WO2025019614A2 - Additive manufacturing gradient printing method and product - Google Patents

Abstract

Disclosed herein are methods of making, systems for, and products produced by, additive manufacturing gradient printing. In certain embodiments, at least a portion of the printed product includes a continuous gradient in a particular property (e.g., stiffness).

Description

ADDITIVE MANUFACTURING GRADIENT PRINTING METHOD AND PRODUCT

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63/527296, filed July 17, 2023; the contents of which is hereby incorporated by reference in its entirety for all purposes.

BACKGROUND

[0002] The field of additive manufacturing (AM), often referred to as “3D printing,” has seen broad adoption across various applications, ranging from bioprinting for medical purposes to mechanical applications optimizing static and dynamic properties. One of the unique features of 3D printing is the ability to program spatially variant mechanical properties by varying the underlying microstructure of an object. This is often used for things like acoustic cloaking, elastic cloaking, etc. The microstructure is traditionally fabricated through two primary methods: 1) the explicit definition of the geometry or 2) implicit definition through tool path algorithms, such as volume-filling infills. In traditional manufacturing spatially varying properties are achieved through discrete lamination of materials of differing material properties. Viscous Thread Printing (VTP) is a technique to produce continuously graded materials within individual layers without the use of explicit cell design or intricate pathing algorithms. VTP uses the dynamics of the printing process to control the microstructure of the object and thus the underlying mechanical properties as a function of space.

[0003] Previous work on spatially variant mechanical material properties spans the use of topology optimization and expert design of cellular geometry. For explicit cell geometry, the printer’s resolution must supersede the cellular structure’s unit cell, typically by an order of magnitude or more. These geometries necessitate intricate cellular design through structures like octet truss unit cells or topology optimization. Yet, the cell size and design constraints often limit the applicability of explicitly defined cellular geometries in printed materials. For example, if a cell, such as an octet, is used, the unit cell must be constrained to a constant size in order to have a constant lattice spacing. This leaves the only control variable to be the diameter of the octet’s trusses. Alternatively, in topology optimization the geometry is less constrained, but the design space is significantly larger and the problem quickly becomes intractable for large objects with a high degree of variation. [0004] The production of foams in additive manufacturing requires either direct extrusion of a pre-foamed microstructure or the production of a network of materials and voids. These voids can be explicitly created as geometric features can be implicitly created by the printing process. Direct foam extrusion has had the widest adoption with applications in construction for the production for casting forms and insulation.

[0005] The creation of intricate cellular structures through traditional 3D printing requires an explicit and detailed definition of geometry. Previous art delves into the use of resin-based printing to fabricate open-cell foams with graded material stiffness. The authors employ a computational method based on a Voronoi cell structure to generate foams with spatially dependent elastic behavior. The previous art constructs a network of beams along the Voronoi cells’ boundaries, using cell shape and size to influence local stiffness. The system can be used to produce anisotropic stiffnesses in the material. The method successfully yields significant elastic differences between areas of prescribed stiffness, achieving a varied elastic stiffness on the order of magnitude from 0.5 to 2.5 MPa. While it is feasible to design and print such structures, the method demands a machine resolution significantly finer than the cell size to achieve the desired homogenized effect. This requirement inherently limits the scale of structures that can be produced.

[0006] Another approach introduces a technique for printing graded foams by dispensing liquid shell-gas droplets and photopolymerizing the shell. The approach creates both open- and closed-cell foams by using either oxygen or nitrogen as the gas to introduce foaming. The technique also achieves graded material properties by altering the cell shape and size. However, the technique demands the use of high-precision printing techniques. The machine stage must be fine enough to produce the bubbles, which form on the order of hundreds of microns. Furthermore, it is noted that the printing speed and dispensing pressure affect the filament width and shape, indicating the need for precise control. The technique can produce varied elastic stiffness of the order of magnitude from 10 to 400 kPa.

[0007] All of these methods underscore the need for high-resolution printers to achieve the desired homogenization effect, limiting their application to small-scale structures. The computational complexity of generating the explicit structure further exacerbates this limitation. In contrast, the approach allows for the definition of a coarse toolpath, akin to a traditional 3D printing infill, and leverages the physics of Viscous Thread Printing (VTP) to implicitly generate fine cellular structure. This distinction underscores the novelty and potential advantages of the disclosed method, particularly in terms of scalability.

SUMMARY

[0008] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This summary is not intended to identify key features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0009] In one aspect, a method of additive manufacturing gradient printing, also known as 3D printing, on a target location is presented, with the method comprising dispensing a viscous fluid from an apparatus, the apparatus comprising a nozzle fluidically connected to a source of the viscous fluid and moveable in relation to the target location, wherein a viscous fluid is fed through and extruded from the nozzle to yield a coiled material; moving the nozzle in relation to the target location based, the movement based on an algorithm configured to produce a structure that includes the coiled material having at least a portion that has a continuous gradient in a property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

DESCRIPTION OF THE DRAWINGS

[0010] The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:

[0011] FIGURE 1 A: An illustration of the method for creating multiple stiffness foams using viscous thread instability printing (VTP). A screenshot of a 3D model in the GUI of the application.

[0012] FIGURE IB: An illustration of the method for creating multiple stiffness foams using viscous thread instability printing (VTP). The corresponding printing tool path for the model, colored by the amount of material to be dispensed.

[0013] FIGURE 1C: Am illustration of the method for creating multiple stiffness foams using viscous thread instability printing (VTP). A photograph of the final printed structure, demonstrating the successful realization of a graded elastic structure.

[0014] FIGURE 2A: Nozzle and thread as seen during VTP, with annotations. [0015] FIGURE 2B: VTP line demonstrating the resulting coiling due to dynamically changing V* during a single linear travel move.

[0016] FIGURE 2C: V* vs Travel plot horizontally to scale with FIGURE 2B and FIGURE 2D.

[0017] FIGURE 2D: Coil Wavelength vs Travel plot horizontally to scale with FIGURE 2B and FIGURE 2C.

[0018] FIGURE 3 : Example of a VTP spread demonstrating the effects of increasing H* (along X-axis) and V* (along Y-axis) as well as the three most significant coiling patterns for VTP. From top to bottom: alternating coiling (light grey border), translating coiling (medium grey border), and accumulation (dark grey border).

[0019] FIGURE 4A: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0020] FIGURE 4B: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0021] FIGURE 4C: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0022] FIGURE 4D: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0023] FIGURE 4E: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0024] FIGURE 4F: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0025] FIGURE 4G: Each sample sets’ respective V* heatmap (with scale), printed transition region, and full effective Young’s modulus data set. Each set of images is horizontally scaled to facilitate vertical alignment for direct comparison of V*, printed region, and effective modulus.

[0026] FIGURE S: Annotated comparison of printed specimens using exemplary custom sliced toolpath generation method vs previous “zipped” method from the top and side profiles respectively.

[0027] FIGURE 6A: Normalized semi-log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4B.

