Three-dimensional concrete printing (3DCP) of topology optimized parts: geometrically informed toolpath and variable material deposition

Abstract

Methods of additive manufacturing are provided including depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The depositing process forms at least one layer of an additively manufactured cementitious structure. In certain aspects, the additively manufactured structure is a topology optimized (TO) structure having a complex geometry. The methods may use geometrically informed techniques, such as a geometrically informed non-planar (GINP) toolpath, while the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii). The robotic additive manufacturing device may be an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

Description

THREE-DIMENSIONAL CONCRETE PRINTING (3DCP) OF TOPOLOGY OPTIMIZED PARTS: GEOMETRICALLY INFORMED TOOLPATH AND VARIABLE MATERIAL DEPOSITIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 563,004, filed on March 8, 2024. The entire disclosure of the above application is incorporated herein by reference.FIELD

[0002] The present disclosure relates to methods of additive manufacturing of a printable cementitious composition to form a topology optimized additively manufactured cementitious structure by using a geometrically informed toolpath and variable material deposition.BACKGROUND

[0003] This section provides background information related to the present disclosure which is not necessarily prior art.

[0004] The rapid pace of urbanization requires constructing homes and infrastructure for an additional 2.3 billion people. Reinforced concrete can help meet this demand. For example, additive manufacturing (AM), also commonly referred to as three-dimensional (3D) printing of cementitious materials, like concrete, can help to achieve this goal through digitizing concrete construction. Additive manufacturing (AM) / three-dimensional (3D) printing is a process by which material is applied in an additive, layer-by-layer formation technique. Additive manufacturing can form structures having complex geometries and freeform shapes and is of particular interest in the construction industry. 3D printing of cementitious materials, like concrete (concrete additive manufacturing or concrete three-dimensional printing - 3DP (3DCP)) offers novel opportunities to digitize the construction industry and reduce the carbon dioxide (CO2) footprint resulting from construction and thus significantly contribute to carbon neutrality by decreasing CO2 emissions, energy consumption, waste, and costs associated with concrete construction by eliminating the need for formwork and minimizing concrete consumption in building structures.

[0005] Currently, a contour crafting technique with 3D concrete printing is one of the most prevalent approaches for construction scale structures. These techniques use a planar toolpath, meaning the toolhead follows a path parallel to the ground or along a single plane,which follows a linear path, to guide the 3DCP tool head. The tool head follows this path and extrudes mortar from the printer head, depositing it in horizontal layers. After each layer is deposited, the extruder nozzle is raised by the height of the deposited layer. This process is repeated to create a concrete mold, which is later filled with rebars and concrete. However, such methods, while widely adopted in research and practice, have geometric limitations when printing overhangs, layer cantilevers, and filament section or angle variations. Thus, it limits the application of 3DCP to simple geometric shapes, such as orthogonal walls, resulting in high consumption of concrete. Further, the surface finishing and resolution are also often low. It would be desirable to overcome these challenges and provide an alternative method of 3D printing concrete to form improved high resolution structures with potentially complex geometries.SUMMARY

[0006] This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

[0007] In certain aspects, the present disclosure relates to a method of additive manufacturing comprising depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The target may be either a substrate or the cementitious composition in a hardened state that was previously deposited. The depositing thus forms at least one layer of an additively manufactured cementitious structure that is topology optimized.

[0008] In certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath.

[0009] In certain further aspects, the methods further comprise developing the geometrically informed non-planar (GINP) toolpath by analyzing formed geometric features.

[0010] In certain aspects, the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the printhead; or (iii) both (i) and (ii).

[0011] In certain further aspects, the depositing comprises (i) regulating the flow rate of cementitious material passing through the printhead. The depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitiousmaterial passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

[0012] In certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath and the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

[0013] In certain aspects, the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

[0014] In certain aspects, the at least one layer comprises a first layer and at least one additional layer and the method further comprises repeating the depositing of the printable cementitious composition in the non-planar toolpath over the first layer to form the at least one additional layer thereon.

[0015] In certain aspects, the cementitious composition comprises ordinary Portland cement and water.

[0016] In certain aspects, the cementitious composition further comprises a reinforcement phase.

[0017] In certain aspects, the additively manufactured cementitious structure further comprises at least one metal reinforcement.

[0018] In certain other aspects, the present disclosure further relates to a method of additive manufacturing a lightweight, complex geometry cementitious structure. The method comprises depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The target may be either a substrate or the cementitious composition in a hardened state that was previously deposited. The depositing forms a plurality of layers to define an additively manufactured lightweight, complex geometry cementitious structure that is topology optimized. The additively manufactured lightweight, complex geometry cementitious structure defines at least one complex region selected from the group consisting of: a branch, a concave region, a convex region, a tubular structure, a sharp angle, and combinations thereof.

