponding examples.

[0075] It is completely clear to the person skilled in the art that all the above-mentioned embodiments can be combined in any combination in the method, computer program product and / or article according to the invention, as long as they are not mutually exclusive. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figures la to le schematically shows how a structure or internal structure according to the invention can be constructed;

[0077] Figure 2a and Figure 2b shows a sample structure obtainable by the method of the invention;

[0078] Figure 3a and Figure 3b schematically shows how a scaling down according to the invention can be performed on the illustrated geometry;

[0079] Figure 4a and Figure 4d schematically shows how a sample object can be infilled with an adaptive scaling structure according to the invention;

[0080] Figures 5a to 5e schematically shows how a sample object can be infilled with an adaptive scaling structure according to another embodiment of the invention;

[0081] Figure 6a and Figure 6b shows an example of the invention;

[0082] Figure 7a and Figure 7b shows a sample internal structure and / or structure according to the present invention; and

[0083] Figure 8 shows an embodiment of the present invention based on the method according to Figures 5a to 5e ;

[0084] Figure 9 is an image of an item without a skin which has been constructed according to the teachings of the present invention. DETAILED DESCRIPTION

[0085] Figures la to le Some method steps for light-weighting and / or designing an item for additive manufacturing according to the present invention are illustrated by means of a step-by-step approach and a simplified example is schematically guided through various processing steps which can lead to a structure according to the present invention.

[0086] Figure la shows a rhombic unit cell 1 which can be used as a basic starting building block for carrying out the method of the present invention. In a first step, a rhombic unit cell 1 having six faces is provided and in the present example it consists of six rhombic faces which are connected by edges 11...22 having a total number of twelve edges 11...22. The rhombic unit cell 1 in the present example forms a rhombicohedron in which none of the angles between two adjacent edges 11...22 is a right angle. In the context of the present invention, rhombic shall always relate to a three-dimensional form.

[0087] The rhombic unit cell 1 as depicted in Figure la is an example representation of such a unit cell. In this example, De Bruijn's grid method is used by inputting four vectors as main inputs and creating a number of plane families, each plane family consisting of a number of parallel planes. In the present example, the number of plane families corresponds to the number of vectors, i.e. four.

[0088] Furthermore, in accordance with the present example, each plane family has three planes. As already detailed in the general description, the number of planes can be varied depending on the desired resolution of the intended geometry of the resulting quasicrystalline structure and is basically limited only by the processing power of the computer system used for designing the item.

[0089] In the present example, three planes are used for each plane family and the spacing between the planes is chosen to be uniform, i.e. with respect to the preceding, each plane is arranged to be equidistant from the respective consecutive plane. All these planes are perpendicular to the vectors. As already detailed above, the arrangement of the planes can be changed to be random or according to certain predetermined distances.

[0090] In a first step, the rhombic unit cell 1 is bisected. The bisecting of the rhombic unit cell 1 is performed by placing two tetrahedrons 30.1, 30.2 with the same volume within the rhombic unit cell 1, such that only the smallest volume of the respective tetrahedron 30.1, 30.2 remains outside the rhombic unit cell 1 and no volume of the rhombic unit cell 1 is not covered by the respective tetrahedron 30.1, 30.2. In Figure la the depiction, the tetrahedrons 30.1, 30.2 are shown with dashed lines. The tetrahedrons 30.1, 30.2 are placed in the rhombic unit cell 1 such that from the edges of the tetrahedrons 30.1, 30.2 each pyramidal tetrahedron is cut out. The contact surface between the two tetrahedrons 30.1, 30.2 will form the intersection face F (see Figure lb ). In the present example, the contact surface between the two tetrahedrons 30.1, 30.2 cuts the side edges 13, 14, 15, 17, 19, 20 in the middle of the respective edge length. The angles of the tetrahedrons 30.1, 30.2 are chosen to match the angles of the rhombic unit cell 1.

[0091] Furthermore, the first tetrahedron 30.1 of the two is assigned to the first group A, while the second tetrahedron 30.2 is assigned to the second group B.

[0092] As shown in Figure lb , the bisecting of the rhombic unit cell 1 results in an intersection face F which is hexagonal, wherein each corner is on a respective side edge of the rhombic unit cell 1 and, in the present example, exactly in the middle of said edge. The rhombic unit cell 1 is bisected into two volumes of equal volume. For the purpose of the present invention, these two volumes have been named unit tri-truncated tetrahedrons 2, 2'. As already outlined above, for the context of the present invention, a truncated tetrahedron can be understood as a regular tetrahedron with four corners cut off. On the other hand, a unit tri-truncated tetrahedron is a tetrahedron with only three of the four corners cut off. Compared to a truncated tetrahedron, a unit tri-truncated tetrahedron has seven faces instead of eight.