[0028] FIGURE 6B: Normalized semi-log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4C.

[0029] FIGURE 6C: Normalized semi-log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4D.

[0030] FIGURE 6D: Normalized semi -log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4E.

[0031] FIGURE 6E: Normalized semi-log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4F.

[0032] FIGURE 6F: Normalized semi -log plots of average effective compressive Young’s Modulus within sample transition zones fitted with exponential trend lines. The shown data is the data between and including the black vertical bars of FIGURE 4G.

[0033] FIGURE 7 Images taken during testing for each sliced and zipped sample group. Each set from left to right depicts the beginning of testing (no deformation), 35 seconds into testing, and time of failure.

[0034] FIGURE 8A: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group. [0035] FIGURE 8B: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0036] FIGURE 8C: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0037] FIGURE 8D: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0038] FIGURE 8E: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0039] FIGURE 8F : Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0040] FIGURE 8G: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0041] FIGURE 8H: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0042] FIGURE 81: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0043] FIGURE 8 J: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0044] FIGURE 8K: Compiled average stress strain curves for each sample group. Note: each stress-strain curve is truncated to the lowest fracture stress within its given sample group.

[0045] FIGURE 9A: Tensile plots containing significant data from Table 1.

[0046] FIGURE 9B: Tensile plots containing significant data from Table 1.

[0047] FIGURE 9C: Tensile plots containing significant data from Table 1. [0048] FIGURE 9D: Tensile plots containing significant data from Table 1.

[0049] FIGURE 10 A: 2D overview of point interpolation.

are identified for query points p_a and pp.

[0050] FIGURE 10B: 2D overview of point interpolation. Relevant intersection region is determined by comparing

to D_T. pp is contained in the intersection region, while p_a is not.

[0051] FIGURE 10C: 2D overview of point interpolation. Finally, pp is assigned TTj using the weighting function as described in the specification, while pp is assigned TT¹.

[0052] FIGURE 11 A: Two examples of different transition functions affecting V*. On the is a linear transition while on the right is a logarithmic transition, both over 75 mm.

[0053] FIGURE 11B: Two examples of different transition functions affecting V*. On the is a linear transition while on the right is a logarithmic transition, both over 75 mm.

[0054] FIGURE 12: A probing the compressive modulus of a dogbone featuring a logarithmic transition between F*’s.

[0055] FIGURE 13A: Compressive modulus measured along the dogbone. The dogbone with a linear V * (bottom figure, dashed line) was printed first and the modulus was characterized as a function of space (top FIGURE curved line). The log-linear fit was applied to this data to arrive at the values needed to invert the behavior. A logarithmic change in V * was applied (bottom figure, dashed curve) and the corresponding modulus was fit to a linear curve (top figure, solid line with measured values). This shows that the exponential relationship between V * and modulus can be accounted for.

[0056] FIGURE 13B: Compressive modulus measured along the dogbone. The dogbone with a linear V * (bottom figure, dashed line) was printed first and the modulus was characterized as a function of space (top FIGURE curved line). The log-linear fit was applied to this data to arrive at the values needed to invert the behavior. A logarithmic change in V * was applied (bottom figure, dashed curve) and the corresponding modulus was fit to a linear curve (top figure, solid line with measured values). This shows that the exponential relationship between V * and modulus can be accounted for.

[0057] FIGURE 14 A: A pattern template that the algorithm uses to instruct the movement of the nozzles to manufacture gradient patterns of coiled material with gradient modulus. [0058] FIGURE 14B: Example of a printed coiled material in a hexagonal pattern.

[0059] FIGURE 14C: Example of patterns of coiled material with gradient modulus printed in alternating rotations of a quadrilateral pattern.

[0060] FIGURE 14D: Close in view of patterns of coiled material with gradient modulus printed in alternating rotations of a quadrilateral pattern.

[0061] FIGURE 14E: Close view of patterns of coiled material with gradient modulus printed in alternating rotations of a quadrilateral pattern.

[0062] FIGURE 15 A: Examples of multi-modulus printing. A cube with low modulus living hinges in the unfolded state.

[0063] FIGURE 15B: Examples of multi-modulus printing. A cube with low modulus living hinges in the folded state.

[0064] FIGURE 15C: Examples of multi -modulus printing. A foot orthotic with low moduli in high stress areas (e.g., ball and heel of foot), V* range 0.15-0.4.

[0065] FIGURES 15D and 15E: Examples of multi-modulus printing. Top-down shots of linear (FIGURE 15D) and logarithmic (FIGURE 15E) transitions between areas of different moduli on the dogbones, V* range 0.15-0.4.

DETAILED DESCRIPTION

[0066] Disclosed in this application are methods and materials to produce by means of additive manufacturing (AM), also known as 3D printing, and Viscous Thread Printing (VTP) foams with gradient property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

[0067] In one aspect, a method of additive manufacturing gradient printing, on a target location is presented, with the method comprising dispensing a viscous fluid from an apparatus, the apparatus comprising a nozzle fluidically connected to a source of the viscous fluid and moveable in relation to the target location, wherein a viscous fluid is fed through and extruded from the nozzle to yield a coiled material; moving the nozzle in relation to the target location based, the movement based on an algorithm configured to produce a structure that includes the coiled material having at least a portion that has a continuous gradient in a property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

[0068] As used herein, the term “continuous gradient” refers to a product resulting from the disclosed method of viscous thread instability printing (VTP) by means additive manufacturing (3D printing) where a physical, mechanical, or structural property of changes from one region of the product to another region of the product in a continuous linear, continuous parabolic, continuous hyperbolic, continuous wave, continuous circular, or combinations thereof.

[0069] FIGURE 1A-FIGURE 1C illustrate the process of the disclosed method for creating multiple stiffness foams using VTP by a rendition of a 3D model in the GUI of the application followed by corresponding printing tool path for the model, colored by the amount of material to be dispensed, and printing the structure, demonstrating the successful realization of a graded elastic structure.

[0070] In some embodiments a method of additive manufacturing gradient printing is presented wherein the coiled material resulting from manufacturing is a foam.

[0071] Disclosed are materials and methods to take advantage of VTP to produce foams with multiple stiffnesses, densities, and continuous gradients between them. By dynamically manipulating print parameters during slicing, an innovative method of generating graded foam structures on a standard FFF 3D printer. With this approach, foams are produced of varying stiffness along the principal axes, decreased print artifacts and boundary defects. In turn, these structures have improved failure performance over previous state-of-the-art by having higher fracture stress, fracture strain, and toughness. This showcases the potential of VTP to revolutionize the fabrication of graded foams for a multitude of applications.

[0072] In some embodiments a method of additive manufacturing gradient printing is presented wherein the foam has the structural property of a density, and the density varies as continuous gradient through at least a portion of the foam.

[0073] In some embodiments a method of additive manufacturing gradient printing is presented wherein the viscous fluid for dispensing is inside a same layer or across the layers.

[0074] In some embodiments a method of additive manufacturing gradient printing is presented wherein the extrusion of the viscous fluid during dispensing results in viscous thread instability.

