WO2021163161A1

WO2021163161A1 - Nonstochastic foam and methods of manufacturing thereof

Info

Publication number: WO2021163161A1
Application number: PCT/US2021/017414
Authority: WO
Inventors: Thomas Hinton; Michael Graffeo; Adam FEINBERG; Christopher SANDINI
Original assignee: Fluidform Inc
Current assignee: Fluidform Inc
Priority date: 2020-02-10
Filing date: 2021-02-10
Publication date: 2021-08-19
Anticipated expiration: 2022-08-10

Abstract

A foam including a thermoset material defining a nonstochastic, regular packing of a plurality of voids. In another embodiment, a foam includes a thermoset material defining a void, a sidewall of the void comprising a triply periodic minimal surface of the thermoset material. In each embodiment, the thermoset material includes a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions defining striations therebetween. A plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion. A volume of the thermoset material has an elastic modulus lower than an elastic modulus of an equivalent volume of thermoset material without voids. Methods for fabricating these foams include depositing into a support material a print material including a plurality of adjacent extrusions with contacting surfaces of pairs of adjacent extrusions defining striations therebetween.

Description

NONSTOCHASTIC FOAM AND METHODS OF MANUFACTURING THEREOF

Related Application

This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/972,432, filed on February 10, 2020, incorporated herein by reference in its entirety.

Background

Thermoset materials provide a variety of superior mechanical, chemical, and electrical properties. They are almost all multi-part resins that are cast into molds to produce complex objects that serve a variety of industries from aerospace, medical manufacturing, automotive, consumer electronics, and chemical manufacturing industries. Despite the expanding need for thermoset materials in demanding applications, there remains to be demonstrated a method for additively manufacturing most thermosets.

Additive manufacturing (AM) affords the ability to quickly iterate on designs and produce geometries that are otherwise impossible to manufacture. Many of the most promising applications of AM technologies lie in reducing the weight of objects intended for use in aerospace, automotive, or other high-performance applications where object mass is expensive to accommodate. There is a demand for the ability to fabricate thermosets in the same way that metal, ceramic, and thermoplastic additive technologies allow for complex, space- and weight-saving designs.

Summary

Embedded printing, as a class of additive manufacturing technologies, may be used to render complex geometries using polymers including thermoset resins. Many geometries that are only possible via embedded printing rely on complex mathematical shapes and patterns to render traditionally bulky items lighter or stiffer than would otherwise be possible with traditional manufacturing technologies such as injection molding. The applications of embedded printing of polymeric materials include medical manufacturing, aerospace, aeronautics, automotive, machines, plants, and consumer electronics. For example, the materials disclosed herein may be used to produce multi-material, part-silicone, part-gel wearable electronic interfaces for medical monitoring.

Utilizing the freeform capabilities of embedded printing technologies allows for the fabrication of foams comprising voids that are patterned according to mathematical constraints. These foams can serve as space filling, lightweight structural materials that more efficiently support or deform for applications such as seat cushions or highly breathable padding inside helmets.

Embodiments of the invention include additive manufacturing with a thermoset polymer resin ink in combination with a fugitive supporting medium to sculpt a stable, liquid-liquid interface defining a nonstochastic foam whose composition and void packing render bulk mechanical properties that can be heterogenous and anisotropic.

Nonstochastic foams possess material properties that are determined by the morphology and composition of additively manufactured material as well as any material potentially contained within voids. These material properties include acoustic, biological, chemical, electrical, magnetic, mechanical, optical, and thermal properties. Thus, the described methods enable the fabrication of foams with tailored properties for a large swath of applications. By variation of foam composition and morphology, properties can be discretely patterned. Material properties can exhibit anisotropy, heterogeneity, and/or homogeneity across the additively manufactured foam. Moreover, composite foam constituents can display orientational and morphological anisotropy, such as the alignment of chopped carbon fibers in an epoxy-carbon composite extrusion.

In an aspect, embodiments of the invention relate to a foam including a thermoset material defining a nonstochastic, regular packing of a plurality of voids. The thermoset material includes a plurality of adjacent extrusions, with (ii) contacting surfaces of pairs of adjacent extrusions define striations therebetween, (iii) a plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion, and (iv) a volume of the thermoset material has an elastic modulus lower than an elastic modulus of an equivalent volume of thermoset material without voids.

One or more of the following features may be included. The thermoset material may include or consist essentially of polyoxybenzylmethylenglycolanhydride (commonly known as Bakelite resin), benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea- formaldehyde resin, vinyl ester resin, and/or a fiber reinforced thermoset resin.

The voids may have a morphology of spherical, spindle-shaped, lumpy, dendritic, stellate, acicular, polygonal, nested (void within printed thermoset within void), elongated, toroidal, branching, interpenetrating, continuous, and/or knotted. The packing of voids may be uniform or periodic. The voids may be discrete, proximate adjacent voids, and/or intersecting. Voids that are discrete are not overlapping. Proximal adjacent voids are voids that are fabricated with negligible overlap, meaning their boundaries are tangent to one another. Intersecting voids possess overlap between one another and can extend throughout the foam.

A supporting medium (e.g., from the manufacturing process) may be trapped in at least one independent, sealed void. The supporting medium may be a hydrophobic non-Newtonian fluid. The supporting medium may be a mixture of oil, water, and surfactant, or a mixture of oil, water, polyacrylic acid, lanolin, and surfactant. The supporting medium may be a gelatin slurry. The supporting medium may be an oil and a copolymer.

The foam may include a plurality of struts joined together at a plurality of nodes.

At least one strut and at least one node may include a same material. At least one strut may include the thermoset material and at least one node may include a second material. At least one node may include the thermoset material and at least one strut may include a second material.

The thermoset material may include or consist essentially of a heterogeneous mixture of at least two materials. The heterogenous mixture may have gradients of material stiffness and the at least two materials may have different molecular weights.

The thermoset material may include a composite material. The composite material may include a homogeneous and/or a heterogeneous mixture of at least two constituent materials.

The thermoset material may be non-photo-curable. The thermoset material may be free of each of a photopolymer and a photoinitiator.

The thermoset material may be free of a rheological additive imparting yield stress greater than 50 Pa.

The thermoset material may include at least one floating body surrounded by at least one void and/or at least one floating body surrounding at least one void.

More than half of the voids may be connected. Less than half of the voids may be connected.

A cushion or a car cushion may include the foam.

In another aspect, a foam includes a thermoset material defining a void, a sidewall of the void including a triply periodic minimal surface of the thermoset material. The thermoset material includes a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions define striations therebetween. A plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the extrusion. A volume of the thermoset material has an elastic modulus lower than an elastic modulus of an equivalent volume of thermoset material without the void.

One or more of the following features may be included. Each exposed surface of the thermoset material may define a plurality of striations. A supporting medium may be trapped in the void. A supporting medium (e.g., from the manufacturing process) may be trapped in at least one independent, sealed void. The supporting medium may be a hydrophobic non-Newtonian fluid. The supporting medium may be a mixture of oil, water, and surfactant, or a mixture of oil, water, polyacrylic acid, lanolin, and surfactant. The supporting medium may be a gelatin slurry. The supporting medium may be an oil and a copolymer.

The thermoset material may further define a plurality of non-intersecting voids.

In still another aspect, embodiments of the invention relate to a method for fabricating a nonstochastic foam. The method includes providing a support material within which the foam is fabricated. A print material is deposited into the support material. The print material includes a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions defining striations therebetween. Depositing includes mechanically supporting at least a portion of the print material by the support material during the depositing to prevent deformation of the print material during deposition; and suspending print material in the support material at a location where the print material is deposited. The print material is transitioned from a fluid to a solid or semi-solid state at the location where the print material is deposited to form the foam. At least a portion of the support material is removed to release the foam from the support material. The print material includes a thermoset material, the foam includes the thermoset material defining a nonstochastic, regular packing of a plurality of voids. A plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion. A volume of the thermoset material has an elastic modulus lower than an elastic modulus of an equivalent volume of the thermoset material without voids.