[0093] Thus, the bisecting results in two unit tri-truncated tetrahedrons 2, 2' corresponding to the tetrahedrons used for the bisecting and fitting as respective half of the rhombic unit cell 1. Each of these unit tri-truncated tetrahedrons 2, 2' belongs to one of the groups A or B. In Figure lb the illustration, the left unit tri-truncated tetrahedron 2 belongs to the group A, while the right unit tri-truncated tetrahedron 2' belongs to the group B. It is completely clear to the person skilled in the art that this division is completely arbitrary and that, for the purpose of illustrating the teachings of the present invention, it is relevant that, based on any one rhombic unit cell, by bisecting the unit cell into two tetrahedrons of equal volume, each of the two groups A, B is created within a structure having a plurality of rhombic unit cells, each forming a labyrinth, as will be further outlined later below.

[0094] In this example, after the simple triangular tetrahedron 2, 2' is initially assigned to either group A or group B, all rhombus cells within a structure follow essentially the same logic. In other words, if the "left" half is selected to belong to group A, then logically all the "left" halves across the entire structure will form the simple triangular tetrahedron 2 belonging to group A.

[0095] By assigning the single triangular tetrahedrons 2 and 2' to a group, two interwoven, continuous, and quasi-periodic infinite polyhedra are created within the structure.

[0096] Figure lc The further steps of the method are illustrated. Skeleton graphs A' and B' are inserted into each of the resulting triangular tetrahedrons 2 and 2'. For example... Figure lc The skeleton diagrams A' and B' depicted are illustrative examples of how such skeleton diagrams can be inserted into the corresponding triangular tetrahedrons 2 and 2'. By doing so for each rhomboid cell of the corresponding structure, skeleton diagrams A' and B' extend to span the entire volume of the structure. Each skeleton diagram A' and B' is connected to one or more skeleton diagrams A' and B' in the adjacent triangular tetrahedrons of the same group. To illustrate group affiliation in this example, the skeleton diagrams are represented by the same letter as the group they belong to, i.e. Figure lc The skeleton diagram A' extends into the volume produced by all the single triangular tetrahedrons 2 belonging to group A.

[0097] In such Figure Id In the example depicted, the skeleton diagram A' branches from two internal nodes N1 and N2. The internal nodes N1 and N2 can be arranged within a specific region N within the volume of the single triangular tetrahedron 2 belonging to group A. This can cause a "trunk" of the tree-like structure of the skeleton diagram within the single triangular tetrahedron 2. The "trunk" has varying dimensions up to a specific embodiment where the first internal node N1 and the second internal node N2 are identical, i.e., at the same location, and the "trunk" length is zero.

[0098] In this example, the first internal node N1 and the second internal node N2 are spaced apart and each branches into three main branches. For clarity of the figures, this branching is illustrated by reference to a single triangular tetrahedron 2' belonging to group B. Here, the first internal node and the second internal node are spaced apart and connected by a trunk b1. Each internal node branches into three main branches, and these main branches cut the surface of the single triangular tetrahedron 2' in a specific region. To construct the skeleton diagram B' belonging to group B, each single triangular tetrahedron 2' connects to an adjacent single triangular tetrahedron and has connecting nodes bi...bl, which contact the connecting nodes of the corresponding adjacent single triangular tetrahedron in specific node faces G...L. For example,Figure Id the branch of the first node of the skeleton graph B' extends through the node face G and cuts this face at the connection node bg. This connection node bg is the point of connection of the respective main branch of the adjacent skeleton graph with Figure Id the skeleton graph of the single tri- truncated tetrahedron 2' of

[0099] The resulting skeleton graphs A', B' span and encompass the entire quasicrystal without being interconnected at any point. Figure le The steps to create a minimal surface filler structure by constructing surfaces equidistant to both skeleton graphs are depicted. This divides the volume, which is filled with filler or designed to be a complete structure constructed from structures according to the invention, into two separate volumes A, B. The structure can dynamically adapt to adjust to the changing geometry of the article and since for simplicity the rhombic unit cells 1 of the invention are chosen from Figures la to le It is therefore clear to the person skilled in the art that within the structure there can be multiple compressed, expanded or distorted rhombic unit cells. Constructing surfaces equidistant to both skeleton graphs can include an approximation of surfaces equidistant to both skeleton graphs.