[0075] In some embodiments a method of additive manufacturing gradient printing is presented wherein dispensing the viscous fluid allows for viscous thread printing. A standard software slicer does not take into account the differences from surfaces to make a transition region and then use the value of a signed distance field. The methods of this disclosure address these limitations in the art. The methods disclosed vary V and H to get the coiling pattern. The foam has a gradient that is non-linear along a single direction but is instead a 2D or 3D gradient structure.

[0076] Parameters used to determine the coiling behavior of VTP inculde the dimensionless velocity variable V* and the dimensionless height variable H*,

where F is the translation speed of the printhead, C is the exit speed of the material from the nozzle, H is the print height, D is the nozzle diameter and a is a die swell constant for the material, which is a material and process dependent constant that is determined empirically. Each of these variables can be controlled either explicitly or implicitly directly through G-code commands. Together, the

combination determines the type of coiling behavior exhibited and spatial frequency of the coiling as well as the coil diameter respectively. The variables are illustrated in FIGURE 2A- FIGURE 2D.

[0077] In some embodiments a method of additive manufacturing gradient printing is presented wherein for the dispensing there are two or more nozzles that are movable independently or parallel of each other.

[0078] In some embodiments a method of additive manufacturing gradient printing is presented wherein the extrusion the nozzle for dispensing of the viscous fluid at a translation speed, an extrusion speed, at a nozzle height, a material and process dependent die swell constant, results in coiling of the extruded material.

[0079] In some embodiments a method of additive manufacturing gradient printing is presented wherein the dispensing from the nozzles results in producing the same object.

[0080] There are three main regimes of coiling that are of interest for VTP foams: translating coiling, alternating coiling, and accumulation shown in FIGURE 3. Translating coiling results from a specific combination

to produce a continuous path of overlapping loops of material. Translating coiling is interesting because it allows for the greatest number of interconnections of a single thread producing a structure that is dense while maintaining porosity and uniformity. Alternating coiling results in coils that are further spaced apart, producing fewer interconnections and a less dense structure. Finally, accumulation is the closest to traditional 3D printing techniques with a low V* and low H* and can produce parts that are nearly 100% dense and extrusion widths many times greater than the nozzle diameter via over-extrusion; however, it does not result in porous structures.

[0081] In another aspect, a coiled material structure resulting from additive manufacturing is presented, with the coiled material structure comprising the coiled material having a variable plurality of successive coils along an x-axis, a y-axis, a z axis, or any vector thereof with at least a portion of the coiled material having continuous gradient in a property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

[0082] In some embodiments, a coiled material is presented, wherein the coiled material is a polymer, a metal, a glass, or a ceramic.

[0083] In some embodiments, a coiled material is presented, wherein the polymer can be thermoplastic polyurethane, polylactic acid, styrene, acrylic, acrylonitrilebutadiene- styrene, nylon, or silicone,

[0084] In some embodiments, a coiled material is presented, wherein the polymer has a pigment dispersed therein.

[0085] In some embodiments, a coiled material is presented, wherein the pigment comprises a metal, a metal alloy, a salt, a ceramic, or combinations thereof.

[0086] In some embodiments, a coiled material is presented, wherein the coiled material can be deposited as a free flowing solid, a melt, a solution or a vapor.

[0087] In some embodiments, a coiled material is presented, wherein the coiled material is crosslinked, sintered, melted, ionized, or combinations thereof.

[0088] Controlling the ^7#' _of _a printed obj ect is done implicitly by setting the correct print and extrusion speeds of the printing process. A G-code command G1 instructs the printer to move from its current position (x₀, y₀, z₀) to a new position (x, y, z) at a certain speed , while extruding de length of material. In a G-code file this looks like G1 Xx Yy Zz E e F , where G1 and the bold capital letters are alphabetical characters, and the lowercase letters represent numerical positions for the printer to parse. The x and y positions are determined by the object’s infill toolpath, whereas z, de and and values to be solved for. The equations to generate G-code information from

inputs are then

where E is the constant speed to feed filament into the nozzle, L is the Euclidean distance of the G-code move, while A_T is the cross-sectional area of thread being extruded accounting for the die swell, and A_T is the cross-sectional area of filament being fed into the extruder. To generate spatially varying V*/H* _areas of constant V* /H ' must first be defined and regions between them are called the transition regions. For notation the method discloses employs a subscript/superscript distinction, where the superscript will always denote a mesh-wise quantity, while a subscript will always denote a point- wise quantity.

[0089] In some embodiments a method of additive manufacturing gradient printing is presented wherein the G-code for moving the nozzle in spatial coordinates has a command, Gl, wherein G1 instructs the nozzle to move from the nozzle current position (JO, O, ^0) to a new position (

form Gl X YyZ^EA<?F/’, where Gl XzY/ Z^ EA<? F/’, wherein Gl and the capital letters are character literals, and the lowercase letters represent numerical values for the printer to parse.

[0090] In some embodiments a method of additive manufacturing gradient printing is presented wherein the additive manufacturing gradient printing by the algorithm for moving the nozzle results in a product.

[0091] In some embodiments a method of additive manufacturing gradient printing is presented wherein A e is the amount of filament extruded in millimeters over each segment and f is the speed at which the printer head travels over the segment in millimeters per minute.

[0092] In another aspect, a software program is presented for the generation of an algorithm for a translating or alternating coil structure of graded viscous thread printed foams resulting from additive manufacturing, the software program comprises a controller within the apparatus of Claim 1, wherein the controller has a communications port; a plurality of sensors configured to generate data based on a material’s physical properties which are communicated through the communications port to the software program; wherein the software program uses the data to generate the algorithm along with input from the user; wherein the communications port is configured to receive the algorithm generated by the software program; and wherein the controller is configured to direct the nozzle of Claim 1 based upon the algorithm generated by the software program to extrude a material resulting in the translating or alternating coil structure.

[0093] First, part of the algorithm of the presented method is to load multiple submeshes into the custom slicer of this disclosure where 12⁷ represents submesh j, d represents the surface of f ⁷, and Q_ = U -g_Mf2⁷ is the total unioned mesh for the set of meshes M. These meshes are assumed to have constant cross-section in z and be nonoverlapping but have some interfacing boundary. Each submesh is given

pair assigned by the user, which are then combined in the notation ^{71-7 =}

}. Other global variables, such as toolpath spacing, effective layer height, transition length and toolpath discretization length, and die swell are also set by the user up front.

[0094] In some embodiments a method of additive manufacturing gradient printing is presented wherein the algorithm programs the moving of the nozzle in spatial coordinates.

[0095] In some embodiments a method of additive manufacturing gradient printing is presented wherein the algorithm for moving the nozzle in spatial coordinates is a G-code that programs movement of the nozzle.

[0096] In some embodiments a method of additive manufacturing gradient printing is presented wherein the additive manufacturing gradient printing by means of the algorithm for moving the nozzle results in a macroscopic pattern.