One or more of the following features may be included. The thermoset material may include or consist essentially of polyoxybenzylmethylenglycolanhydride, benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea-formaldehyde resin, vinyl ester resin, and/or a fiber reinforced thermoset resin.

A pattern in which the print material is suspended may determine a distribution of the voids in the thermoset material. A pattern in which the print material is suspended may determine an aspect ratio, volume, axes of symmetry, orientation, surface area, and/or Hausdorff dimension of the voids. At least one void may be occupied by support material. The support material may include a hydrophobic non-Newtonian fluid. The support material may include a mixture of oil, water, polyacrylic acid, lanolin, and surfactant. The support material may include a gelatin slurry. The support material may be a mixture of oil, surfactant, and water. The support material may include an oil and a copolymer.

In yet another aspect, embodiments of the invention relate to a method for fabricating a nonstochastic foam. The method includes providing a support material within which the foam is fabricated. A print material is deposited into the support material. The print material includes a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions defining striations therebetween. Depositing includes mechanically supporting at least a portion of the print material by the support material during the depositing to prevent deformation of the print material during deposition; and suspending print material in the support material at a location where the print material is deposited. The print material is transitioned from a fluid to a solid or semi-solid state at the location where the print material is deposited to form the foam. At least a portion of the support material is removed to release the foam from the support material. The print material includes a thermoset material, the foam includes the thermoset material defining a void, a sidewall of the void including a triply periodic minimal surface of the thermoset material. The thermoset material includes a plurality of adjacent extrusions. A plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion. A volume of the thermoset material has an elastic modulus lower than an elastic modulus of an equivalent volume of the thermoset material without voids.

A pattern in which the print material is suspended may determine a distribution of the voids in the thermoset material. A pattern in which the print material is suspended may determine an aspect ratio, volume, axes of symmetry, orientation, surface area, and/or Hausdorff dimension of the voids.

The support material may include a hydrophobic non-Newtonian fluid. The support material may include a mixture of oil, water, polyacrylic acid, lanolin, and surfactant. The support material may include a gelatin slurry. The support material may be a mixture of oil, surfactant, and water. The support material may include an oil and a copolymer.

Brief Description of Figures

The foregoing features and advantages of embodiments of the invention will become more apparent from a reading of the following description in connection with the accompanying drawings, in which:

Figure 1 is a perspective view of a foam with striations on all of its surfaces, in accordance with an embodiment of the invention;

Figure 2A is a perspective view of a foam seat cushion in accordance with an embodiment of the invention;

Figure 2B is a schematic cross-sectional view of the cushion of Figure 2A, illustrating a hierarchical internal void architecture with cubic subdivided cells with varying elastic modulus;

Figure 2C is a schematic cross-sectional view of the cushion of Figure 2A illustrating variation in foam cell density;

Figure 2D is a top view of a foam including a triply periodic minimal surface with periodic, interconnected void space in accordance with an embodiment of the invention; Figure 2E and 2F are top and perspective views, respectively, of a foam including a triply periodic minimal surface with interconnections between voids and striations on surfaces, in accordance with an embodiment of the invention;

Figure 3A - 3D are perspective views of foams with triply periodic minimal surfaces, in accordance with embodiments of the invention;

Figures 4A - 4D are perspective views illustrating voids and striations in foams formed in accordance with embodiments of the invention;

Figure 5 is a schematic diagram illustrating the extrusion of thermoset material during an embedding fused material (EFM) process, thereby forming extrusions with striations disposed therebetween, in accordance with an embodiment of the invention;

Figure 6 is a schematic diagram illustrating hierarchical elastic modulus in a cushion, in accordance with an embodiment of the invention;

Figures 7A is a front view illustrating the formation of a cushion in accordance with an embodiment of the invention;

Figure 7B is a photograph of the cushion of Figure 7A with a hierarchical gyroid lattice;

Figure 8 is a photograph of a second car cushion, fabricated in accordance with an embodiment of the invention;

Figure 9 is a photograph of cylindrical material with different elastic moduli, fabricated in accordance with an embodiment of the invention; and

Figure 10 a photograph of a gyroid lattice displaying multiple axes of symmetry and a nonstochastic uniform patterning of void and material, fabricated in accordance with an embodiment of the invention.

Detailed Description

As used herein, "foam" means a solid material including voids that impart specific material properties such as lightweight, specific mechanical properties, thermal insulating properties, acoustic properties, and/or other physical properties.

As used herein, a "void" is a region in a printed structure that does not include the printed material, e.g., a pocket of gas or a second material disposed in the printed material. As used herein, "nonstochastic, regular packing of voids" means a non-random arrangement of voids that is determined by the files, software, and machine movements used to determine extrusion of thermoset material into supporting material. Pores or gaps in the thermoset material left by trapped regions of supporting material that are unintentional, not controlled, or stochastic are not considered herein to be nonstochastic voids, but such voids are considered to be a feature of EFM.

As used herein, "regular packing of voids" means voids with locations denoting a non-random pattern in space.

As used herein, a "nested void" is a void within printed material within a void.

As used herein, an "extrusion" means a rod-shaped filament of polymer that is created by the pumping of polymeric material out of an extruder nozzle while the nozzle moves relative to the foam being additively manufactured.

Foam behavior may be classified as metamaterial behavior if it is only displayed by the foam and not any stochastic combination of the foam's constituents.

In accordance with embodiments of the invention, a foam is a bulk material having purposely defined void space with regularly packed voids. These voids may be a small or large fraction of the material volume, e.g., the material may have 1% to 99+% void space, e.g., 50% to 85% with the exact amount depending on application and performance requirements. The foams described herein are formed from thermoset materials, such that a volume of thermoset material in the foam has an elastic modulus lower than an elastic modulus of an equivalent volume of the thermoset material without voids. For example, the elastic modulus of 8 cubic inches of thermoset material defining a foam in accordance with embodiments of the invention may be 100 kPa, while the elastic modulus of the same volume of the same thermoset material without voids may be 1 MPa. For example, a the elastic modulus of a printed polyurethane foam may be as low as 105 kPa, while the modulus of an equivalent volume of polyurethane is 6 MPa.

An embedded printing process (described below) enables 3D printing a material with a specific structure to create voids with specifically defined shapes and distribution, i.e., nonstochastic, regular packing of voids. The 3D printed material is one or more materials compatible with the embedded printing process such as silicone resin, polyurethane resin, and phenolic resin. Voids are defined as the regions within the structure being printed that do not contain printed material. The voids may all be of the same shape, of different shapes, or some combination thereof. The morphology of the voids may be, e.g., spherical, spindle-shaped, lumpy, dendritic, stellate, acicular, polygonal, nested, elongated, toroidal, branching, interpenetrating, continuous, and/or knotted. The packing of the voids is preferably regular, e.g., uniform or periodic. The voids may be organized, i.e., packed, in a regular repeating lattice structure based on a unit cell or multiple unit cells (e.g., body-centered cubic or face-centered cubic), or a combination thereof. Voids are also referred to herein as cells of the foam. The voids may be discrete, proximate adjacent voids, or intersecting.

The shape, size and packing of the printed voids can result in a bulk material with customized, predetermined isotropic or anisotropic properties. Further, the bulk material can have spatially heterogeneous properties that can vary over a length scale corresponding to the major Feret diameter of single voids, or larger.