[0100] In this example, the structure 10 is depicted with two respective skeleton graphs A', B' and respective interior volumes A, B, which the skeleton graphs A', B' extend through, belong to one specific group A or group B.

[0101] In this specific example, the minimization of the squared mean curvature of the surfaces equidistant to both graphs has been applied by FEM-based computer processing. Depending on the spatial, geometrical and mechanical constraints and load cases given for the article, with this method the structure is unique and specifically adapted to this article. With this most basic principle of the invention, a method is provided with which an infinite number of articles can be constructed whose structure composition is as described above or which comprise a structure as described above as filler and interior structure for load bearing or other structural reasons. Furthermore, since the method of the invention essentially perfectly divides a given volume into two equal labyrinths, applications where it is desirable to divide a volume into two compartments greatly benefit from the teachings of the invention.

[0102] Figure 2a It is illustrated how an article 50 can be constructed with multiple rhombic unit cells 1, 1', 1". In this example of Figure 2a In this example of the invention, for illustrative purposes, a total of four rhombic unit cells 1, 1', 1" are shown, of which two rhombic unit cells 1", 1" are identical to each other and the other two unit cells 1, 1' are different to each other and to the rhombic unit cells 1", 1" of the type described before. As can be seen from Figure 2aAs can be seen, the skeleton A' extending through volume A separated from volume B by structure 10 spans through each diamond cell 1, 1', 1". The structure can be extended with more cells based on the specific needs of the item to be manufactured, and in Figure 2b In the figure it is illustrated that no matter how large an item is formed, and how many cells are added, the basic building blocks follow the same principle as the diamond cell 1, and the corresponding single trirectangular tetrahedron 2, 2' still forms the basic building block and enables the placement of the corresponding skeleton A', B' extending through the inner volume A, B and spanning the entire volume of the item.

[0103] One advantageous concept of the invention is illustrated in Figure 3a and Figure 3b The method of the invention can easily be adapted to cater for items of different geometrical shapes and can guide the optimization of the structural integrity and load situation for a large number of items by scaling the structure according to the geometrical shape of the item.

[0104] Figure 3a An example is shown where the infill for the front end of the item is adapted by applying a hyperbolic scaling to the skeleton A', the item comprising a skin 23, where the skin 23 defines the item shape. Of course, the same scaling applies to the skeleton B' as well (although not shown in the figure for clarity).

[0105] Starting from the tapering of the front end of the item, the inner structure is scaled by densifying the skeleton A' to a denser skeleton A". This prevents the tapering geometry of the front end of the item to have an inner structure with a weak point at any point below the surface of the skin 23. By scaling down the skeleton A', the resulting minimal surface structure of the inner structure for the item adapts to the geometry, providing optimized stability and infill in all geometries. This enables the additive manufacturing of items with optimized inner structure and infill by using smaller scale infill where the geometry requires it or larger scale infill where preferred (not shown in the figure). Figure 3a The scaling can also be done not only influenced by the three-dimensional geometry of the item, but also depending on the load situation of the respective item and the printer parameters.

[0106] Figure 3b An alternative example is depicted in the figure where a local densification is applied to the central part of an item which is basically in the shape of a dumbbell. The skeleton A' is hyperbolically scaled to a denser skeleton A". This denser structure will be obtained by superimposing the item shape on the skeleton which has been outside the item. By scaling a more dense region is created, under which the skin 23 is supported by a more dense inner structure, i.e. providing higher stability to the item.

[0107] Figures 4a to 4d An aspect of the invention is depicted, wherein a basic set of two mutually entangled skeleton graphs A', B' created according to the method of the invention is adapted as a filler for an item having an item shape 25. The item shape 25 is essentially an L-shaped item; in a first step of using said pair of skeleton graphs A', B', the item shape 25 is superimposed into the grid formed by the two skeleton graphs A', B'.

[0108] Figure 4a How such an item shape 25 is placed is shown from a top view.

[0109] In Figure 4b , the item shape 25 is still shown in a top view, but in contrast, the skeleton graph A' is densified into a dense skeleton graph A" by hyperbolic scaling. For ease of representation, the skeleton graph B' and its respective scaling to a dense skeleton graph B" is omitted. It can be seen that from left to right, the protrusions of the item shape 25 are filled with more "comparative" skeleton graphs to the left. This leads to a more dense area providing better structural integrity and potential skin support. Although it is to be noted that the skeleton graphs serve as a template or blueprint for the quasi-periodic minimal surfaces that will divide the internal volume of the item shape 25 into two labyrinths A, B, which will respectively fit the skeleton graphs A', A". The scaling of the skeleton graphs thus leads to a scaling of the quasi-periodic minimal surfaces that will be additively manufactured in the resulting item to the filler of the present sample item.