[0097] This disclosure begins the slicing process by taking Q_ and feeding it to a traditional slicer (Slic3r), which generates a toolpath traversing the entire space Q_. Then follows is a refinement of each of the linear toolpath sections into subsection of length d < d-mnx which establishes the resolution of the Z⁷^ transitions.

[0098] The transition algorithm of the disclosed method associates each point along the toolpath p_t with interpolated values by determining the weighted average of all the relevant submesh values. Relevant submeshes are determined by finding the distance between point pt to dfY. Here, the disclosed method uses the signed distance between

point is said to be in a transition region f2^T if the distance from point pt to some df2⁷ is less than the user defined transition length, that is

< D_T => p_t E f2^T . Then the weights contributed by each submesh are:

and the / values at point

are

[0099] To test the disclosed slicer algorithm samples were made and compared using the disclosed algorithm using various transition lengths, with the base materials and a simple base slicer. For all specimens labeled TLXX, the above method was implemented for a bisected ASTM dogbone structure. For specimens labeled VO.15 and VO.40, they were sliced with a normal slicer and altered the output G-code file directly using equations 3-5 through a custom python script. Finally, for the specimen labeled Zipped, each half of the dogbone was sliced separately and then “zip” the two separate G-code files together where layer 1 of the first file is printed and then layer 1 of the second file is printed in sequence, and so on. This represents the previous state-of-the-art for multi-material printing of VTP foams.

[0100] For the validation ASTM Standard D638-10 Type III dogbones were printed out of NinjaTek NinjaFlex thermoplastic polyurethane (TPU). However, many types of polymers or materials can be utilized in the techniques presented in this disclosure.

[0101] In some embodiments a method of additive manufacturing gradient printing is presented wherein the dispensing coiled material is a polymer, a glass, a metal, or a ceramic.

[0102] In some embodiments a method of additive manufacturing gradient printing is presented wherein the polymer can be thermoplastic polyurethane, polylactic acid, styrene, acrylic, acrylonitrile-butadiene-styrene, nylon, or silicone,

[0103] In some embodiments a method of additive manufacturing gradient printing is presented wherein the polymer has a pigment dispersed. [0104] In some embodiments a method of additive manufacturing gradient printing is presented wherein the pigment can comprise of a metal, a metal alloy, a salt, or combinations thereof.

[0105] In some embodiments a method of additive manufacturing gradient printing is presented wherein the dispensing coiled material can be deposited as a free flowing solid, a melt, a solution, or a vapor.

[0106] In some embodiments a method of additive manufacturing gradient printing is presented wherein the dispensing coiled material is crosslinked, sintered, melted, ionized, forms a solid by means of evaporation of a solvent, or combinations thereof.

[0107] In some embodiments a method of additive manufacturing gradient printing is presented wherein an electrostatic charge is placed upon the viscous fluid during dispensing.

[0108] The dogbone STL was split in half at the midway mark and various transition lengths were applied to create a linear gradient in V" along the axial direction of the dogbone. Localized compression tests were conducted at 5 mm increments with a 10 mm diameter probe along the transition length to capture the variation in compressive modulus of the foams. The probe was printed on a Carbon Ml out of UMA-90. ASTM Standard D638-10 tensile tests were performed on an Instron 68 SC-2 to measure the effective tensile modulus of the dogbone specimen as well capture fracture stress, fracture strain, and toughness.

[0109] In some embodiments a method of additive manufacturing gradient printing is presented wherein the foam has the mechanical property of a modulus, and the modulus is a continuous gradient of modulus properties.

[0110] FIGURE 5 illustrates the impacts of the two slicing methods. The upper row presents the result of the disclosed new slicing algorithm creating a continuous toolpath, while the lower row depicts a specimen created using the zipped method. Both cases reveal a distinct interface between V* — 0.40 and V* — 0.15. However, a noticeable ‘bump’ artifact emerges in the side view of the zipped version, resulting from the overlapping printed paths at the interface. The two slicers have qualitatively different edge crispness, as the zipped method introduces thickening at the edges. Additionally, the non- continuous movements of the zipped method introduces travel artifacts that are embedded in the print. [OHl] This result illustrates the utility of the disclosed new slicing method for VTP foams in padding applications such as padding such as automotive seats, orthotics, and personal protective equipment. The defects from zipped sections would create unpleasant pressure points in these applications. The new slicer by contrast produces structures with a less pronounced pressure point.

[0112] In some embodiments a method of additive manufacturing gradient printing is presented wherein the seat produced by the method of additive manufacturing gradient printing is a seat, a furniture, a filter, or a medical implant.

[0113] In some embodiments a method of additive manufacturing gradient printing is presented wherein the seat produced by the method of additive manufacturing gradient printing is used for an automobile or an aircraft.

[0114] FIGURE 4 A - FIGURE 4G details the local compressive modulus testing conducted on the dogbone structure. Here, V* linearly increases from 0.15 to 0.40, with varying transition lengths represented by vertical black lines for clarity. The compressive modulus remains largely unchanged outside the transition region, whereas inside this region, observed is a distinct modulus alteration. This phenomenon is further investigated in FIGURE 6A - FIGURE 6F where an exponential curve of the form f (x) = Ae^yx is fitted solely to the transition regions. In each subplot, the transition region is normalized to length one, allowing for direct comparison of the exponent term, corresponding to the line’s slope in the semi-log plot. As the transition region increases (i.e., acquires more data) the y term converges which indicates that the modulus as a function of V* is constant for transition lengths greater than zero.

[0115] FIGURE 7 shows an abbreviated timelapse of the tensile tests from each TL family. The images capture three critical points: test initiation, mid-test at the 35-second mark, and the test conclusion. From these elements it can be seen that the transition length leads to distributed strain across the top and bottom halves of the samples for transition lengths 20mm and larger. This creates a more uniform transmission between the sections under loading.

[0116] FIGURE 8 A - FIGURE 8K presents the mean stress-strain curve for each TL family, enclosed by their respective max and min boundaries. Due to variability in test durations within each TL family, data was truncated at the shortest test time to enable average calculation. The stiffest specimen (V015) is truncated vertically in the topmost plot to focus on the transition specimens, while the most compliant specimen (V040) lies beneath the transition specimens. The stress-strain curves for all TL families closely align, suggesting similar performance in modulus, fracture stress, fracture strain, and toughness. Table 1 and FIGURE 9A - FIGURE 9D summarize the results from these stress-strain curves.

[0117] It was found that dogbones with transitional regions exhibit similar elasticity to naively zipped dogbones. However, the dogbones notably outperform the zipped versions, exhibiting higher fracture stress, enhanced fracture strain, and superior toughness. This improved performance holds even in the context of zero-length transitions (TL00), where the VTP-sliced dogbones outperformed the zipped versions. This is attributed to the continuous toolpath created by the disclosed method.