The length of the filaments of material, i.e., the extrusions, being 3D printed in the embedded system can vary from 100 pm up to 100 m, e.g., 1 mm to 10 cm, depending on the hardware available to print the material. A minimum length depends on the fluid pumping and 3D movement resolution of the system. A maximum length is determined by the reach of the 3D printer's X, Y, and Z axes along with the total volume of material an extruder can pump out. A diameter of the voids can vary from 10 pm up to 1 m, e.g., 1 mm to 4 mm. A cross sectional aspect ratio of extruded filaments may be larger than 1, e.g., greater than 4, indicating a flattened filament with a larger cross sectional width in the XY plane than height in the orthogonal Z axis, where XY is orthogonal to the nozzle's axis of fluid flow, and Z is parallel. Extruded filament aspect ratio can vary depending on many things including the speed of the extruder's translational motion in the supporting material as well as the volumetric flow rate of the extruder. Aspect ratios of 1 are considered easier to plan for in pathing an extruder movement in 3D space; however, extrusions of thermoset material with tall or wide cross-sectional geometries can encourage enhanced fusion between filaments across a printed object.

Embodiments of the invention include a foam with an unsupported cell geometry composed of multiple different materials, e.g., a thermoset material including - or consisting of - a heterogeneous mixture of at least two materials. The heterogenous mixture may include a gradient of material stiffness, with the at least two materials having different molecular weights. The two materials may be the same polymer with different molecular weights, thereby increasing the range of possible starting materials and simplifying the manufacturing of foam in accordance with embodiments of the invention.

In some embodiments, the thermoset material may include a composite material, e.g., a homogeneous or a heterogeneous mixture of at least two constituent materials, i.e., two materials that are not one continuous phase. Rather, the two materials may include, e.g., phases of fluid- solid, crystalline-amorphous, or fibrous-amorphous.

The foam may be closed cell, with less than half of the voids being connected. Trapped pockets of air or material (e.g., supporting medium) may be completely surrounded by extruded thermoset material, i.e., a supporting medium may be trapped in at least one independent sealed void. Examples of such supporting medium include a hydrophobic non-Newtonian fluid; a mixture of surfactant, oil, and water; a mixture of oil, water, polyacrylic acid, lanolin, and surfactant; or a gelatin slurry.

The foam may be open cell, with voids connected to each other, e.g., more than half of the voids being connected.

A foam may include a 3-dimensional cubic lattice with struts representing the edges of cubes and nodes representing the corners of cubes. The lattice may be constructed from two materials, such as silicone and polyurethane. The material may include at least one strut and at least one node including the same material. In some embodiments, at least one strut and one node may include different materials. This foam may be made by additive manufacturing, e.g., by embedding fused material (EFM), as described below.

A void is a space which lacks thermoset and possesses boundaries that are defined by extruded thermoset. Repeating and hierarchical voids can establish patterns and gradients in 3D. Thermoset material can compose a triply periodic minimal surface, and this surface can partition voids into two separate, interconnected groups. Voids pack together in 3D space with hierarchical or crystalline spacing.

Voids can be nested so as to allow for the encapsulation of supporting material within extruded material within supporting material within extruded material. Such nested voids are not connected to the surrounding extruded material of the foam; thus, they are termed floating voids. Bodies of thermoset surrounded by a void but not connected to surrounding thermoset are termed floating bodies. The thermoset material may include at least one floating body surrounded by at least one void and/or at least one floating body surround at least one void.

In some embodiments, a foam includes a non-photopolymerizable polymer containing a liquid trapped n its voids.

Referring to Figure 1, a foam 100 constructed using EFM typically displays striations 110 on all of its surfaces. Extrusions 120 laid down during EFM in a perimeter-tracing as well as rectilinear/back- and-forth fashion are visible on the top surface of the illustrated foam. Between these extrusions, striations 110 are clearly visible. On the sides of the object, striations between layers of material are clearly visible.

Referring to Figure 2A, a seat cushion 200 is as an example of an object made from foam in which the inclusion of a nonstochastic, regular packing of a plurality of voids enables gradients of mechanical properties. In particular, referring to Figure 2B, a cross section of the cushion has a hierarchical internal void architecture constructed of cubic subdivided cells, i.e., voids 210. Material with a higher elastic modulus 220 surrounds material with a lower elastic modulus 230. Tighter spacing of voids leads to overall increased mechanical stiffness. Conversely, lower density void spacing results in a softer bulk material behavior toward the center of the cushion. In this embodiment, extrusions define struts of polymer, with extrusions overlapping at triangular vertices, i.e., nodes. As struts span greater distances between nodes, the bulk modulus for the foam material drops.

The isometric perspective of Figure 2C demonstrates how three-dimensional packing of voids 210 is possible. Striations 110 between extrusions are most clearly visible where extrusions are extruded parallel to one another at the edge of the cushion. In such an object, the striations visible in Figure 2C are hidden unless the object is destructively disassembled to reveal the striations.

Referring to Figure 2D, a triply periodic minimal surface, specifically a gyroid 240, is an example of a foam that has a periodic, interconnected void architecture. Figure 2D represents a gyroid with two separated voids 250 composed of repeating structure span the entirety of the gyroid. These two separated voids permeate the entire extent of the gyroid without intersecting with one another. In many gyroids, separate voids of repeating structure can span the volume of the gyroid without connecting.

Figures 2E-F illustrate the striated appearance of all surfaces of the gyroid foam 240 when fabricated from thermoset using EFM. All surfaces display striations 110 regardless of orientation. Both the seat cushion 200 and the gyroid foam 240 exhibit a mechanical stiffness that is less than the stiffness of equivalent volumes of cast thermoset material.

Figure 3A - 3D are additional figures illustrating foams displaying triply periodic minimal surfaces. Figure 3A depicts a gyroid foam 300 showing a singular void 310 permeating the entire volume of the foam. Figure 3B is a rendering of the void 310 contained in the foam 300 of Figure 3A. Figure 3C depicts overlap between the two models, showing how the gyroid 300 and void 310 are non overlapping but share a common boundary. Figure 3D is an example of a gyroid foam 320 with two, non-intersecting voids 330 spanning the entire volume of the foam. Referring to Figures 4A - 4D, additional examples are provided of various foam configurations with striations formed between contacting surfaces of adjacent extrusions. Referring to Figure 4A, a top surface of a foam 400 has striations 110 defined by adjacent extrusions 120. Referring to Figure 4B, striations are formed between most layers of extrusions 120. Referring to Figure 4C, a foam 430 has horizontal striations 110 between layers of extrusions 120. Referring to Figure 4D, a foam 440 has striations 110 visible along all surfaces.

Foam fabrication method

A foam with purposely defined void space may be formed by an embedded printing process, e.g., the embedded printing process described in U.S. Patent No. 10,150,258, incorporated herein by reference in its entirety.

As described in U.S. Patent No. 10,150, 258, during printing, fused materials are embedded within a support bath, where the embedded material is initially a fluid or flowable material that transitions to a solid or semi-solid state after deposition. The method can be used in the process of additive manufacturing (AM), also commonly referred to as freeform fabrication or 3D printing, of materials to fabricate 2D or 3D structures and objects based on a 3D digital design, which may be difficult using traditional techniques or current additive manufacturing approaches. While specific examples of thermoset materials and their characteristics are provided below, EFM is not limited to printing materials with a specific, pre-polymerization viscosity or yield stress, and other materials with different characteristics may be printed.

The thermoset materials can include fluids that have substantially low elastic modulus when being printed. Traditionally, printing such a fluid in air may be difficult because the fluid may flow away from the deposition site, losing its printed structure.

The thermoset materials can include solid materials that have an elastic modulus in the range of approximately 10 GPa to 0.1 kPa. These solid materials may sag or deform if printed in air. For example, stiff materials such as epoxy resins, silicone resins, and phenolic resins can be printed using EFM.

The thermoset materials can include materials that have an elastic modulus that is initially low and increases over time due to crosslinking or assembly of the material. The final elastic modulus of these materials may be in the GPa range after crosslinking or assembly, but the material may be difficult to print using other techniques because the extruded material yield stress and/or elastic modulus was much lower during the EFM process. An example of such materials includes an epoxy resin that is mixed but has not yet cured, so it is a liquid during printing but then cures over time into a rigid polymer. Another example is a polydimethylsiloxane (PDMS) elastomer (e.g., Sylgard 184,

Dow Corning) that can be mixed as a prepolymer, printed as a liquid, and then cured for 48 hours at room temperature while still embedded in the support material.