[0110] Figure 4c The same item is shown in a front view with the dense A-set of skeleton graphs, i.e. where the protrusions extend into the direction of the viewer.

[0111] In a similar way, Figure 4d The item shape 25 is depicted in a side view, where similar to Figure 4b , the densification of the skeleton graph A' to the dense skeleton graph A" increases from left to right.

[0112] In all of the above figures, the unscaled original skeleton graph A' is shown as a dashed skeleton graph for reference purposes and to illustrate the concept.

[0113] Figures 5a to 5e An alternative way of adapting the filler to the specific geometry and load bearing needs of the item is illustrated, although it can also be additionally used in the above described method. The illustration is meant to guide the overall method and is not intended to be a working example in real life. For this reason, the figure is simplified in some ways. One such simplification is that only one skeleton graph A' is depicted. In a real implementation, of course, the following description of the thinning skeleton graph will apply to a pair of two graphs (as created by the method shown in figure 1 above).

[0114] Figure 5aIt is depicted how the object with object shape 25 is superimposed on the basic uniform density unscaled skeleton map A'. The density is chosen as high as required for this example and most often driven by the expected requirements of the object shape regarding load bearing and geometry, i.e. as high as the highest required final density in the object.

[0115] In Fig. 5b(s), the object structure 25 undergoes a first analysis, in which the object shape 25 and the geometry dictate which regions need to be more densely populated and which can be populated less densely. To this end, the object is divided into cubes of a certain size, such that each cube contains at least several trunks of the skeleton map, preferably more than three trunks, even more preferably 5 to 8 trunks, even more preferably less than 100 trunks. At present, a distinction is made between two types of cubes: the cube(s) 45 that support the build process and the cube(s) 46 at the object boundaries. Depending on the cube type determination, an operation of removing cells of the skeleton map can be performed in a particular cube. In the context of the present invention, a cell of the skeleton map is understood to be a branch inside one particular single triakisdodecahedron. Of course, since they always occur in pairs, this means removing two branches of the skeleton map, i.e. a pair of branches inside two single triakisdodecahedra that originally belonged to the same rhombic dodecahedron cell.

[0116] Fig. 5b(q) depicts a second analysis performed on the object structure 25, in which a voxel-based load case analysis is again performed with the help of cubes, where each cube spans a number of voxels, preferably the same number of voxels per cube. This can be performed by classifying the cubes based on their stress / strain requirements and properties. In this example, a distinction is made between five types: zero stress cube(s) 40, small positive stress (compression) cube(s) 41, small negative stress (tension) cube(s) 42, high positive stress (compression) cube(s) 43 and high negative stress (tension) cube(s). Depending on the properties, a particular operation can be predetermined: for example, depending on the parameters of the load case analysis, substantially all or most of the cells can be removed within the zero stress cube(s) 40, half of the cells can be removed within the small positive stress (compression) cube(s) 41, etc. Of course, in a real-world situation, many more incremental steps and corresponding adaptations are made, and the cube(s) are rather small.

[0117] The resulting adapted skeleton A'" (B'" is omitted for clarity in the figure) is generated individually for the article shape 25 analysis, resulting in a conforming shape section thinned A-set skeleton A'"(s) as shown in figure 5c(s), and a conforming load section thinned A-set skeleton A'"(q) as depicted in figure 5c(q).

[0118] As Figure 5d The resulting combined scaled skeleton A'" resulting from unifying A'"(s) and A'"(q) is implemented for the complete article structure 25, and has a low density area (thinned high resolution skeleton) O'" and a high density area (high resolution skeleton) P'" as shown in figure 5c.

[0119] Figure 5e A final debugging step is shown, in which open end segments A'"(x) have been removed, i.e. segments that are not connected to any other segment and end in empty. Furthermore, from the outermost segment(s) (i.e. the segment that will pass through the skin of the article) the part outside the skin A'"(o) is removed and replaced by a mirror image A'"(m) of the segment part A'"(i) inside the article. The mirror image is a mirror image of the inside part reflected about the skin at the location where the segment passes through. After this debugging step, a Voronoi analysis as described earlier is performed and a zero mean curvature surface is calculated between the skeletons. This determines that the resulting minimal surface M (similar to the structure 10 of the earlier example) contacts the article surface 50 in a substantially perpendicular direction, thus providing an ideal load conduit from the surface to the infill. In this context, substantially perpendicular can be understood to include a deviation between 1 and 5 degrees from a 90 degree angle.