[0019] In certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, complex geometry cementitious structure. The depositing further comprises employing a geometricallyinformed variable (GIV) material deposition method that (i) regulates a flow rate of the cementitious composition passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

[0020] In certain aspects, the depositing comprises (i) regulating the flow rate of the cementitious material passing through the printhead. The depositing occurs at a first flow rate for a first duration. The method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

[0021] In certain aspects, the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

[0022] In certain aspects, the present disclosure relates to a method of additive manufacturing a lightweight, freeform, complex geometry cementitious structure. The method comprises depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The target is either a substrate or the cementitious composition in a hardened state that was previously deposited. The depositing forms a plurality of layers to define an additively manufactured lightweight, freeform, complex geometry cementitious structure that is topology optimized and defines at least one complex region comprising a tubular region. Further, at least one metal reinforcement is disposed in the tubular region.

[0023] In certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, freeform, complex geometry cementitious structure. The depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of the cementitious composition passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

[0024] In certain aspects, the depositing comprises (i) regulating a flow rate of the cementitious material passing through the printhead. The depositing occurs at a first flow rate for a first duration. The method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

[0025] In certain aspects, the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

[0026] In certain aspects, the additively manufactured lightweight, freeform, complex geometry cementitious structure comprises a shell wall.

[0027] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.DRAWINGS

[0028] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0029] FIGS. 1A-1D show images of conventional processes currently used for three- dimensional concrete printing (3DCP) constructed by Peri 3D construction and CIVE to build a two-story single-family home in Houston, Texas. In FIG. 1A, a 3DCP of a concrete mold is shown that is later filled with rebar and concrete. FIGS. IB, 1C, and ID each show various walls of the structure formed in FIG. 1A, as they are being constructed each demonstrating different aspects of the geometric limitations when printing overhangs, layer cantilevers, and low-quality surface finishing when using a traditional planar 3D printer toolpath.

[0030] FIGS. 2A-2C show a portion of a topologically optimized form using a planar tool pathing method in conventional three-dimensional concrete printing (3DCP). FIG. 2A shows a portion of a topologically optimized form for a cementitious structure. FIG. 2B shows a detailed view / close-up of the “staircase effect” resulting from cantilevering of each layer when using a conventional 3DCP planar toolpath. FIG. 2C shows in further detail how these cantilevering layers of extruded filament limit the angle of tubular features to impose geometric limitations.

[0031] FIGS. 3A-3C show an example of a known topology optimization process allowing changes in size, shape, and topology to achieve the equivalent or better structural performance of lightweight structural elements. FIG. 3 A shows a load case (with a fixed support load shown at arrow F) and bounding conditions. FIG. 3B shows the same structure in FIG. 3A with a designed solution (with a fixed support load shown at arrow F). FIG. 3C shows placement of material in the trajectory of forces (shown at arrow F) with a material reduction.

[0032] FIGS. 4A-4C show examples of using a non-planar toolpath in combination with three-dimensional concrete printing (3DCP) to form a cementitious structure having a tubular geometry with sharp concave and convex geometric features. FIG. 4A shows a new method for controlling the tool path of a printhead in 3D printing, by using a non-planar Geometrically Informed Non-Planar (GINP) toolpath. FIG. 4B shows a 3D-printed tubular cementitious structure created using GINP-toolpath and GIV-material deposition according to certain aspects of the present disclosure. FIG. 4C shows that as the printing head moves from concave to convex areas, a respective height within each layer can change (e.g., here increase).

[0033] FIGS. 5A-5B show a computational model that enables generating a non-planar (Geometrically Informed Non-Planar (GINP) toolpath) for any given geometry for three- dimensional concrete printing (3DCP). Such a model can also generate data for variable material flow rates along the toolpath, as shown in FIG. 5A. This variable material flow rate can then be calculated in relation to the maximum and minimum layer heights (LH), as shown in FIG. 5B.

[0034] FIGS. 6A-6F show an example of a method for creating ultra-lightweight, freeform reinforced concrete building elements in the form of a shell wall according to certain aspects of the present disclosure. FIG. 6A shows a schematic of a printhead of a robotic additive manufacturing device being used in a non-planar toolpath to form a shell wall having complex curvatures and two distinct formed channels for receiving reinforcement metal rods or rebar. FIG. 6B shows a schematic of the shell wall after formation via the robotic additive manufacturing device in FIG. 6A, where a human stands next to it to demonstrate height. FIGS. 6C and 6D are images taken from a front view and a side view of a portion of the shell wall during construction via non-planar three-dimensional concrete printing (3DCP) in accordance with various aspects of the present disclosure at nearly the same point as is shown in the model of FIG. 6A. FIGS. 6E and 6F show different views of a fully constructed shell wall formed according to certain aspects of the present disclosure.