The thermoset materials are printed inside a temporary support material that can be removed later by, e.g., heating or cooling the support material to dissolve or melt the support material, or removing cations to disrupt crosslinking of the support material. Additional techniques for removing the support material include vibration, irradiation with ultraviolet, infrared, or visible light, chemical processes, or application of a constant or oscillating electric or magnetic field.

The support material may be any material that acts as a yield stress fluid. The support material may demonstrate a significant shear thinning behavior such that the support material acts like a solid material during deposition of the structure materials and then acts like a fluid when the nozzle is moved through the support material such that the nozzle movement does not disturb the deposited structure material. The support material may exhibit viscoplastic behavior where it acts as a solid below a threshold shear stress and flows like a liquid above the threshold shear stress. The characteristic that makes a support material suitable for EFM is an elastic behavior that yields to viscous flow at a known shear stress. In EFM, the yielding is caused by the shearing force of an extruder moving through the support material, affecting the support material in a number of ways. The extruder may change the support material by imposing a mechanical load via shear, pressure, or vibration. The extruder could irradiate or heat the support material to thin it. Alternatively, a suitable material may lose viscosity under vibration, heating, or irradiation that occurs locally to the extruder.

For example, the support material can include a Bingham plastic, or Bingham plastic-like, material that is a solid material when not perturbed, but yields and provides minimal resistance when a nozzle moves through it. The support material can include other materials with viscoplastic behavior, such as Flerschel-Buckley fluid. Bingham plastics and Flerschel-Buckley fluids are viscoplastic materials included in the "shear-thinning" or "yield-stress fluid" category. Below a specific shear stress, these materials appear as a solid material. Above a threshold shear force, these materials behave as a fluid. A Bingham plastic may not necessarily "shear thin," but rather may act much like a Newtonian fluid once it begins to flow. In contrast, the Flerschel-Buckley fluid undergoes shear thinning once it begins to flow.

Thus, a 3D printer can lower a syringe-based extruder into the support material and move around and deposit material in arbitrary 3D geometries. The extruded material stays in place once the tip of the extruder moves away, thus forming the 3D printed object. Once the complete 3D object is printed and the structural material has sufficiently assembled, the support material is removed.

Referring to Figure 5, a nozzle 500 of an EFM 3D printer (not shown) may deposit a print material 510 including a plurality of adjacent extrusions 120 of a polymer resin, e.g., thermoset material in a support material, to build up a foam. Depositing includes mechanically supporting at least a portion of the print material by the support material to prevent deformation of the print material during deposition. Print material is suspended in the support material at a location where the print material is deposited. The print material transitions from a fluid to a solid or semi-solid state at the location where the print material is deposited to form the foam. At least a portion of the support material is removed to release the foam from the support material. This printing method may be used to form a foam including thermoset material defining a nonstochastic, regular packing of voids described herein, with a plurality of molecules in each extrusion being aligned in a direction parallel to a striation defined by the surface of the extrusion. The printing method may also be used to form a foam including a thermoset material defining a void, with a sidewall of the void including a triply periodic minimal surface of the thermoset material, and a plurality of molecules in each extrusion being aligned in a direction parallel to a striation defined by the extrusion.

As the extrusions 120 are deposited, they may fuse with or touch adjacent extrusions. A seam indicates the contacting surfaces of adjacent extrusions that contact each other. This area of contact, i.e., seam, appears as a striation 110 on a surface of the printed object. In other words, striations are contacting surfaces between adjacent extrusions. The direction 520 of extrusion is also the orientation of polymeric molecules, which are disposed in the extrusions 120 parallel to the striations between extrusions.

On both sides of each striation, within the contacting extrusions, molecules are aligned parallel to a plane defined by the striation. The chains of polymer in the extrusions are aligned parallel to the direction of extrusion and to any adjacent striations. Due to the shear force of extruding a viscous liquid, polymer chains in the extruded thermoset material align parallel to the axis of extrusion. As the nozzle 3-dimensionally translates during EFM, the shearing of the polymer into the bath causes the polymer chains at the point of extrusion to be parallel to the direction of the extruder's travel at that point. Where two extrusions touch and form a striation, the polymeric material within both extrusions is parallel to the striation. The nature of this polymeric alignment is inherent to the EFM process. Where single extrusions exist without contacting other extrusions, polymer chains are oriented parallel to the long axis of each extrusion. Alignment of molecules within polymers typically provides enhanced mechanical properties along the direction of alignment. In thermoset materials, mechanical properties such as elastic modulus, strain to failure, and ultimate tensile strength may be controlled and enhanced by the alignment of polymer molecules relative to the direction of mechanical testing.

The alignment of molecules within a polymer dictates the direction along which the molecules can bear the greatest tensile load. Since molecular alignment can be dictated by the extruder and corresponds to the presence of striations, molecular alignment can be arranged to bear a load across a given foam more or less effectively. Accordingly, the path traveled by the extruder in extruding thermoset material during printing can be used to program anisotropy in mechanical properties within the foam. A foam may be printed using a variety of different extrusion pathing schemes that result in varying behaviors across foams that are otherwise identical in thermoset and void volumes.

X-ray diffraction may be used to measure molecular orientation, i.e., molecular alignment within a polymer. Scattering of x-rays is enhanced perpendicular to the direction of molecular orientation. The spread of the scattering can be quantified by the full-width at half-maximum (FWHM) (See, e.g., Salim A Ghodbane et al 2019 Biofabrication 11045004, incorporated herein by reference in its entiry). Foams printed using EFM in accordance with embodiments of the invention contain extrusions with measurable FWFIM values that are less than 75°.

In EFM, a structure can be printed in any direction in 3D space. In addition to the typical 3D printing that is done layer by layer in XY planes, structures can also be printed layer by layer in a non-XY plane, such as the XZ plane, or a plane at any angle. A structure can also be printed in a non-planar fashion in a curved path, such as a helix. Structures with material mechanical properties that are different in the plane of printing versus orthogonal to the plane of printing can thus be printed using EFM. In particular, the fabricated structures can have three-dimensions, and the fabricated structure can have anisotropic mechanical properties in a direction that lies within the XY plane. For example, EFM can be used to print the direction of conductive traces in a circuit in 3D, lines of stress concentration in a simulated object under mechanical load, or 3D contour-tracing extrusions to produce less of a stair-step pattern that is normally seen in the layers of additively manufactured objects.

Some AM techniques rely on the triggered assembly or reorganization of a material using targeted heating, photopolymerization, or jetted glues to bind a powder substrate. EFM is more similar to Fused Deposition Modeling (FDM), but in FDM, material is deposited on top of a previously deposited layer, which provides the necessary mechanical support to build multiple layers since this process occurs in an environment with no buoyant or conformal supports and requires the co- printing of supporting structures. In contrast, EFM deposits material near previously deposited material, but not necessarily on top of it. Specifically, the support bath material provides mechanical support with the deposited, embedded materials able to fuse in any direction as long as proximity is sufficient. To accomplish this, fusible material is deposited into the support bath material, which behaves as a physical and buoyant, non-Newtonian support. Support materials are usually as stiff as the intended deposit and placed underneath or neighboring the deposit to prevent deformation of the deposit. In EFM, the support material surrounds the printed material, such that the deposited material is embedded inside the support material during printing. After printing, the object can be removed from the support as an intact object.

EFM can print any fluid that transitions to a solid or semi-solid state after deposition, including thermoset materials

Support materials used in EFM can include any slurry or fluid exhibiting properties which allow it to support the embedding of a fusible material. Some examples of support materials are mayonnaise, albumin-foams, gelatin slurries, poly(N-isopropylacrylamide) (PNIPAAM) slurries, polyacrylate slurries, alginate slurries, alkyd slurries, styrenic polymer gel slurries, polyamide gel slurries, organogel slurries, and structured fluids displaying non-Newtonian, Bingham Plastic behaviors, or other viscoplastic materials such as Flerschel-Buckley fluid. Conditions inside the support materials could be used to trigger the transition of the embedded material from fluid to solid or semi-solid state.