[0118] Table 1 shows the tensile modulus averaging 2.046 MPa across all transition families with a standard deviation of 0.115 MPa while the zipped dogbone has a modulus of 2.185 MPa. This indicates that tensile modulus of the dogbones is nominally constant as long as the average value of V* across the length of the dogbone is constant. V* is defined to be the integral of

over the entire length of the dogbone where x is the location on the dogbone and L is the desired transition length. In the case of a linear U*it is equivalent to the average of the maximum and minimum V* values multiplied by the dogbone length. This value is constant for both VTP sliced dogbones as well as the zipped dogbones. There is a clear indication that a simple method of determining dogbone tensile equivalence is to compare the V* value obtained from a curve.

[0119] While V* is linear in x, the compressive modulus E_c{x, L) changes exponentially as seen in FIGURE 4 A - FIGURE 4G and FIGURE 6 A - FIGURE 6F. Values of the exponential fits (7 and A) were averaged from FIGURE 6A - FIGURE 6F to determine a general fit for the transition region

The modulus is also exponential in V* because V* is linear in x. This means that with a logarithmic definition of *(U ) a linear transition of modulus is achievable. [0120] Table 1 also shows that the fracture stress, fracture strain, and toughness are consistent regardless of transition length, while the zipped dogbones performed at a much lower level. Predictably, the zipped dogbones, without a continuous toolpath between the differing V* regions, fractured much earlier than the continuous transitions, likely due print errors and stress concentration at the interface. Compared directly to the TL00 sample, there was an approximate 33% increase in fracture strain and a 10% increase in fracture stress simply by using the continuous toolpath method without any transition length. This demonstrates that simply having a continuous toolpath between disparate areas can significantly improve the reliability of the sample and further benefits are seen when applying the transition over a region.

[0121] In some embodiments a method of additive manufacturing gradient printing is presented wherein the coils change in type, size of periodicity while being connected as a continuous strand during dispensing.

Table 1. Summary statistics for the tensile tests performed on the dogbones. Each row represents the average followed by standard deviation of 5 tests on dogbones printed with the same parameters. The mean of averages and mean of standard deviations of the samples printed with the new technique are given. The previous state-of-the-art and homogenous dogbone summaries are given at the bottom. No data is presented for VO.40 and VO.15 because the tests did not result in fracture.

[0122] A further extension of the disclosed methods is interpolating V*/H*, FIGURE 10A - FIGURE 10C. Viscous Thread Printing (VTP) operates as a constant extrusion process, requiring a single, uninterrupted tool path to fill the entirety of Q To do this a few design constraints are implemented: 1) meshes must be non-overlapping but share a boundary with at least one other mesh, 2) meshes can share a boundary with at most one other mesh. An implication of these two constraints is that the union of all meshes, denoted as

must form a single, continuous domain. Q is then sliced in a traditional manner and return a single tool path across the unioned domain. Finally, the tool path was refined into smaller segments and query points along the tool path using the disclosed interpolation scheme to determine the 7 t each point. The end result is a 3D- printable file, called GCode, with extrusion values that match the continuous space of graded V *IH * values.

[0123] The combination of union and intersections is a further extension of the disclosed methods. The are defined to be non-overlapping with a shared boundary. This is done to have a clearly defined surface inside of Q that will serve as the mid-point of the interpolation scheme. In theory, touching and non-overlapping domains will have a continuous and void free union; however, the triangular meshes common in 3D printing introduce floating point error which may be enough to introduce void artifacts on the interior of a unioned mesh. Thus, augment to all the submeshes a small amount to find Q through an algorithm outlined below in algorithm 1. The mesh intersections are computed in a similar manner via first augmentation and then a mesh boolean intersection operation. The augmentation by small c ensures that meshes will overlap only with their adjacent counterparts and not meshes an appreciable distance away. Once again, because < is small compared to mesh size the intersection meshes approximate shared boundaries between meshes well.

[0124] Interpolation scheme is a further extension of the disclosed methods. FIGURE 10A - FIGURE 10C illustrates a 2D overview of point interpolation. To determine the /rfor every point along the tool path in Q it is first look at the general case of interpolation. The method first associates a TT⁷ with each

which define regions of constant /ZA The method then query a point p/ . Q to determine 71/ This is done by first calculating the signed squared distance functions first to each f to determine which mesh Pi belongs to. Because the meshes are assumed to be non-overlapping, but have an interfacing boundary,

can be guaranteed to be uniquely mapped to a single

up to the submesh boundary.

[0125] The disclosed method then calculates a signed distance

between p^ and each intersection mesh. The method cannot use the same squared distance sign as before, however, because there may be cases where a point is closer to an unshared boundary than a shared one, which would lead to an inaccurate distance calculation from the intersection. Each intersection is associated with two submeshes Q⁷ and , a transition length and a weighting function w x;s') that defines how ovaries within the transition region. A transition region has orientation and is denoted by

where the orientation k informs the direction from Q⁷ to Q . Thus, a point is said to be in a transition region if where the sign of

determines if pps in

or ^fc. Once again, y?, can

be uniquely determined to belong to a single transition region due to the assumption that mesh boundaries may only be shared by one other mesh.

[0126] Because the transition region is associated with an orientation between two meshes the method can define a mapping w [0, 1] as a weighting

function between

to Q^across a length D_T. Specifically, for the points inside Q

k negative, and for the points in Q Z^ is positive. The user may freely choose the direction of interpolation function across the mesh boundary. More formally,

where x = — and s is a weighting function specific parameter. The VTP parameters can

[0127] The weighting functions presented in this work are listed here as w(x; s) where xis the distance from the transition intersection normalized by the transition length D_T and s is a transition function specific parameter set by the user. The meaning of parameter v is unique to the specific weighting function and is called out in each section, or if a function does not use s, it is omitted. All weighting functions guarantee continuity with the associated with the ends of the transition and other constraining equations are listed if used. The one exception is the empirically derived logarithmic function which was fit to data and not analytically derived.

[0130] where the control parameter vsets the slope of the function at x= 0

14] w ' (x; s) = s

[0131] A special case of the cubic function is s= 1.5 which also guarantees U ¹ continuity at the ends of the transition region.

[0132] Experimentally fit logarithmic is a subset of the methods being presented in this disclosure. The logarithmic function was derived by inverting the log-linear fit of the measured modulus data E(x). Because of error in the measurement, the V* do not align perfectly at the boundary conditions x

where E(x) = 23.9 lx + 13.26 a = 4.79 b = -3.11

Cube root

[0133] A custom VTP slicer program was built utilizing libslic3r for initial toolpath generation and libigl for the GUI and some geometry operations, with all other algorithmic implementation details being part of the disclosed method. An example of implementation is shown in FIGURE 11A - FIGURE 11B which shows an interpolative slicing algorithm for continuously graded stiffness in VTP foams. The VTP slicer is able to import meshes of multiple formats, assign a U and H* to each mesh, and define the transitions between these different meshes. The users are also given an option to view an intersection and can select a specific one, which will be highlighted on the GUI. The transition can be defined in terms of what function it takes on, the direction of that transition, and the length of the transition. The disclosed method is able to define the other miscellanea involved in 3D printing such as layer height, line spacing, etc.