[0035] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.DETAILED DESCRIPTION

[0036] Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific compositions, components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may beembodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.

[0037] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, elements, compositions, steps, integers, operations, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Although the open-ended term “comprising,” is to be understood as a non-restrictive term used to describe and claim various embodiments set forth herein, in certain aspects, the term may alternatively be understood to instead be a more limiting and restrictive term, such as “consisting of’ or “consisting essentially of.” Thus, for any given embodiment reciting compositions, materials, components, elements, features, integers, operations, and / or process steps, the present disclosure also specifically includes embodiments consisting of, or consisting essentially of, such recited compositions, materials, components, elements, features, integers, operations, and / or process steps. In the case of “consisting of,” the alternative embodiment excludes any additional compositions, materials, components, elements, features, integers, operations, and / or process steps, while in the case of “consisting essentially of,” any additional compositions, materials, components, elements, features, integers, operations, and / or process steps that materially affect the basic and novel characteristics are excluded from such an embodiment, but any compositions, materials, components, elements, features, integers, operations, and / or process steps that do not materially affect the basic and novel characteristics can be included in the embodiment.

[0038] Any method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be taken, unless otherwise indicated.

[0039] When a component, element, or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other component, element, or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer,there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0040] Although the terms first, second, third, etc. may be used herein to describe various steps, elements, components, regions, layers and / or sections, these steps, elements, components, regions, layers and / or sections should not be limited by these terms, unless otherwise indicated. These terms may be only used to distinguish one step, element, component, region, layer or section from another step, element, component, region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first step, element, component, region, layer or section discussed below could be termed a second step, element, component, region, layer or section without departing from the teachings of the example embodiments.

[0041] Spatially or temporally relative terms, such as “before,” “after,” “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially or temporally relative terms may be intended to encompass different orientations of the device or system in use or operation in addition to the orientation depicted in the figures.

[0042] Throughout this disclosure, the numerical values represent approximate measures or limits to ranges to encompass minor deviations from the given values and embodiments having about the value mentioned as well as those having exactly the value mentioned. Other than in the working examples provided at the end of the detailed description, all numerical values of parameters (e.g., of quantities or conditions) in this specification, including the appended claims, are to be understood as being modified in all instances by the term “about” whether or not “about” actually appears before the numerical value. “About” indicates that the stated numerical value allows some slight imprecision (with some approach to exactness in the value; approximately or reasonably close to the value; nearly). If the imprecision provided by “about” is not otherwise understood in the art with this ordinary meaning, then “about” as used herein indicates at least variations that may arise from ordinary methods of measuring and using such parameters. For example, “about” may comprise a variation of less than or equal to 5%, optionally less than or equal to 4%, optionally less than or equal to 3%, optionally less than or equal to 2%, optionally less than or equal to 1%, optionally less than or equal to 0.5%, and in certain aspects, optionally less than or equal to 0.1%.

[0043] In addition, disclosure of ranges includes disclosure of all values and further divided ranges within the entire range, including endpoints and sub-ranges given for the ranges.

[0044] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0045] Efficient concrete design and construction methods are needed to meet growing demand for buildings and infrastructure, while minimizing environmental impact. As discussed above, current techniques for 3D concrete printing use a planar toolpath, parallel to the ground or along a single plane, to guide the 3DCP tool head. These current techniques limit the application of 3DCP to simple geometric shapes, such as orthogonal walls, because they encounter difficulty when printing overhangs, layer cantilevers, and filament section or angle variations. Further, the surface finishing and resolution are also often low. By way of example, FIGS. 1A-1D show a conventional method of 3DCP with a 3D printing device 20 to form a concrete mold 30 having various walls 32 that is later filled with rebar (reinforcement metal) and concrete to construct a two-story house. The 3DCP method forms multiple layers 34 to create the walls 32 and other structures. As can be seen, such a construction method suffers from geometric limitations when printing overhangs, layer cantilevers, and low-quality surface finishing when using a traditional planar toolpath, where uneven layers 34 / walls 32 and defects occur.