[0120] Figure 6a It is shown how a specific example of the invention can be executed for a manufacturing process of an additively manufactured article (which will typically require multiple build supports). The article 50 comprises an infill of a structure 10 of a minimal surface obtainable by the method of the invention. The structure is adapted to the shape 25 of the article, and is built from a build platform in a process 62 by adding print layers 54.

[0121] By the invention, it is made possible to manufacture using a minimum number of build supports. This is exemplarily shown in Figure 6b .

[0122] The currently used method for additive manufacturing includes building the article from successive layers initially placed on a build platform 51. The currently art methods using metal as the additive material have to cope with a maximum angle of 45° between layers, after which build supports are required during the build process to hold the layers in place, to conduct heat and to prevent the article from deforming in production. For the purpose of this example, a selective laser melting rapid prototyping method is performed for additive manufacturing of an article having an article shape 25, wherein the article shape 25 has a slope of less than 45° on one part with respect to the build support 53. The selective laser melting manufacturing method is performed in a powder bed by using a laser (typically a ytterbium fiber laser) to selectively melt out the desired shape in one plane within the powder bed, while successive powder layers are applied to the shape in synchronization with the laser operation.

[0123] In Figure 6b In this example of the art, the required support structure 52 according to the current art is shown for illustrative purposes in comparison with the build support 53 that is sufficient to perform additive manufacturing of an article 50 having a particular article shape 25. For the purpose of this example, the article shape 25 corresponds to the outer skin of the article. Starting from the build support 53, a plurality of print layers 54 are added in the direction of the build process 62. The printing starts with the first layer of the contact area 55 of the article 50, which contacts the resting area of the build support 53. The deposition of the layers 54 is performed in the direction of the build process 62. As the construction of the structure 10 progresses, the center of gravity 58, 59, 57 of the article shifts from the middle of the contact area 55 to the left, i.e. in the direction of the overhanging part on the left. The center of gravity trajectory 57 is shown in Figure 6b to depict the shift of the center of gravity 58, 59, 57, 60 as layers are added. For example, after a few layers have formed the overhanging part on the left, the center of gravity 58 is shifted from the center of the contact area 55. The center of gravity 58, 59, 57, 60 moves further to the left until at a certain point in time the center of gravity 59 is significantly shifted, and at the point in time X the center of gravity 60 has reached the vertical delimitation mark 56 of the contact area. Progress beyond this delimitation mark 56 shifts the center of gravity beyond the contact area 55, after which the article 50 is at risk of toppling and damaging the shape when no support is used at this given angle. The maximum angle of the current art without support structure required in the printing of the current art is shown as the maximum current art angle 61 of the unsupported build. This is essentially a 45° angle.

[0124] At the point in time X the upper boundary 60.1 of the printed article is reached and the center of gravity is about to pass the vertical delimitation mark 56.

[0125] To print the depicted article, approximately at the upper border (where the center of gravity of the article moves beyond or just at the contact area vertical delimitation) at time point X only one build support 53, instead of having multiple build supports 52, is sufficient to support the article and provide sufficient stability for the continuation of the overhanging portion on the left. The maximum current state of the art angle 61 of the un-supported build is shown for reference. According to the teachings of the present invention, sufficient support is provided by the infill structure 10, making it possible to print at steeper angles with less support than previously required.

[0126] In addition to enabling building articles at steeper angles, the present invention and the method disclosed herein also provide advantages in selective laser melting by providing optimized heat dissipation inside the build structure. Since the minimal surfaces of the present invention always dissipate heat in the optimal path, the article is more effectively dissipated to the build platform, which can enable increasing the printing speed and / or increasing the smoothness and / or stability of the melted surface.

[0127] For the present example, an EOS GmbH type M290 printer equipped with a 400W Ytterbium fiber laser is used. As an alloy, NEOS Maraging Steel MS1 / 1, 2709 is used, available from EOS, with a grain size of 20 to 65 pm. The resulting article can take the shape shown in Figure 7a and Figure 7b In Figure 7a the outer skin has been omitted (corresponding to article shape 25) to show the infill and internal structure of the article 50. The internal volume of the article is subdivided into two labyrinths A, B. The structure 10 is a minimal surface structure and comprises enlarged regions O and reduced regions P, in which the hyperbolic scaling as described above has been performed to achieve certain structural features in a given region.