In another embodiment of the invention, the supporting material during EFM may be a liquid crystalline fluid including a surfactant, an oil, and a polar solvent. The structure of the fluid could be one of an inverted lyotropic fluid, with oil surrounding crystalline assemblies of surfactant and water. In accordance with some embodiments of the invention, during fabrication, the foam is composed of one fluid material interfacing with another fluid material. Material deposition creates a fluid-fluid boundary between the deposited material and the supporting material. This interface is stable and persists while deposited material cures, despite the two materials being fluid during interface formation. The addition of material serves to define the boundary between deposited material and voids.

In some embodiments, EFM enables greater freedom in forming foams than vat-based photopolymerization techniques as well as thermoplastic extrusion techniques for additive manufacturing. In contrast to EFM, these methods typically do not allow the formation of foams with struts and nodes that are unsupported during fabrication. As such, voids in materials formed by such methods need to have faces that, when oriented parallel to the build plate, are not liable to collapse under their weight of the overlying material or the stresses induced during the AM process. Powder-based techniques for additive manufacturing cannot produce foams from most commercially available thermoset materials. EFM can utilize thermosets to create foams with no geometric constraint to their architecture.

A foam may be constructed by adding deposited material in a serial or parallel fashion to segregate the support material into connected (open-cell) and disconnected (closed-cell) regions. In a parallel fashion, material is added by multiple extruders at once. In a serial fashion, material is added by a single extruder. The bounding box around all fluid-fluid interfaces is the print volume.

Foam may be constructed by a layer-wise planar addition of material as well as a non-planar 3D addition of material. In a dense foam consisting of closed cells, it may be easier to deposit material in layers with the intended voids appearing as gaps in each layer until all layers stacked to form the foam. On the other hand, one may construct an open cell foam consisting of a continuous void permeating a 3D structure of thermoset by drawing out thermoset to define the boundaries of the foam and only connecting the extruded material in a fashion to isolate void space within the foam. Alternatively, mathematical algorithms can generate planar extruder trajectories to render a triply periodic minimal surface such as a gyroid that contains at least one void spanning the entire foam volume. Each of these foams may be fabricated using a variety of approaches not limited to the exemplary methods described herein.

The use of material extrusion to fabricate a foam allows for discretization of deposited material composition. This may be achieved by combining different materials by mixing before extruding as one continuous strand of material. This discretization means that, in some embodiments, a foam may be composed of many different deposited materials. For example, a cube-shaped gyroid foam with a continuous void may be composed of silicone rubber that is a mixture of different molecular weight prepolymers mixed before extrusion. The ratio of the component silicones can vary across the volume of the gyroid foam. The mechanical properties of the gyroid foam's deposited material may then vary in accordance with the deposited material's compositional variance. Another example may be a composite material where the polymer of the composite and the filler can vary in mixing ratio. A carbon fiber epoxy composite, for example, may be printed in an open celled foam and display high carbon fiber content along struts within the lattice, making the struts stronger in tension. At the nodes of the printed lattice, the composition may be dominated by epoxy polymer, thus making the nodes more flexible. The use of material extrusion to fabricate a foam also allows for extruder switching. Switching extruders, either with separate nozzles or through the same nozzle, during printing allows for the use of multiple different materials that are incompatible in mixing but may be assembled together during a printing process. For example, a silicone rubber and a urethane rubber may be simultaneously extruded by different extruders to fabricate a gyroid foam from the two separate materials. Such a gyroid foam possesses two separate deposited material compositions, and voids filled with supporting material during EFM. Were the supporting material removed, such a foam would then consist of an assembly of silicone and urethane rubbers.

The use of a nozzle to extrude allows using a nozzle to impart a mechanical shear to the extruded material during extrusion. For example, a nozzle may be rotated or vibrated in such a way as to shear the fluid extrusion in a circular fashion. The molecules of the extruded material may adopt a helical pattern of alignment rather than a linear one, but the net alignment across the extrusion still remains parallel to the direction of extrusion. This shear-based patterning may be varied by variation of the actuation of the extruder nozzle. Oscillation of the extruder nozzle may thin extruded materials displaying thixotropic rheology.

The use of an extruder to fabricate a foam allows for variation in extruded material flow rate during extrusion. An example of this is a progressive cavity pump or syringe pump imparting a differential pressure on the extruded fluid that results in a pre-determined flow rate in accordance with fluid rheology as well as the compliance of various mechanical components associated with plumbing the fluid to the nozzle of the extruder. Variation of the extrusion flow rate may result in an extruded material filament that is variable in diameter and possesses mechanical properties along its length that vary in accordance to the material diameter. As an example, a gyroid foam may be constructed from a material such as silicone rubber that is extruded in thin struts intersecting at larger diameter nodes. The 3D printer may extrude the silicone rubber at a low flow rate while drawing struts of the gyroid and high flow rates when drawing the nodes of the gyroid. In the resulting gyroid, the struts are less stiff than the nodes because the struts possess less material than the nodes.

Since supporting materials are fluids, it is possible to extrude them as if they were another print material for use in EFM. Volumes of support material used in EFM can be wholly or partially extruded using extruders dedicated to dispensing supporting materials. Support materials can thus be multimodal in composition, chemical behavior, and rheology. The use of multiple support materials in a bath can augment the ability to print fluid materials that are otherwise chemically incompatible with one another or require the presence of chemical mechanisms for curing or performing well during EFM. Combinations of the above mixing, material switching, and flow rate modulation are possible. For example, an open celled foam displaying simple strut-node morphology surrounding a single continuous void may be printed using both silicone and urethane rubbers. A portion of the foam may be composed of a gradient of different molecular weight silicones. A neighboring portion of the foam may be composed of a gradient of different molecular weight urethanes. The supporting material at the intersection of the extruders may be of a chemical composition to allow for the fusion of silicone rubber to urethane rubber. The extruder may vibrate and increase material flow rate to fuse together the different thermoset polymers at the points of overlap between them.

Foam characteristics

A structure formed in accordance with the described method may include partitioned regions of supporting material. Since these regions of supporting material are transient and serve to support the deposited thermoset material, they are considered void or not-deposited material.

Material addition during fabrication acts to partition support medium and define void boundary. Thus, within a printed object, partitioned regions of supporting material may define a pattern that reflects the deposited material and vice-versa. This patterning via partitioning of the support material is, by definition, nonstochastic.

Partitioned regions of supporting material within the bounding box of deposited material may remain connected to the surrounding supporting material or be disconnected and trapped within the deposited material.

Partitioned regions of supporting material are dynamic and capable of transformation to a more flowable state, since, in EFM, the supporting material is sensitive to some stimulus which renders it less viscous or more flowable.

During fabrication, the foam is composed of one fluid material interfacing with another fluid material. As an example of such interfacing during printing, regions of supporting material that are within the print (i.e., within the object being printed) and connected to the surrounding support material typically have a viscosity sufficiently low to flow out of the printed object, leaving behind empty space.

Regions of transformed supporting material within the printed object that are not connected to the surrounding support material are incapable of flowing out of the printed object, but they may be capable of diffusion if the deposited material is porous to the trapped support material. As an example, a low molecular weight mineral oil-based support may be trapped in a silicone resin print, but the support can diffuse through the silicone under certain conditions of temperature, pressure, and solvent exposure.

In some embodiments, transformed support material trapped inside the deposited material may not be able to diffuse out through the deposited material, thus it becomes a stimulus-responsive fluid trapped in the voids. Other AM methods, such as powder- and photopolymerization-based approaches can create foams that trap raw material (powder or photopolymer resin), but the trapped material is similar to the material comprising the foam. In contrast, the disclosed method enables the formation of foams with one material defining a structure with voids and a second material disposed within the voids.