[0046] More specifically, the commonly used planar toolpath approach in 3D concrete printing processes has proven to be a challenge, because it is not capable of handling the complex geometries produced through topology optimization (TO). Topology optimization is a technique that generates an efficient distribution of material based on performance criteria, such as strength or weight, for a given set of supports. Designs generated from TO often feature intricate shapes, such as branching and angular tubular forms, as well as a hierarchical arrangement of materials at varying scales (as shown in FIGS. 2A-2C). For example, in FIG. 2A, a portion of a topologically optimized form 40 and the planar tool pathing method used in conventional 3DCP is shown. FIG. 2B shows a detailed view / close-up of the “staircase effect” resulting from cantilevering of each layer 42. FIG. 2C further highlights how these cantilevering layers 42 of extruded filament (the “staircase effect”) limit the angle of tubular features 44 and ultimately impose geometric limitations. As shown, the angle is about 50°. Therefore, such designs pose difficulties or are even impossible to fabricate using the typical 3D concrete printing methods that employ planar toolpaths. Further, the properties, especially rheology, of the printable cementitious composition pose further challenges to fabricating such complex structures.

[0047] In accordance with certain aspects of the present disclosure, 3D printing technologies can be used to enable the creation of lightweight and / or complex structures generated by topology optimization (TO). Topology optimization (TO) is a known method that can generate the most efficient distribution of material based on performance criteria, such as strength or weight for a given set of support (see e.g., structures shown in FIGS. 2A-2C). An example of topology optimization (TO) is shown in FIGS. 3A-3C excerpted from Adrei Jipa et al. “3D-Printed Stay-in-Place Formwork for Topologically Optimized Concrete Slabs,” Conference Paper: TxA Emerging Design + Technology, San Antonio, Texas, USA, Vol. 3, DOI: 10.3929 / ethz-b-000237082 (November 2016), the relevant portions of which are incorporated herein by reference, which demonstrates how a topology optimization process allows for changes in size, shape, and topology to achieve the equivalent or better structural performance of lightweight concrete structural elements. FIG. 3A shows a load case (with a fixed support load shown at arrow F) and twenty bounding conditions. FIG. 3B shows the same structure in FIG. 3A with a designed solution (with a fixed support load shown at arrow F). Finally, FIG. 3C shows placement of material in the trajectory of forces (shown at arrow F) via topology optimization to achieve an approximate 53.1% material reduction, where a lightweight structure 50 with a complex geometry is formed. By only placing material in the trajectory of forces, the TO method enables the materially optimal design of parts for any given sets of support and force loads.

[0048] Combining 3D printing technologies and material optimization methods, such as topology optimization (TO), can create ultra-lightweight parts comprising cementitious materials with high structural performance. Thus, the present disclosure pertains to methods for additive manufacturing of cementitious materials (e.g., 3D concrete printing (3DCP)) that further can use topology optimization methods to form structures exhibiting complex geometries, such as branching tubular shapes with sharp angles, by use of a non-planar path for the deposition of the cementitious material, which cannot be realized using traditional planar toolpath methods in conventional 3D concrete printing. Generally, complex geometry cementitious structures may defines at least one complex region, for example, a feature or region selected from the group consisting of: a branch, a concave region, a convex region, a tubular structure, a sharp angle, and any combinations thereof. As noted above, such complex geometries may further include overhangs, cantilevers, and the like, as well. In certain aspects, by non-planar path, it is meant that the printhead may follow a curved or spiral path rather than straight lines. Further, by coupling the 3DCP with the topology optimizing methods, concrete consumption may be minimized. This is achieved by developing a new framework forcontrolling the tool path and material deposition by considering the geometry and / or shape of the concrete part that is being 3D printed and the constraints of concrete rheology.

[0049] In various aspects, the present disclosure provides an alternative method of additive manufacturing of an extrusion-based 3D printing of cementitious material, like concrete. The present disclosure contemplates an automated additive manufacturing process that can be done by using a robotic additive manufacturing device (three-dimensional printer) that may be automated, for example, with robotics and other computer numerical control (CNC) driven machinery in certain variations. For example, the methods of additive manufacturing of a cementitious material may comprise applying a precursor of a cementitious material that may optionally comprise a reinforcement phase or material, such as fibers or particles, directed towards a target by an automated print head.