[0134] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein the software program communicates to a system comprising an apparatus, the system further comprising a smart device communicatively coupled to the apparatus, wherein the smart device is configured to issue the instructions to the apparatus.

[0135] As it stands, the disclosed slicer is capable of processing parts intended to have multiple densities, if the following constraints hold:

• As discussed in the previous section, the meshes must interface to form a continuous domain, with a mesh sharing a boundary with at most one other mesh.

• Q must only produce one polygon when sliced with a z-oriented plane. The reason for this is that introducing multiple polygons on a single layer would necessitate a discontinuous toolpath or undesired strands outside the geometry definition.

[0136] Mesh Augmentation is part of the methods of this disclosure. As mentioned above, touching and non-overlapping domains should have a continuous and void free union; however, floating point errors may be enough to introduce undesired artifacts in the combined mesh. To augment the mesh and ensure well-formed Boolean operations are possible the disclosed methods expand the mesh by a small distance e. Since 6 is small (approximately 2-3 orders of magnitude smaller than the mesh itself), it is determined the computed Q approximates the entire domain well without distorting the original design intent of the shape.

Table 2: An Interpolative Slicing Algorithm for Continuously Graded Stiffness in Viscous Thread Printed Foams

[0137] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein the software program encodes to generate a Mesh Boolean Operation.

[0138] Toolpath Refinement is part of the methods of this disclosure. After the union of all the submeshes was computed, the submeshes were fed into libslic3r in order to get a toolpath that covers the whole mesh. A toolpath in this case is nothing more than a list of segments, which indicate what path the nozzle of the FDM printer is to follow. The algorithm can only vary printer behavior across different segments, so for changes in 7^* or H * to be perceivable, these segments are needed to be short. The toolpath segments received from libslic3r are rather coarse; however, with each segment spanning the entire part, and its endpoints lying on the boundary of Q The algorithm therefore runs a refinement operation on it so that the toolpath has the necessary resolution. The algorithm does this by discretizing each toolpath segment into multiple segments of a length specified by the user. This gives the algorithm a list of small toolpath segments with which the algorithm can associate a * and H* . The query point used to determine the V* and H* of each segment is its end point, which as part of the method is fed into the interpolation function.

[0139] Toolpath Interpolation. To implement the interpolation function, the interpolation function is to first find a point’s associated mesh by utilizing the minimum of the signed distance from pj to d Q^], denoted as D- = minSDF(pj, Q^]), where D- < 0 implies that pi E Q^] . Similarly, it is required to find all D[, the signed distance from point pi to an intersection. However, using a signed distance function will always result in a non-negative distance since the intersections are slim meshes with virtually no volume, and any points inside the intersection mesh can be assumed to have zero distance to its boundary. For interpolation functions with derivative functions symmetric around the y axis, the workaround is quite straightforward because the direction of the intersection does not matter. Thus, W[ for pi E Q^] can be calculated as if

is always the second mesh with the positive Di. However, for other types of functions, such as the logarithm, the direction matters, and the algorithm must keep track of the directions for each intersection and manually adjust the signs of Di based on the direction and the mesh associated with Pi as mentioned above.

and the direction identified, V*/H* can easily be obtained using the interpolation functions defined in Appendix A. When all the points on the toolpath are characterized, the slicer is ready to translate the V* and H* values into G-Code variables.

Table 3. An Interpolative Slicing Algorithm for Continuously Graded Stiffness in Viscous Thread Printed Foams.

[0140] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein software program encodes to find a dimensionless velocity variable, V*, and a dimensionless height variable, H*.

[0141] In some embodiments a method of additive manufacturing gradient printing is presented wherein the method of additive manufacturing gradient printing generates a foam, wherein the velocity and height of the nozzle during dispensing is varied, the extrusion rate is varied or the velocity, the height of the nozzle and the extrusion rate are varied simultaneously to inducing multiple codings from a continuous extrusion path.

[0142] Next, the G-Code needs to be generated. Once the V *IH* of each point by inputting it into the algorithm is determined, the position of the toolpath in space can be determined and generate the remaining variables needed to fully characterize the print. These parameters ultimately are translated into G-code commands that the FDM printer can execute, which is now described as follows. [0143] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein the software program produces a G-code command.

[0144] A G-code command G1 instructs the printer to move from its current position (x₀, yo, ^zo) ^{t0 a new} position (x, y, z) at a certain speed f, while extruding A e length of material. In a G-code file this looks like G1 Xx Yy Zz E A e Ff, where G1 and the capital letters are character literals, and the lowercase letters represent numerical values for the printer to parse. The x and y positions are determined by the object’s infill toolpath, whereas z, e and, f are values to be solved for.

[0145] The first value required is the distance by which is needed to raise each point in order to achieve the desired coiling behavior. This value can be calculated by using the associated H* of each point, using the following formula, where dz is the layer height and DN is the nozzle diameter, z_Off_set = aD_NH* — dz. Since Hbslic3r gives us the toolpath directly on top of each layer with no offset, it is simply added z_opp_set to the current z-value of each point to get the final position of the nozzle.

[0146] The remaining values to generate for each G-code command are A e, the amount of filament extruded in millimeters over each segment, and , the speed at which the printer head travels over the segment in millimeters per minute. Using the V* associated with the point, these values can be derived using the formulas 4 and 5 presented above where L is the distance between pi and Pi— i-

the previous point selected is printer specific, generally being close to the origin. Once these values are determined, then all of the information that characterizes the behavior of the printer is in hand and can write the G-code that will produce the specified part.

[0147] With the algorithm characterized, VTP control and characterization can be performed. The data gathered on an apparatus shown in FIGURE 13 A - FIGURE 13B from the printed ASTM Standard D638-10 Type III dogbone structures provide a quantitative demonstration of the disclosed method’s ability to control the modulus through graded VTP parameters. An initial linear U* gradient (dashed line) with a transition length of 40 mm was used across the 60 mm neck length. F* values at the ends were 0.15 on the left and 0.4 on the right. The linear F * gradient resulted in an exponential decrease in themodulus from left to right (solid curve and measurements). This outcome is evident in the modulus data, which were fitted with an exponential curve (A(x ) = 4.79e , 2 •

0.987) as described above. [0148] To further validate the disclosed method, the approach is adjusted in response to these findings. A logarithmic sweep is implemented of U* (dashed curve) using the fitted parameters from the initial linear gradient. Due to measurement error in the exponential fit, the U* values are discontinuous as the ends of the transition region and are 0.1415 on the left and 0.3795 on the right. Despite this error, the logarithmic V * successfully achieved a linear decrease in modulus across the dogbone (E (x) = -24.15% + 11.47, R² 0.977) (solid line and measurements), as opposed to the initial exponential decrease.

[0149] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein the translating or alternating coil structure has a gradient in a physical property, a mechanical property, a structural property, or combinations thereof.