Any printed article with regular, nonstochastic gaps in three dimensions in the printed material may be termed a foam, with the gaps in printed material being voids.

Any printed article occupying a region of support material and not being 100% composed of deposited material can be defined as a "foam" having voids or areas in three dimensions that lack deposited material but are still considered part of the printed article.

A distinguishing characteristic of some foams that may be fabricated only by using EFM is the presence of unsupported extrusions of print material, with the print material including material that would typically collapse or deform in its original fluid form. For example, only EFM may be used to fabricate a foam containing high aspect ratio (e.g., 1 or greater or 4 or greater) filaments of extruded silicone rubber that is not modified to cure quickly upon extrusion by UV exposure or other stimulus, i.e., the foam may not contain additives that enhance curing in response to some stimulus that immediately follows extrusion of the material but is not related to chemical interaction between the resin and the support material. Such unsupported high aspect ratio filaments may not be printed with other AM methods, as high aspect fluid silicone rubber collapse if not supported before solidification.

The thermoset material printed in EFM to fabricate a foam may be incapable of being stacked in FDM-style 3D printing conducted in open air. Accordingly, the material printable by EFM may possess rheological behavior including thixotropy or yield stress that is insufficient to support its weight when stacked in layers in air. For example, as a test of printability in air, one may print two or more 200 pm-thick layers, each made of extrusions 250 pm in diameter, with 400 pm center-to- center horizontal spacing between extrusions. Each layer's orientation of parallel fibers may be offset from the previous layer by a 90° rotation. The result appears as a set of horizontal, stacked cylinders, with a vertical overlap of 25 pm between layers as well as between the bottom layer and the surface printed onto. Fluid excluded by this overlap is allowed to flow onto neighboring bodies, e.g., extrusions or a build surface. In EFM, such a print has no overlap at a bottom surface. When this print is executed with a fluid having a low yield stress (assumed to be lower than 50 Pa), the fluid deforms instead of retaining a physical structure that is within 20% of the intended object's vertical height of approximately 425 pm. An example of a fluid possessing low yield stress is, e.g., Dow Corning Sylgard 184 with 0.25% w/v FISH thixotropic additive. This fluid is incapable of being stacked in air on top of itself without additional additives, but it is capable of printing in EFM. Accordingly, the thermoset material may be free of a rheological additive imparting yield stress greater than 50 Pa.

The thermoset material may also be free of photo-crosslinking additives that are typically added to stabilize fluids 3D printed in air or as part of a photopolymer 3D printing technique. Accordingly, the thermoset material may be non-photo-curable, without the inclusion of photopolymers and photoinitiators. An advantage of being able to use non-photo-curable materials with embodiments of the invention is the capability to use commercially available resins, rather than having to reformulate a resin to render it photo-curable.

The material may be free of additives intended to accelerate heat-driven crosslinking. The material may be free of shear thinning additives. The material may also possess a yield stress that is too low to permit its printing in open air but is sufficient to improve printing within EFM. The material may also possess thixotropy that is sufficient to support its fabrication inside a supporting bath material but is not sufficient to support 3D printing in open air. The material may be a resin that is intended for injection molding processes that has a small amount of inert rheological additive included to impart a modified thixotropic or yield stress behavior. If the material printed possesses a yield stress lower than 50 Pa and no photopolymer or photoinitiator, then it is likely suitable for EFM and not for another technique. Of course, this particular advantage of EFM does not preclude materials that are suitable for printing with other techniques from being printed using EFM.

Some printed materials may possess fluid behavior for an indefinite period of time after printing until sufficiently heated or driven to cure by some stimulus. Printed constructs formed by EFM typically include an actively gelling or crosslinking material that takes no longer than 48 hours to finish curing. Exceptions include materials that may interact with a chemical present in the bath to initiate gelation; in some cases, these materials gel exceptionally fast upon chemical interaction with the bath. Gelation behavior may not be monolithic, especially for printed materials that interact chemically with the supporting material. An example may include silicone resin, which can crosslink at its exterior if a catalyst for crosslinking is present in the support. The exterior gels first then the gelation proceeds inward, following the diffusion of the crosslinker into the extruded silicone resin until a given extrusion is completely gelled. Premixed silicone rubber that is actively curing, printed into a hydrophobic, lipophilic supporting material can diffuse outward before losing fluidity and solidifying into a hard rubber. Until the polymerization reaction is complete, the silicone is either in a fluid state (very low levels of curing) or in a tacky, elastomeric solid state (intermediate level of curing). Alternatively, silicone prepolymer can be printed into a supporting material that is laced with curing agent and initiates curing at the exterior of the prepolymer extrusion. Urethanes and urethane foam materials printed into a bath can react quickly and solidify into a rubber almost immediately, or they can be catalyzed by the presence of water and other chemicals in the supporting material. They can adopt a gelled fluid front or react internally to progress from a fluid to a solid state, much like premixed silicone resins. Most materials printed in EFM adopt one of these two modalities - they either cure with time and energy input (premixed silicone and urethane being good examples), or they cure due to some chemical stimulus present in the printing process. During the curing process, the printed materials possess temporary fluid states that are generally vulnerable to subtle forces that, in other 3D printing techniques, drive deformation in the printed material. For printing silicone by EFM, it is possible to print a UV curable silicone resin. It is also possible to EFM print a silicone that is thickened with a rheological additive to grant it a yield stress behavior and/or sufficient thixotropy to allow it to be stacked in a non-supporting medium. In both cases, the fluid prints do not experience a state while printing by EFM where the printed material is vulnerable to deformation by gravity. EFM printing can support both of the inks used in those two examples, but it can also support the printing of material that isn't endowed with a stimulus-based fast curing mechanism or rheological property to prevent sag in open air.

Another distinguishing characteristic of some foams that may be fabricated only via EFM is a material composition including thermoset polymers that were not modified to polymerize quickly upon exposure to some external stimulus. Polymer solutions that do not quickly adopt a higher viscosity post-extrusion are impossible to print without comprehensive supporting structures that not only prop-up the fluid material being deposited but also constrain its volume to prevent reorganization and consolidation of the liquid along the length of its extruded filament form. An example of such a foam composition is a platinum-catalyst silicone rubber such as Dow Corning Sylgard 184, which typically requires hours at elevated temperature to fully cure. Printing a foam from such a thermoset is possible with EFM, as a support bath provides support for the extruded material and also accelerates its polymerization.

Additional suitable thermoset materials include polyoxybenzylmethylenglycolanhydride (commonly known as Bakelite resin), benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea-formaldehyde resin, vinyl ester resin, and a fiber reinforced thermoset resin.

The thermoset material may include a heterogenous mixture of at least two materials, such as a mixture of the suitable thermoset materials listed above.

Material formed in accordance with embodiments of the invention may be customized for use in many applications such as:

• a cushion for a car, printed in a silicone gyroid

• seat cushions, seat backs with integrated or separate head rests, arm rests in cars, airplanes, and furniture

• acoustic insulating foam in building, automotive, airplane, and sound engineering

• helmet and other personal protective equipment designed to withstand impact (elbow, knee, shoulder pads) in sports (hockey, football, lacrosse, mountain biking, skiing/snowboarding, skateboarding) and transportation (cycling, motorcycling) footwear (sneakers, sandals, dress shoes) for both improved comfort and for tailoring of bedding (pillows, mattresses, bolsters and supports) orthopedic braces grips and handles on products for control (tools, sports gear, hunting gear, anes/crutches/walkers) protective and non-skid flooring and floor pads ergonomic aids (wrist pads, mouse pads, postural aids) light-weight structural foams foams with superior thermal insulation properties due to hierarchical structuring of internal oid architecture for application in oven design, flexible clothing toys/fidget/stress relief objects with unusual mechanical behaviors complex, 3 dimensional flexures for use in soft robotic actuators impact resistant ballistic armor

• metamaterials for the isolation of mechanical oscillations

• optical metamaterials

• lattices for reducing weight of ceramic structural components

• unidirectional progressive foam spring utilizing trapped spheres of foam within spherical voids to act as secondary compression members within the overall foam lattice whose struts and nodes serve as primary compression members.