[0050] Thus, the present disclosure provides methods of additive manufacturing of a cementitious composition to form an additively manufactured cementitious structure that is topology optimized, as discussed above, for example, defining complex structures. A complex structure has at least one feature such as branching, bifurcations, and sharp angles, among other features. Thus, in certain aspects, the methods are directed to geometrically informed variables that are used to control the deposition process. In certain aspects, a method of additive manufacturing is contemplated that comprises depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The printhead is often part of an end effector of a robotic arm. The printing head / printhead typically comprises at least one aperture, for example, an aperture of a nozzle of a 3D printhead, where the printable cementitious composition passes and is deposited onto a target. Notably, the printhead / aperture may define different extruded shapes, such as round, rectangular, or irregular shapes. In the fresh state, the cementitious composition is flowable and extrudable. The cementitious composition may be deposited in a flowing continuous stream that is formed by a deposited ribbon or filament of the cementitious material. The cementitious composition also transforms into a hardened state, for example, exhibiting typical tensile strengths associated with cementitious compositions, such as greater than or equal to about 2.5 MPa and a compressive strength at 100 hours of greater than or equal to about 20 MPa. In certain variations, the target is a substrate or the target is the cementitious composition in a hardened state that was previously deposited via the additive manufacturing process. In this manner, a layer-by-layer deposition process can occur to form a bonded layered structure from the cementitious composition. In certain aspects, the deposited filaments or layers can optionally be aligned normal to the axis ofloading. In this manner, the depositing forms at least one layer of an additively manufactured cementitious structure. In certain variations, the robotic additive manufacturing device is an automated three-dimensional printer, which may be disposed on a robotic arm, and may be at least partially controlled by a computer numerical control (CNC) system.

[0051] In certain variations, the present disclosure provides a computational model that incorporates nonplanar and variable material deposition based on the shape and geometric features of the topology-optimized parts. This allows for efficient use of material by placing it precisely where it is needed for structural purposes while eliminating unnecessary overbuilding with excessive amounts of materials. In certain aspects, the present technology first provides a geometrically informed non-planar toolpath method developed based on formed geometric features of the structure. A Geometrically Informed Non-Planar (GINP) toolpath is a curved or spiral path for the printing head to follow rather than straight lines. Second, a geometrically informed variable (GIV) material deposition method is employed to regulate an amount of cementitious material dispensed or passed through the printing head during the printing process. Geometrically Informed Variable (GIV) Material Deposition refers to a technique regulating the amount of material being deposited along the toolpath based on the shape of the printed parts. The material flow rate can be adjusted by the material flow rate or speed of the robot.

[0052] As such, in certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath. In other aspects, the methods of the present disclosure further comprise developing the geometrically informed non-planar (GINP) toolpath by analyzing formed geometric features, as described further below.

[0053] In yet other aspects, the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii). For example, where the depositing comprises (i) regulating the flow rate of cementitious material passing through the printhead, the depositing may occur at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration. In this manner, a variable amount of material may be deposited in select regions of the target, for example, providing variable thickness of the deposited layer.

[0054] In certain variations, the methods involve employing both a geometrically informed non-planar (GINP) toolpath and employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

[0055] For example, in FIGS. 4A-4C, an example using this methodology and framework permits the deposition of less material in concave areas of the shape than in convex regions. FIGS. 4A-4C show examples of using a non-planar toolpath in combination with three- dimensional concrete printing (3DCP) to form a cementitious structure having a tubular geometry with sharp concave and convex geometric features. More specifically, in FIG. 4A, a new method for controlling the tool path of a printhead in 3D printing, by using a non-planar Geometrically Informed Non-Planar (GINP) toolpath, to form a 3DCP structure is shown. FIG. 4B shows a 3D-printed tubular cementitious structure created using GINP-toolpath and GIV-material deposition according to certain aspects of the present disclosure. Thus, the combination of GINP-Toolpath and GIV-Material Deposition in FIG. 4B allows for the 3D printing of structures with tubular geometries, sharp overhangs, and intricate designs, such as those produced by topology optimization (TO) or other material optimization methods. FIG. 4C shows that as the printing head moves from concave to convex areas, a respective height within each layer can change (e.g., here increase). For example, an initial height “Hl” of a given layer as shown is substantially larger than a second height “H2” of the same layer in a different region, as indicated. In certain aspects, a mathematical equation is formulated that incorporates the factors of toolpath length, robotic motion velocity, and pumping flow rate in the material deposition process. A series of geometric designs and prototyping experiments are used to measure derivations, accuracy, and precision, validating the effectiveness of these methods. Evaluation includes 3D scanning and photogrammetry techniques of the printed cementitious structures, allowing a comparison of the final printed mesh / structure to the original design.

[0056] FIGS. 5A-5B show a computational model that enables generating a non-planar (Geometrically Informed Non-Planar (GINP) toolpath) for any given geometry for three- dimensional concrete printing (3DCP) according to certain aspects of the present disclosure. Such a model can also generate data for variable material flow rates along the toolpath, as shown in FIG. 5A. This variable material flow rate can then be calculated in relation to the maximum and minimum layer heights (LH), as shown in FIG. 5B. More specifically, FIG. 5B shows a central axis 60 where two points in the center of a layer are shown. Additional points within the structure are demarcated. Point 1 (Pl) and closest point (CPI) define a first local layer height (LH1). Further, Point 2 (P2) and closest point (CP2) define a second local layer height (LH2). A speed of the robot moving the printhead (V) can be calculated. A maximum layer height is about 75% of a printhead nozzle diameter, while a minimum layer height is about 25% printhead nozzle diameter.