[0128] In contrast to Figure 7a , Figure 7b the article 50 of does not have an outer skin, and the article surface corresponds to the structure 10 itself. The substantially barbell-shaped article 50 also divides its volume into two labyrinths A, B. Also illustrated are enlarged regions O in which the density of the structure 10 is less, and reduced regions P in which the structure 10 is densified, such as to form a more stable surface.

[0129] Figure 8 An article obtainable by the method described in Figures 5a to 5e is shown, in which thinning of the skeleton picture segments is performed by removing individual segments and / or the backbone of the skeleton picture based on the article shape and / or build parameters and / or stress / strain analysis, to create a structure 10 in Figure 8The depicted local denser and local less dense regions. The object shape 25 is shown without a skin, which has been removed to better provide an internal view. If the object shape 25 would be present, the object shape 25 would be substantially a cube.

[0130] The object has several regions, which depending on the shape and / or load case analysis, have been found to be printable with a low density infill, or which have been found to require a high density infill. Inside the object, the aperiodic minimal surface subdivides the volume into two labyrinths A and B, separated by the structure 10 forming the infill. The structure 10 is the minimal surface M. In the upper right corner of the object, a low density region O”’ is visible, thinned from the high resolution skeleton graph. And to the left of O”’, approximately in the upper left corner of the object, a high density region P”’ is visible, which maintains the original density of the high resolution skeleton graph.

[0131] Figure 9 is a photo showing an object 50 printed according to the method of the invention.

[0132] The objects obtained by the method of the invention can be used for a large number of applications. One of the most basic applications is to use the objects as shown in Figure 9 Fig. 1 as building blocks for lightweight construction, where stability and weight are important factors. The method of the invention shows that the printing of metal structures is possible and provides objects with great stability, light and with optimized heat dissipation, while dividing the volume into two different and independent labyrinths.

[0133] In another example of the invention, the method and teachings of the invention are used as a pre-processing of an object intended for additive manufacturing by using computer software that integrates executable files suitable for performing the invention. A common additive manufacturing design and pre-processing workflow includes a first step of generating a three-dimensional model. Most commonly, this is done by CAD design, tuning or querying a corresponding model.

[0134] In a second step, forces are simulated. This can be done by finite element simulation (FEM) and can further include a sizing and optimization step for tuning the design or changing the topology according to the needs of the force simulation. Preparing for printing includes light weighting and applying simple infills, which increases the number of polygons in the simulation. A print simulation is then performed to check if the print recipe can be printed in reality. Required external and internal support bodies are also integrated in this method step. To perform the printing, slicing is performed depending on the build process parameters and printer settings, which are driven by the main hardware. This build step then corresponds roughly to layer by layer, depending on the previous step of slicing the object for additive manufacturing.

[0135] The invention comprises alternative or additional tools for performing the light-weighting and for providing the infill as outlined in the pre-processing steps above.

[0136] Alternatively or additionally, the method of the invention can also be used to create a structure from a raw material. This means that the method of the invention can be used to create a structure in which the infill as produced as detailed above is the structure itself.

[0137] Therefore, another aspect of the invention relates to an article having the features described earlier that can be obtained by the method described above. A further aspect also relates to a computer program product comprising operating instructions and / or a skeleton map required for applying the pre-processing to the article based on the teachings of the invention.

[0138] Although the examples here are described with selective laser melting, the person skilled in the art can easily recognize that the method of the invention is equally applicable to any other type of additive manufacturing technology, such as reduction polymerization, material jetting, binder jetting, material extrusion, directed energy deposition or sheet lamination as required by the respective printing vendor and for the purpose of the article in question.

[0139] The teachings of the invention provide a method and an article with superior properties and attributes, opening up new fields of application for structural materials and effectively printing geometries, and requiring less post-processing such as removal of burrs and / or support structures. Since the surface divides the volume of the article into two complete labyrinths, the article produced by the method of the invention can also be more easily excluded from material. Essentially, two small holes placed in the correct position of the article are sufficient to remove by expelling or blowing out the material.