[0150] In an embodiment a software program for generation of an algorithm is presented for a translating or alternating coil structure, wherein the gradient in a physical property, the mechanical property, the structural property, or combinations thereof is a porosity, a stiffness, a hardness, a permeability, a tensile, a modulus, an elongation, an elasticity, or combinations thereof.

[0151] This result, as illustrated in FIGURE 13 A - FIGURE 13B, confirms that the modulus of the printed material can be manipulated by adjustment of the VTP parameters. FIGURE 14A - FIGURE 14E shows a modeled template in which the algorithm uses to print materials in hexagonal and quadrilateral patterns. The data show that the disclosed method provides a robust and flexible approach to controlling mechanical properties of 3D printed materials.

[0152] Next, the disclosed methods were tested in applications that use multimodulus and graded modulus structures, as demonstrated in FIGURE 15 A - FIGURE 15E. First, a cube was generated with low modulus living hinges (F *=0.15 or 0.4, transition length zero), shown in its unfolded state, and in its folded state, which exemplifies the potential for creating complex, foldable structures. Low modulus hinges allow for easy folding and unfolding, which could be beneficial in applications such as soft robotics, packaging or deployable structures. The ability to print structures with varying stiffness within a single print can significantly enhance the functionality of these systems. For instance, areas of the structure that need to be rigid can be printed with a high-modulus material, while areas that need to flex or fold can be printed with a low-modulus material. This could allow for the creation of deployable structures with complex folding patterns or robots that have shock absorbing features built into the frame.

[0153] The foot orthotic (7*=0.15-0.4, linear transitions, 10 mm), designed with low modulus in areas of high stress such as the ball and heel of the foot, exemplifies the potential to create customized and comfort-enhancing products using the disclosed method. The ability to vary the modulus within a single print allows the creation of personalized cushioning objects that can provide targeted support. This application has significant implications for the field of orthotics, where custom-fit devices can greatly improve user comfort and functionality. Beyond orthotics, this method could also be applied to create custom cushioning for wheelchair seats and sockets for prostheses, improving comfort and reducing the risk of pressure sores or skin lesions.

[0154] The linear and logarithmic transitions between areas of different moduli on the dogbones (V * from 0.15 to 0.4, linear/log transitions, 40 mm transition length) demonstrate the disclosed method’s ability to create graded structures with continuous material property transitions. This capability is crucial in applications requiring gradual property transitions, such as load-bearing structures or components subjected to varying stress conditions. For instance, aerospace and automotive industries could leverage this for components that need to withstand different pressure, temperature, or impact conditions. Similarly, in biomedical engineering, graded materials could be useful for designing implants or prosthetics with varying tissue-mimicking properties.

[0155] The complete disclosure of all patents, patent applications, and publications, and electronically available material cited herein are incorporated by reference in their entirety. Supplementary materials referenced in publications (such as supplementary tables, supplementary figures, supplementary materials and methods, and/or supplementary experimental data) are likewise incorporated by reference in their entirety. In the event that any inconsistency exists between the disclosure of the present application and the disclosure(s) of any document incorporated herein by reference, the disclosure of the present application shall govern. The foregoing detailed description and examples have been given for clarity of understanding only. No unnecessary limitations are to be understood therefrom. The invention is not limited to the exact details shown and described, for variations obvious to one skilled in the art will be included within the invention defined by the claims. [0156] The description of embodiments of the disclosure is not intended to be exhaustive or to limit the disclosure to the precise form disclosed. While the specific embodiments of, and examples for, the disclosure are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the disclosure.

[0157] Specific elements of any foregoing embodiments can be combined or substituted for elements in other embodiments. Moreover, the inclusion of specific elements in at least some of these embodiments may be optional, wherein further embodiments may include one or more embodiments that specifically exclude one or more of these specific elements. Furthermore, while advantages associated with certain embodiments of the disclosure have been described in the context of these embodiments, other embodiments may also exhibit such advantages, and not all embodiments need necessarily exhibit such advantages to fall within the scope of the disclosure.

[0158] As used herein and unless otherwise indicated, the terms “a” and “an” are taken to mean “one”, “at least one” or “one or more”. Unless otherwise required by context, singular terms used herein shall include pluralities and plural terms shall include the singular.

[0159] Unless the context clearly requires otherwise, throughout the description and the claims, the words ‘comprise’, ‘comprising’, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”. Words using the singular or plural number also include the plural and singular number, respectively. Additionally, the words “herein,” “above,” and “below” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of the application.

[0160] Unless otherwise indicated, all numbers expressing quantities of components, molecular weights, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless otherwise indicated to the contrary, the numerical parameters set forth in the specification and claims are approximations that may vary depending upon the desired properties sought to be obtained by the present invention. At the very least, and not as an attempt to limit the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. [0161] Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. All numerical values, however, inherently contain a range necessarily resulting from the standard deviation found in their respective testing measurements.

[0162] All headings are for the convenience of the reader and should not be used to limit the meaning of the text that follows the heading, unless so specified.

[0163] All of the references cited herein are incorporated by reference. Aspects of the disclosure can be modified, if necessary, to employ the systems, functions, and concepts of the above references and application to provide yet further embodiments of the disclosure. These and other changes can be made to the disclosure in light of the detailed description.

[0164] It will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except as by the claims.

Claims

CLAIMS The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A method of additive manufacturing gradient printing on a target location, the method comprising: dispensing a viscous fluid from an apparatus, the apparatus comprising a nozzle fluidically connected to a source of the viscous fluid and moveable in relation to the target location, wherein a viscous fluid is fed through and extruded from the nozzle to yield a translating or alternating coil structure; moving the nozzle in relation to the target location based, the movement based on an algorithm configured to produce a structure that includes a translating or alternating coil structure having at least a portion that has a continuous gradient in a property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

2. The method of additive manufacturing gradient printing of Claim 1 , wherein for the dispensing there are two or more nozzles that are movable independently or parallel of each other.

3. The method of additive manufacturing gradient printing of Claims 1 or 2, wherein for the dispensing there are two or more nozzles, wherein the dispensing from the nozzles results in producing the same object.

4. The method of additive manufacturing gradient printing of any of the previous claims, wherein the viscous fluid for dispensing is inside a same layer or across the layers.

5. The method of additive manufacturing gradient printing of any of the previous claims, wherein the extrusion of the viscous fluid during dispensing results in viscous thread instability.

6. The method of additive manufacturing gradient printing of any of the previous claims, wherein dispensing the viscous fluid allows for viscous thread printing.

7. The method of additive manufacturing gradient printing of any of the previous claims, wherein the extrusion the nozzle for dispensing of the viscous fluid at a translation speed, an extrusion speed, at a nozzle height, a material and process dependent die swell constant, or any combination of the variables results in coiling of the extruded material.

8. The method of additive manufacturing gradient printing of any of the previous claims, wherein the coils change in type, size of periodicity while being connected as a continuous strand during dispensing.