[0057] As noted above, the printable cementitious composition may be any of those known for additive manufacturing (e.g., 3D printing) having a fresh state and a hardened state. In the fresh state, the cementitious composition is flowable and extrudable during the additive manufacturing process, so that it may be processed, pumped, and extruded at an aperture of a nozzle during printing. However, in the hardened state, the composition desirably exhibits strain hardening behavior. In the hardened state, the cementitious composition further exhibits buildability and rapid hardening. In certain variations, the cementitious composition comprises a pozzolanic material, such as ordinary Portland cement, fly ash, and the like. The cementitious composition may further comprise an aggregate, such as a fine aggregate, or a reinforcement phase of a particle or fiber. The cementitious composition may comprise water. Other conventional ingredients may include high range water reducing agent (HRWRA), viscosity modifying agents, and other cementitious additives.

[0058] In various aspects, the methods of the present disclosure provide an innovative non-planar tool-path and segmentation approach for the robotic 3D printing of topologically optimized concrete structures In certain aspects, material usage in concrete slabs is substantially reduced, for example, by up to about 75%, to help reduce the environmental impact of the concrete industry.

[0059] As discussed above, topology optimization helps to lower concrete consumption. By coupling 3D concrete printing and topology optimization techniques to create ultralightweight concrete structures in real-world applications, material waste and carbon dioxide (CO2) emissions are reduced. In certain aspects, the methods of the present disclosure can be used for 3D printing of lightweight concrete slabs, as they account for a large portion of the overall material consumption in concrete structures (up to 80%). By providing an ability to reduce a slab’s weight, this will also serve to minimize the concrete in the foundation and vertical structural parts, improving the overall structural performance, and ultimately reduce a structure’s or building's embodied carbon footprint.

[0060] In certain aspects, the present disclosure contemplates developing a new framework for controlling the tool path and material deposition by considering geometry or a shape of the concrete part that is 3D printed, as well as the constraints of concrete rheology. As noted above, this involves both developing a geometrically informed non-planar toolpath method based on formed geometric features by developing a Geometrically Informed Non- Planar (GINP) toolpath and a Geometrically Informed Variable (GIV) Material Deposition technique to regulate the amount of material being deposited along the toolpath based on theshape of the parts being printed. As noted above, the material flow rate can be adjusted by the material flow rate or speed of the robot.

[0061] Further, the present disclosure contemplates developing a parametric model that generates data for GINP-toolpath, robotic motion parameters (e.g., velocity), and material deposition rate by considering a shape of the 3DCP part. In certain variations, this model can utilize the following equation along with the equation(s) used to establish the Geometrically Informed Non-Planar (GINP) toolpath and a Geometrically Informed Variable (GIV) Material Deposition to produce varying robotic motion velocity and material deposition.V = (Eq. 1), where F is a cementitious material flow rate [mm3 / s], V is robot printing speed [mm / s], and SA is surface area of the deposited material (for example, a rectangular- shaped filament may have a surface area calculated by w x h, where width (w) is multiplied by height ( / ?) as of the deposited material or a round- shaped extruded filament would have a surface area of it x i2, where r is a radius of the cross-sectional shape of the extruded filament).

[0062] In certain aspects, a topology-optimized 3DCP program may be provided. For example, a fabrication-informed computational design model and a parametric framework can be employed. This includes sets of robust algorithms that automatically generate the segmentation of a slab into parts, the interface between the elements, the non-planar toolpath, and the data for material deposition and robotic motion.

[0063] Prototyping, data acquisition, and evaluation can help to refine the methods described above. For example, a series of small-scale prototypes (0.5 meters high) can be produced to assess the mathematical equation and to enhance the 3DCP fabrication system. Essential fabrication data can be recorded using COMPAS FAB software and compared with the initial geometric model. A 1:1 scale slab demonstrator (1.5 x 4 meters) can be produced for investigating the assembly logic of prefabricated parts that form the slab and for informing the development of a computational design model with segmentation strategies. The 1:1 prototype helps to identify optimal combinations of segmentation, toolpath, and material deposition strategies concerning the slab's geometry and hierarchies of parts. Such design tools can effectively determine the best combination of these parameters for any specific application, whether it involves compression or tension, which was previously not possible.