• a metamaterial displaying a negative Poisson's ratio

• sponges with superior absorbent or adsorptive properties

• inflatable actuators or cushions with nonplanar deflection behaviors such as an inflatable cushion for a wheelchair to alleviate pressure points on a patient with paraplegia.

Examples of Applications

Hierarchical, silicone rubber cushion

Referring to Figure 6, a cross section of a rectangular cushion 600 displays hierarchical internal void architecture constructed of cubic cells. Arrows extend from the top of the model down, with the length of the arrows being inversely proportional to the elastic modulus. The lowest elastic modulus 610 is near the center, a higher elastic modulus 620 is proximate the center region, and the highest elastic modulus 630 is at the edges of the cushion.

This object is constructed by hierarchically dividing the interior of a rectangular volume into cubic cells. The digital model of a rectangular volume is imported into open source slicing software PrusaSlicer. G-code is generated from this file. The file is sliced into 300 pm layers. Each extrusion is assumed to be 700 pm wide. The amount of extrusion necessary to fabricate a filament may be limited by the extruding mechanism used. A small stepping motor driving a syringe pump may not be capable of extruding more than 40 pL/s. On the other hand, a progressive cavity pump may be capable of driving more than 10 mL/s. Fluid pumping capacity drives the maximum extrusion diameter possible. Likewise, minimum resolution in fluid pumping drives minimum extrusion diameter. For typical 3D printers used in EFM, fluid extrusion rate typically varies between 0.1 pL/s to 50 pL/s. Where two fluid extrusions are to overlap and fuse, they possess appropriate diameters and spacing to enable contact with, overlap, and subsequent fusion with one another. Where disparate fluid extrusions are not overlapping, they are spaced and sized in such a fashion to prevent overlap and potential fusion with one another. Each layer is then filled with a cubic pattern of filaments occupying 40% of the total space of the open layer. Percentage of object filled with extruded filament is determined by software and coupled to material properties of the printed object. The user of the 3D printer has the capability of determining a custom percentage between 0% and 100%.

The minimum distance from the center of each cubic cell within each layer to the horizontal exterior of the object is measured. Cubic cells that are not on the top or bottom of the object and more than d mm from the exterior, with d being the edge length of a cubic cell are grouped together to form larger cubic cells. Combined cells that are larger than 2d from the edge of the object are combined into even larger cells. The result is a hierarchical patterning of cubic cell architecture with the largest cubic cells residing in the innermost portion of each layer. The patterning of material composing the edges and vertices of these cubic cells crosses open space and partitions the support material into a singular interconnected void occupying a percentage of the model's volume. The population of cell edges and vertices, also known as elastic solids with struts and nodes in a lattice, determines the rectangular foam's stiffness in a given direction in a given region. Since the population of these struts and nodes is densest near the periphery of the rectangular cubic foam, the vertical foam stiffness is greatest near the periphery. Likewise, since the density of struts and nodes is lowest near the center, the vertical foam stiffness is lowest near the center. The cushion may be made of silicone rubber.

Silicone cushion

Referring to Figures 7A-7B, a silicone cushion for a car was printed with a hierarchical gyroid lattice using embedded additive manufacturing. The EFM process starts with importing a file of a cushion into open source slicing software PrusaSlicer. G-code is generated from this cushion file. The cushion file is sliced into 300 pm layers. Each extrusion is assumed to be 700 pm wide. Each layer of is then filled with a gyroidal pattern of filaments occupying 20% of the total space of the open layer. Gyroidal patterning crosses open space and partitions the support material into a singular interconnected gyroidal void occupying 80% of the model's volume.

Referring to Figure 7A, the g-code is then run on a 3D printer 700 utilizing a progressive cavity pump extruder which, through a static mixing head, extrudes a combination of 10 parts Sylgard 184 premixed with 0.5% w/v FISH thixotropic additive and 1 part Sylgard 184 curing agent. The silicone rubber is embedded into the supporting medium 710 which allows for EFM of silicone rubber. The supporting medium is, e.g., a hydrophobic non-Newtonian fluid. After printing, the supporting medium bath is heated to 80°C to cure the silicone print for 3 hours. A printer that can be used to print this silicone cushion includes a motion system capable of moving a fluid extruder in paths defining linear, arc, and splined trajectories along 3 or more axes. The extrusion system on this printer may be able to extrude thermosetting resins along with hydrogels and organogels. The extruder may have a needle that is small enough to project into the support medium and deposit material in a manner consistent with EFM. The printer may possess a progressive cavity pump, gear pump, or syringe pump extruder mounted on an X axis that is actuated on the Z axis. During printing, the printer may include a bed of support material in a container that is attached to and actuated along the Y axis. Extrusion along with 3D movements may be driven by stepper motors or servos. The timing of stepper or servo movements may be coordinated by the firmware of the printer which is itself loaded and run on a 32-bit ARM CPU. Stepper and servo motors may be driven by specialized IC's located on the motherboard along with the primary CPU. G-code for instructing printer firmware on necessary movements may be hosted in flash memory on the motherboard or streamed across a serial bus from a separate computer. The printer may include aluminum extrusions and milled aluminum plates. Each axis may ride along linear guides. Each axis may possess a belted transmission coupling the stepper motor to the actuated components.

In this example, a modified Creality CR10-S53D printer was used to print the silicone cushion. Each axis was replaced with milled aluminum plates with affixed linear guides. The X axis moves the extruder using a belted stepper motor. The Y axis moves the bed of support material using a belted stepper motor. The Z axis uses leadscrews coupled to stepper motors to actuate the X axis. The extruder is a Beinlich Visco.mini2k and it utilizes two progressive cavity pumps to actuate fluid material to a mixing manifold. The extruder is driven by stepper motors. The mixing manifold on the extruder is connected to a static mixer that combines the output from each half of the extruder into a continuous, well-mixed stream of fluid. At the exit of the static mixer, a needle serves as the nozzle for the extruder.

Printing on this printer is executed by manually moving the nozzle(needle) sufficiently deep into the bath of support material to allow for embedding of the extruded material.

Referring to Figure 7B, the completed cushion 720 composed of silicone rubber is removed from the bath by adding table salt to the bath material, which liquefies and releases the print. The print can then be removed and handled as any other 3D printed article.

The printed cushion possesses a void space of approximately 80% surrounding printed silicone rubber comprising the remaining 20%. The gyroid structure of the majority of the silicone is complementary to the gyroidal void surrounding the silicone. The silicone gyroid foam is fused together at intersections of extruded material and is considered a singular piece of silicone. Extrusions of silicone within the print are approximately 0.21 mm² in cross sectional area. The aspect ratio of each filament varies according to its location on top of or suspended in 3D space within the gyroid lattice. Some filaments of extruded material bridge gaps between manifold surfaces of silicone and are thus circular in cross section. Some filaments that layered one on top of the other are more squished and have a higher aspect ratio.

Urethane cushion

To print a urethane cushion, the file of a cushion is imported into open source slicing software PrusaSlicer and g-code generated, as discussed above with respect to the silicone cushion.

The g-code is then run on a 3D printer, e.g., a Creality CR10-S5- 3D printer, utilizing a progressive cavity pump extruder which, through a static mixing head, extrudes a combination of 1 part A and 1 part B of polyurethane prepolymer mixtures. The urethane rubber is embedded into the supporting medium which allows for EFM of urethane rubber. A suitable supporting medium may be, e.g., a mixture of oil, water, polyacrylic acid, lanolin, and surfactant.

After printing, the bath is heated to 80°C to cure the printed article for 3 hours. The completed cushion composed of urethane rubber is removed from the bath by adding table salt to the bath material, which liquefies and releases the print. The printed article can then be removed and handled as any other 3D printed article.