[0140] Reference signs

[0141] 1 rhombic unit cell

[0142] 1'second rhombic unit cell

[0143] 1 " third rhombic unit cell

[0144] 2 single tri- truncated tetrahedron group A

[0145] 2' single tri-truncated tetrahedron group B

[0146] 10 structure

[0147] 11 first edge

[0148] 12 second edge

[0149] 13 third edge

[0150] 14 fourth edge

[0151] 15 fifth edge

[0152] 16 sixth edge

[0153] 17 seventh edge

[0154] 18 eighth edge

[0155] 19 ninth edge

[0156] 20 tenth edge

[0157] 21 eleventh edge

[0158] 22 twelfth edge

[0159] 23 skin

[0160] 24 hyperbolic scaling

[0161] 25 article shape

[0162] 30.1 tetrahedron A group

[0163] 30.2 tetrahedron B group

[0164] 40 zero stress voxel

[0165] 41 voxel with very small positive stress (compression)

[0166] 42 voxel with very small negative stress (tension)

[0167] 43 voxel with high positive stress (compression)

[0168] 44 voxel with high negative stress (tension)

[0169] 45 voxel supporting build process

[0170] 46 voxel at article boundary

[0171] 50 article

[0172] 51 build platform

[0173] 52 build support of current technology

[0174] 53 build support

[0175] 54 print layer

[0176] 55 contact area

[0177] 56 contact area vertical delimiter

[0178] 57 center of gravity ("COG") trajectory

[0179] 58 article COG at time point #1

[0180] 58.1 Item upper boundary at time point #1

[0181] 59 Item COG at time point #4

[0182] 59.1 Item upper boundary at time point #4

[0183] 60 Item COG at time point X

[0184] 60.1 Item upper boundary at time point X (COG moved outside of contact area)

[0185] 61 Maximum current technology angle of unsupported construct

[0186] 62 Process

[0187] A First set of labyrinths

[0188] A' A set of skeleton maps

[0189] A" Dense A set of skeleton maps

[0190] A''' (s) A set of skeleton maps with compliant shape sections thinned

[0191] A''' (q) A set of skeleton maps with compliant load sections thinned

[0192] A''' Partially thinned A set of skeleton maps: unification of A''' (s) and A''' (q)

[0193] A''' (i) Inner portion of outermost segment of partially thinned A set of skeleton maps

[0194] A''' (o) Outer segment of outermost segment of partially thinned A set of skeleton maps

[0195] A''' (m) Mirrored copy of inner portion of outermost segment of partially thinned A set of skeleton maps

[0196] A''' (x) Open end segment of partially thinned A set of skeleton maps

[0197] B Second set of labyrinths

[0198] B' B set of skeleton maps

[0199] B" Dense B set of skeleton maps

[0200] F Intersection face

[0201] G First node face

[0202] H Second node face

[0203] I Third node face

[0204] J Fourth node face

[0205] K Fifth node face

[0206] L Sixth node face

[0207] M Minimal surface

[0208] N Variable area of interior node

[0209] N1 First interior node (skeleton group A)

[0210] N2 Second interior node (skeleton group A)

[0211] O Low density area (enlarged skeleton map)

[0212] O' Low density area (thinned high resolution skeleton map)

[0213] P High density area (reduced skeleton map)

[0214] P' High density area (high resolution skeleton map)

[0215] S Item shape analysis

[0216] Q Load case analysis (FEM simulation)

[0217] b1 "Trunk"

[0218] bg First node face of connecting node

[0219] bh Second node face of connecting node

[0220] bi Third node face of connecting node

[0221] bj Fourth node face of connecting node

[0222] bk Fifth node face of connecting node

[0223] bl Sixth node face of connecting node

Claims

1. A method for lightweighting and / or design of an article for additive manufacturing, wherein the article comprises one or more constituent article components each having a structure, each or some of the one or more constituent article components having an internal structure, the method comprising the steps of: filling and / or building each of the one or more constituent article components with a quasicrystal structure, wherein the quasicrystal structure is a three-dimensional quasicrystal made of two or more rhombohedral unit cells; and bisecting one or more rhombohedral unit cells such that the faces resulting from the bisecting have a hexagonal form, thereby creating two equal single-triakisoctahedra from each unit cell, wherein the single-triakisoctahedra is a tetrahedron with only three of its four corners cut off and has seven faces, wherein filling and / or building each of the one or more constituent article components is filling and / or building with a quasiperiodic or aperiodic minimal surface filler and / or a quasiperiodic or aperiodic minimal surface design structure and using the quasicrystal structure as a framework to produce the quasiperiodic or aperiodic minimal surface filler and / or the quasiperiodic or aperiodic minimal surface design structure.

2. The method according to claim 1, wherein the method further comprises the step of creating the geometry of the quasicrystal, the step comprising: a. inputting at least four principal vectors; b. creating a number of sets of parallel planes equal to the number of principal vectors input in step a., wherein each set of parallel planes comprises at least three parallel planes.

3. The method according to claim 2, wherein some of the planes in one set of parallel planes are evenly spaced, or all of the planes in one set of parallel planes are evenly spaced.