[0064] FIGS. 6A-6F show a model of and a constructed example for an ultra- lightweight, freeform reinforced concrete building element 70 in the form of a shell wall according to certain aspects of the present disclosure. Construction of a “shell wall” 70 demonstrates a computational design and robotic 3D printing technology that effectivelycombines topology optimization with 3D concrete printing. FIG. 6A shows a schematic of a printhead 80 of a robotic additive manufacturing device 82 being used in a non-planar toolpath to form a shell wall 70 having complex curvatures 72 and two distinct formed channels 74 for receiving reinforcement metal rods (rebar) 76 for structural reinforcement. FIG. 6B shows a schematic of the shell wall 70 after formation via the robotic additive manufacturing device 82 in FIG. 6A, where a human 84 stands next to it to demonstrate height. FIGS. 6C and 6D are images taken from a front view and a side view of a portion of the shell wall 70 during construction via non-planar three-dimensional concrete printing (3DCP) in accordance with various aspects of the present disclosure at nearly the same point as is shown in the model of FIG. 6A. FIGS. 6E and 6F show a fully constructed shell wall 70 formed according to certain aspects of the present disclosure.

[0065] First, a computational model was developed for forming the shell wall 70 that employed a non-planar tool path (e.g., Geometrically Informed Non-Planar (GINP) toolpath) and variable material deposition (e.g., Geometrically Informed Variable (GIV) Material Deposition) based on the shape and geometric features of the topology-optimized parts, here the shell wall 70. One of the advanced features of that model is the ability to regenerate forms to closely match the initial optimization, while taking into account any fabrication and material constraints. The model automatically generates data for 3D printing, non-planner tool paths, and variable material extrusion rates.

[0066] The shell wall 70 formed in FIG. 6E is believed to be the first lightweight, structurally reinforced freeform concrete wall 3D printed. This innovative wall system features a geometry optimized to support its load case, with material distributed in a hierarchical grid of curved ribs ranging in diameter from 65 to 150 millimeters. The non-load-bearing areas between these ribs are just 6.5 to 8 centimeters deep, enabling the sandwiching of insulation between two concrete shells that are only 2.5 millimeters thick. The fields of concrete between the ribs are domed to increase stability and minimize material usage. In this embodiment, the shell wall 70 weighs only 160 kilograms about a 72% reduction in weight compared to a conventional, solid concrete wall of equivalent size.

[0067] In certain aspects, the present disclosure contemplates method of additive manufacturing a lightweight, complex geometry cementitious structure. Such a method may comprise depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The target may be either a substrate or the cementitious composition in a hardened state that was previously deposited. Thedepositing forms a plurality of layers to define an additively manufactured lightweight, complex geometry cementitious structure that is topology optimized. In certain aspects, the additively manufactured lightweight, complex geometry cementitious structure defines at least one complex region, for example, selected from the group consisting of: a branch, a concave region, a convex region, a tubular structure, a sharp angle, and any combinations thereof. A sharp angle in certain aspects may be considered to be less than 50°, for example, optionally less than or equal to about 45°, optionally less than or equal to about 40°, optionally less than or equal to about 35°, optionally less than or equal to about 30°, and in certain aspects, optionally less than or equal to about 25°.

[0068] The method may involve any of the variations described above. In one aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, complex geometry cementitious structure. Further, the depositing includes employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of cementitious material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii). In one variation, the depositing comprises (i) regulating the flow rate of cementitious material passing through the printhead, wherein the depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration. The robotic additive manufacturing device may be an automated three- dimensional printer at least partially controlled by a computer numerical control (CNC) system.

[0069] In yet further aspects, the present disclosure contemplates a method of additive manufacturing a lightweight, freeform, complex geometry cementitious structure. The method may comprise depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target. The target may be either a substrate or the cementitious composition in a hardened state that was previously deposited. The depositing forms a plurality of layers to define an additively manufactured lightweight, freeform, complex geometry cementitious structure that is topology optimized and defines at least one complex region comprising a tubular region. Further, at least one metal reinforcement is disposed in the tubular region.

[0070] In certain aspects, the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, freeform, complex geometry cementitious structure. The depositing further comprises employing ageometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of cementitious material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii). In certain aspects, the depositing comprises (i) regulating a flow rate of cementitious material passing through the printhead. The depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration. In further aspects, the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system. In certain variations, the additively manufactured lightweight, freeform, complex geometry cementitious structure comprises a shell wall.

[0071] In this manner, the methods according to various aspects of the present disclosure provide 3D printing methods that allow for minimal or waste-free concrete construction and efficient use of material by placing it precisely where it is needed for structural purposes. Such 3D printing methods also facilitate the practical implementation of 3D concrete printing by using commonly available concrete, rather than relying on highly specialized mixes. Further, in this variation, the shell wall uses a significantly smaller amount of concrete and rebar than the much larger quantities that would typically be required for a wall of the same dimensions. Thus, the present disclosure provides a lightweight and affordable 3D concrete printing system for forming complex structures that have been topology optimized, like the shell wall, to increase accessibility of the technology.