9. The method of additive manufacturing gradient printing of any of the previous claims, wherein the translating or alternating coil structure resulting from manufacturing is a foam.

10. The method of additive manufacturing gradient printing of Claim 9, wherein the foam has the structural property of a density, and the density varies as continuous gradient through at least a portion of the foam.

11. The method of additive manufacturing gradient printing of Claim 9, wherein the foam has the mechanical property of a modulus, and the modulus is a continuous gradient of modulus properties.

12. The method of additive manufacturing gradient printing of Claims 9-11, wherein the method of additive manufacturing gradient printing generates a foam, wherein the velocity and height of the nozzle during dispensing is varied, the extrusion rate is varied or the velocity, the height of the nozzle and the extrusion rate are varied simultaneously to inducing multiple codings from a continuous extrusion path.

13. The method of additive manufacturing gradient printing of any of the previous claims, wherein the dispensing translating or alternating coil structure is a polymer, a glass, a metal, or a ceramic.

14. The method of additive manufacturing gradient printing of Claim 13, wherein the polymer can be thermoplastic polyurethane, polylactic acid, styrene, acrylic, acrylonitrile-butadiene-styrene, nylon, or silicone,

15. The method of additive manufacturing gradient printing of Claim 14, wherein the polymer has a pigment dispersed.

16. The method of additive manufacturing gradient printing of Claim 15, wherein the pigment can comprise of a metal, a metal alloy, a salt, or combinations thereof.

17. The method of additive manufacturing gradient printing of any of the previous claims, wherein the dispensing translating or alternating coil structure can be deposited as a free flowing solid, a melt, a solution, or a vapor.

18. The method of additive manufacturing gradient printing of any of the previous claims, wherein the dispensing translating or alternating coil structure is crosslinked, sintered, melted, ionized, forms a solid by means of evaporation of a solvent, or combinations thereof.

19. The method of additive manufacturing gradient printing of any of the previous claims, wherein an electrostatic charge is placed upon the viscous fluid during dispensing.

20. The method of additive manufacturing gradient printing of any of the previous claims, wherein the algorithm programs the moving of the nozzle in spatial coordinates.

21. The method of additive manufacturing gradient printing of any of the previous claims, wherein the algorithm for moving the nozzle in spatial coordinates is a G- code that programs movement of the nozzle.

22. The method of additive manufacturing gradient printing of any of the previous claims, wherein the G-code for moving the nozzle in spatial coordinates has a command, Gl, wherein G1 instructs the nozzle to move from the nozzle current position (JO, O, ^0) to a new position

form Gl X YyZ^EA<?F/', where Gl XzY/ Z^ EA<? F/’, wherein Gl and the capital letters are character literals, and the lowercase letters represent numerical values for the printer to parse.

23. The method of additive manufacturing gradient printing of Claim 22, wherein A e is the amount of filament extruded in millimeters over each segment and is the speed at which the printer head travels over the segment in millimeters per minute.

24. The method of additive manufacturing gradient printing of any of the previous claims, wherein the additive manufacturing gradient printing by means of the algorithm for moving the nozzle results in a macroscopic pattern.

25. The method of additive manufacturing gradient printing of any of the previous claims, wherein the additive manufacturing gradient printing by the algorithm for moving the nozzle results in a product.

26. The method of additive manufacturing gradient printing of any of the previous claims, wherein a product resulting from any of the previous claims is a seat, a furniture, a filter, or a medical implant.

27. The method of additive manufacturing gradient printing of any of the previous claims, wherein the seat resulting from any of the previous claims is used for an automobile or an aircraft.

28. The method of additive manufacturing gradient printing of any of the previous claims, wherein the structural property, the mechanical property, the physical property, and combinations thereof of the translating or alternating coil structure is a porosity, a stiffness, a hardness, a permeability, a tensile, a modulus, an elongation, an elasticity, or combinations thereof.

29. A translating or alternating coil structure resulting from additive manufacturing, the translating or alternating coil structure comprising: the translating or alternating coil structure having a variable plurality of successive coils along an x-axis, a y-axis, a z axis, or any vector thereof with at least a portion of the translating or alternating coil structure having continuous gradient in a property selected from the group consisting of a structural property, a mechanical property, a physical property, and combinations thereof.

30. The translating or alternating coil structure of Claim 29, wherein the translating or alternating coil structure is a polymer, a metal, a glass, or a ceramic.

31. The translating or alternating coil structure of Claim 30, wherein the polymer can be thermoplastic polyurethane, polylactic acid, styrene, acrylic, acrylonitrile- butadiene-styrene, nylon, or silicone,

32. The translating or alternating coil structure of claim 31 , wherein the polymer has a pigment dispersed therein.

33. The translating or alternating coil structure of Claim 32, wherein the pigment comprises a metal, a metal alloy, a salt, a ceramic, or combinations thereof.

34. The translating or alternating coil structure of Claims 29-33, wherein the translating or alternating coil structure can be deposited as a free flowing solid, a melt, a solution or a vapor.

35. The translating or alternating coil structure of any of Claims 29-34, wherein the translating or alternating coil structure is crosslinked, sintered, melted, ionized, or combinations thereof.

36. A software program for generation of an algorithm for a translating or alternating coil structure of graded viscous thread printed foams resulting from additive manufacturing, the software program comprising: a controller within the apparatus of Claim 1, wherein the controller has a communications port; a plurality of sensors configured to generate data based on a material’s physical properties which are communicated through the communications port to the software program; wherein the software program uses the data to generate the algorithm along with input from the user; wherein the communications port is configured to receive the algorithm generated by the software program; and wherein the controller is configured to direct the nozzle of Claim 1 based upon the algorithm generated by the software program to extrude a material resulting in the translating or alternating coil structure.

37. The software program for generation of an algorithm for a translating or alternating coil structure of Claim 36, wherein the software program communicates to a system comprising the apparatus of Claim 1, the system further comprising a smart device communicatively coupled to the apparatus, wherein the smart device is configured to issue the instructions to the apparatus.

38. The software program for generation of an algorithm for a translating or alternating coil structure of Claims 36 or 37, wherein the software program encodes to generate a Mesh Boolean Operation.

39. The software program for generation of an algorithm for a translating or alternating coil structure of Claims 36-38, wherein the software program encodes to find a dimensionless velocity variable, V*, and a dimensionless height variable, H*.

40. The software program for generation of an algorithm for a translating or alternating coil structure of Claims 36-39, wherein the software program produces a G- code command.

41. The software program for generation of an algorithm for a translating or alternating coil structure of Claims 36-40, wherein the translating or alternating coil structure has a gradient in a physical property, a mechanical property, a structural property, or combinations thereof.

42. The software program for generation of an algorithm for a translating or alternating coil structure of Claims 36-41, the gradient in a physical property, the mechanical property, the structural property, or combinations thereof is a porosity, a stiffness, a hardness, a permeability, a tensile, a modulus, an elongation, an elasticity, or combinations thereof.