4. The method according to claim 2, wherein some of the planes in one set of parallel planes are randomly spaced, or all of the planes in one set of parallel planes are randomly spaced.

5. The method according to claim 2, wherein some of the planes in one set of parallel planes are spaced according to a predetermined pattern, or all of the planes in one set of parallel planes are spaced according to a predetermined pattern.

6. The method according to claim 2, wherein some of the planes in one set of parallel planes are evenly spaced, and some of the planes are randomly spaced, and some of the planes are spaced according to a predetermined pattern.

7. The method of claim 1, further comprising the step of: assigning each single-triakisoctahedron to one of two groups, such that two labyrinths A, B are formed.

8. The method according to claim 7, further comprising the step of inserting one or more skeleton graphs into each type of rhombohedral unit cell, the step comprising: inserting one skeleton graph A', B' into each single-triakisoctahedron, such that two interlaced skeleton graphs A', B' are created that span the entire quasicrystal and are not interconnected at any point.

9. The method according to claim 8, wherein the skeleton graphs A', B' each extend through one of the two labyrinths A, B, or wherein each skeleton graph A', B' extends through a group of single-triakisoctahedra.

10. The method of claim 2, further comprising selecting a number of planes in each set of parallel planes as a measure of resolution of a desired internal structure.

11. The method of claim 10, wherein the selecting is performed separately for any of the one or more constituent article components having an internal structure.

12. The method of claim 8, further comprising: downscaling the skeletal graphs A', B' outside the one or more constituent article components each having an internal structure to create a dense skeletal graph A", B" or downscaling the skeletal graphs A', B' outside the one or more constituent article components each having an internal structure to create a locally dense skeletal graph A", B".

13. The method of claim 12, wherein the quasicrystal structure, the skeletal graphs A', B', the dense skeletal graph A", B" or the locally dense skeletal graph A", B" is used to define a quasiperiodic minimal surface.

14. The method of claim 12, wherein the quasicrystal structure is used to define a non-periodic minimal surface.

15. A method for lightweighting and / or design of an additively manufactured article, wherein the article comprises one or more constituent article components each having a structure, each or some of the one or more constituent article components having an internal structure, the method being the method of any one of claims 1 to 14, the method further comprising the steps of: a. providing two skeletal graphs A', B', wherein the two skeletal graphs A', B' each extend through a set of single tri- truncated tetrahedra such that two interlaced skeletal graphs A', B' are created that span the entire quasicrystal and are not interconnected at any point; b. removing cells and / or segments from the skeletal graphs A', B' depending on a local stress / strain analysis.

16. A computer program product for pre-processing an additively manufactured article comprising one or more article components, each article component having an internal structure, the computer program product being adapted for performing the method of any one of claims 1 to 15 when executed on a computer.

17. An additively manufactured article obtainable by performing the method of any one of claims 1 to 14, the article comprising a quasicrystal structure and / or a quasiperiodic minimal surface filler and / or a quasiperiodic minimal surface design structure and / or a non-periodic minimal surface filler and / or a non-periodic minimal surface design structure.

18. The article of claim 17, wherein the article comprises a skin and a filler, and wherein a substantially zero mean curvature surface filler contacts the skin at a substantially perpendicular angle or a minimal surface filler contacts the skin at a substantially perpendicular angle.

19. The article of any one of claims 17 or 18, wherein the article comprises one or more low density regions O, O" and / or one or more high density regions P"'.

20. Use of a pair of skeleton graphs A', B' for a pre-processing step of an additive manufacturing job, wherein, The pair of skeleton graphs A', B' can be obtained by the method according to claim 15, wherein the pair of skeleton graphs A', B' is superimposed with a model of an item and the skeleton graphs A', B' are hyperbolically scaled to obtain a pair of dense skeleton graphs A'', B'' such that a template for a minimal surface filler for the item is created based on a minimal and equidistant surface between the pair of skeleton graphs A', B' or the pair of dense skeleton graphs A'', B''.

21. Use according to claim 20, wherein the pair of skeleton graphs A', B' is provided with a high density area P''' corresponding to a highest density required for any area and / or geometry of the item.

22. Use of a pair of skeleton graphs A', B' for a pre-processing step of an additive manufacturing job, wherein, The pair of skeleton graphs A', B' can be obtained by the method according to claim 15, wherein the pair of skeleton graphs A', B' is superimposed with a model of an item and segments of the skeleton graphs A', B' are removed depending on an item shape analysis and / or a load case analysis to obtain adapted skeleton graphs A''', B'''.

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