[0072] The present disclosure thus contemplates efficient concrete design and construction methods to meet demand for concrete buildings and infrastructure, while minimizing environmental impact. Combining 3D printing technologies and material optimization methods such as topology optimization (TO) and using non-planar tool paths for printheads of 3D concrete printing devices successfully creates ultra-lightweight cementitious / concrete structures with high structural performance. This includes structures that due to topology optimization methods result in complex geometries, such as branching tubular shapes with sharp angles, which cannot be realized using traditional planner toolpath methods in 3D concrete printing. The present disclosure thus contemplates non-planner toolpath methods, establishing a fabrication framework to produce any topology-optimized concrete structures to form lightweight concrete slabs that typically make up about 80% of a building's total mass.

[0073] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to thatparticular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

Claims

CLAIMSWhat is claimed is:

1. A method of additive manufacturing comprising: depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target that is either a substrate or the cementitious composition in a hardened state that was previously deposited, wherein the depositing forms at least one layer of an additively manufactured cementitious structure that is topology optimized.

2. The method of claim 1, wherein the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath.

3. The method of claim 2, further comprising developing the geometrically informed non-planar (GINP) toolpath by analyzing formed geometric features.

4. The method of claim 1, wherein the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of the cementitious composition passing through the printhead during the depositing; (ii) regulates a speed of the printhead; or (iii) both (i) and (ii).

5. The method of claim 4, wherein the depositing comprises (i) regulating the flow rate of cementitious material passing through the printhead, wherein the depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

6. The method of claim 1, wherein the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath and the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of material passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

7. The method of claim 1, wherein the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

8. The method of claim 1, wherein the at least one layer comprises a first layer and at least one additional layer and the method further comprises repeating the depositing of theprintable cementitious composition in the non-planar toolpath over the first layer to form the at least one additional layer thereon.

9. The method of claim 1, wherein the cementitious composition comprises ordinary Portland cement and water.

10. The method of claim 9, wherein the cementitious composition further comprises a reinforcement phase.

11. The method of claim 1, wherein the additively manufactured cementitious structure further comprises at least one metal reinforcement.

12. A method of additive manufacturing a lightweight, complex geometry cementitious structure, the method comprising: depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target that is either a substrate or the cementitious composition in a hardened state that was previously deposited, wherein the depositing forms a plurality of layers to define an additively manufactured lightweight, complex geometry cementitious structure that is topology optimized and defines at least one complex region selected from the group consisting of: a branch, a concave region, a convex region, a tubular structure, a sharp angle, and combinations thereof.

13. The method of claim 12, wherein the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, complex geometry cementitious structure and the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of the cementitious composition passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

14. The method of claim 13, wherein the depositing comprises (i) regulating the flow rate of the cementitious material passing through the printhead, wherein the depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

15. The method of claim 12, wherein the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

16. A method of additive manufacturing a lightweight, freeform, complex geometry cementitious structure, the method comprising: depositing a printable cementitious composition in a non-planar toolpath by passing the printable cementitious composition through a printhead of a robotic additive manufacturing device to deposit the cementitious composition onto a target that is either a substrate or the cementitious composition in a hardened state that was previously deposited, wherein the depositing forms a plurality of layers to define an additively manufactured lightweight, freeform, complex geometry cementitious structure that is topology optimized and defines at least one complex region comprising a tubular region, wherein at least one metal reinforcement is disposed in the tubular region.

17. The method of claim 16, wherein the non-planar toolpath is a geometrically informed non-planar (GINP) toolpath generated by analyzing formed geometric features of the lightweight, freeform, complex geometry cementitious structure and the depositing further comprises employing a geometrically informed variable (GIV) material deposition method that (i) regulates a flow rate of the cementitious composition passing through the printhead during the depositing; (ii) regulates a speed of the print head; or (iii) both (i) and (ii).

18. The method of claim 16, wherein the depositing comprises (i) regulating a flow rate of the cementitious material passing through the printhead, wherein the depositing occurs at a first flow rate for a first duration and the method further comprises adjusting the flow rate of the cementitious material passing through the printhead to a second flow rate distinct from the first flow rate for a second duration.

19. The method of claim 16, wherein the robotic additive manufacturing device is an automated three-dimensional printer at least partially controlled by a computer numerical control (CNC) system.

20. The method of claim 16, wherein the additively manufactured lightweight, freeform, complex geometry cementitious structure comprises a shell wall.

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