The printed cushion possesses a void space of approximately 60% surrounding printed urethane rubber constitutes the remaining 40%. Small regions of urethane within the print are 80% material and 20% void space containing trapped support material, e.g., a mixture of oil, water, polyacrylic acid, lanolin, and surfactant.

The gyroid structure of the majority of the urethane is complementary to the gyroidal void surrounding the urethane. The urethane gyroid foam is fused together at intersections of extruded material and is considered a singular piece of urethane foam/rubber. Extrusions of urethane within the print are approximately 0.21 mm² in cross sectional area. The aspect ratio of each filament varies according to its location on top of or suspended in 3D space within the gyroid lattice. Some filaments of extruded material bridge gaps between manifold surfaces of urethane and are thus circular in cross section. Some filaments layered, one on top of the other are more squished and have a higher aspect ratio.

Second silicone cushion Referring to Figure 8, a second car cushion 800 displaying a gyroid void was printed from silicone. As in Figures 7A-7B, this printed cushion includes a gyroidal void 810 filling 80% of the volume of the cushion, with the remaining 20% being the gyroidal silicone 820. This gyroidal silicone was constructed from 500 pm layers and 700 pm wide extrusions. Cylinder with varying elastic moduli

Referring to Figure 9, an exemplary cylindrical thermoset material 900 has different elastic moduli as measured from the top down at edges and center. The cylindrical material was generated by filling the interior of a cylinder with a gyroid occupying 12% of the total cylindrical volume and then slicing the cylinder into 300 pm layers. Each layer includes two 300 pm-wide filaments, i.e., extrusions, disposed in parallel around the circumference of the layer along with the interior gyroid paths. The result is a cylinder with circumferential shell 910 of silicone surrounding a gyroidal silicone foam 920. Compression of the interior gyroid foam displays a lower elastic modulus than compression of the exterior skin. Elastic moduli are determined by the packing of material within the printed article and not the composition of the material. Gyroid lattice

Referring to Figure 10, an example of a gyroid lattice 1000 includes multiple axes of symmetry and a nonstochastic uniform patterning of void 1010 and material 1020. This gyroid was generated by filling a cylindrical volume with a 20% gyroid foam and then layerwise constructing the gyroid from silicone rubber extrusions. Each layer is 300 pm thick. The described embodiments of the invention are intended to be merely exemplary and numerous variations and modifications are intended to be within the scope of the present invention as defined in the appended claims.

Claims

What is claimed is:

1. A foam comprising: a thermoset material defining a nonstochastic, regular packing of a plurality of voids, wherein (i) the thermoset material comprises a plurality of adjacent extrusions, (ii) contacting surfaces of pairs of adjacent extrusions define striations therebetween, (iii) a plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion, and (iv) a volume of the thermoset material comprises an elastic modulus lower than an elastic modulus of an equivalent volume of thermoset material without voids.

2. The foam of claim 1, wherein the thermoset material comprises at least one material selected from the group consisting of polyoxybenzylmethylenglycolanhydride, benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea-formaldehyde resin, vinyl ester resin, and a fiber reinforced thermoset resin.

3. The foam of claim 1, wherein the voids comprise a morphology selected from the group consisting of spherical, spindle-shaped, lumpy, dendritic, stellate, acicular, polygonal, nested, elongated, toroidal, branching, interpenetrating, continuous, and knotted.

4. The foam of claim 1, wherein the packing of voids is at least one of uniform or periodic.

5. The foam of claim 1, wherein the voids are at least one of discrete, proximate adjacent voids, or intersecting.

6. The foam of claim 1, further comprising a supporting medium trapped in at least one independent sealed void.

7. The foam of claim 6, wherein the supporting medium is selected from the group consisting of a hydrophobic non-Newtonian fluid; a mixture of surfactant, oil, and water; a mixture of oil, water, polyacrylic acid, lanolin, and surfactant; a gelatin slurry; and a mixture of an oil and a copolymer.

8. The foam of claim 1, wherein the foam comprises a plurality of struts joined together at a plurality of nodes.

9. The foam of claim 8, wherein at least one strut and at least one node comprise a same material.

10. The foam of claim 8, wherein at least one strut comprises the thermoset material and at least one node comprises a second material.

11. The foam of claim 8, wherein at least one node comprises the thermoset material and at least one strut comprises a second material.

12. The foam of claim 1, wherein the thermoset material comprises a heterogeneous mixture of at least two materials.

13. The foam of claim 12, wherein the thermoset material consists essentially of a heterogeneous mixture of the at least two materials.

14. The foam of claim 12, wherein the heterogenous mixture comprises a gradient of material stiffness and the at least two materials have different molecular weights.

15. The foam of claim 1, wherein the thermoset material comprises a composite material.

16. The foam of claim 15, wherein the composite material comprises at least one of a homogeneous or a heterogeneous mixture of at least two constituent materials.

17. The foam of claim 1, wherein the thermoset material is non-photo-curable.

18. The foam of claim 17, wherein the thermoset material is free of each of a photopolymer and a photoinitiator.

19. The foam of claim 1, wherein the thermoset material is free of a rheological additive imparting yield stress greater than 50 Pa.

20. The foam of claim 1, wherein the thermoset material comprises at least one floating body surrounded by at least one void.

21. The foam of claim 1, wherein the thermoset material comprises at least one floating body surrounding at least one void.

22. The foam of claim 1, wherein more than half of the voids are connected.

23. The foam of claim 1, wherein less than half of the voids are connected.

24. A cushion comprising the foam of claim 1.

25. A car cushion comprising the foam of claim 1.

26. A foam comprising: a thermoset material defining a void, a sidewall of the void comprising a triply periodic minimal surface of the thermoset material, wherein (i) the thermoset material comprises a plurality of adjacent extrusions, (ii) contacting surfaces of pairs of adjacent extrusions define striations therebetween, (iii) a plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the extrusion, and (iv) a volume of the thermoset material comprises an elastic modulus lower than an elastic modulus of an equivalent volume of thermoset material without the void.

27. The foam of claim 26, wherein each exposed surface of the thermoset material defines a plurality of striations.

28. The foam of claim 27, further comprising a supporting medium trapped in the void.

29. The foam of claim 28, wherein the supporting medium is selected from the group consisting of a hydrophobic non-Newtonian fluid; a mixture of surfactant, oil, and water; a mixture of oil, water, polyacrylic acid, lanolin, and surfactant; a gelatin slurry; and a mixture of an oil and a copolymer.

30. The foam of claim 26, wherein the thermoset material comprises a heterogeneous mixture of at least two materials.

31. The foam of claim 30, wherein the thermoset material consists essentially of a heterogeneous mixture of the at least two materials.

32. The foam of claim 30, wherein the heterogenous mixture comprises a gradient of material stiffness and the at least two materials have different molecular weights.

33. The foam of claim 26, wherein the thermoset material comprises a composite material.

34. The foam of claim 33, wherein the composite material comprises at least one of a homogeneous or a heterogeneous mixture of at least two constituent materials.

35. The foam of claim 26, wherein the thermoset material is non-photo-curable.

36. The foam of claim 35, wherein the thermoset material is free of each of a photopolymer and a photoinitiator.

37. The foam of claim 26, wherein the thermoset material is free of a rheological additive imparting yield stress greater than 50 Pa.

38. The foam of claim 26, wherein the thermoset material comprises at least one floating body surrounded by the void.

39. The foam of claim 26, wherein the thermoset material comprises at least one floating body surrounding the void.

40. The foam of claim 26, wherein the thermoset material further defines a plurality of non intersecting voids.

41. A method for fabricating a nonstochastic foam, the method comprising the steps of: providing a support material within which the foam is fabricated; depositing, into the support material, a print material comprising a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions defining striations therebetween, wherein depositing comprises: mechanically supporting at least a portion of the print material by the support material during the depositing to prevent deformation of the print material during deposition; suspending print material in the support material at a location where the print material is deposited; and transitioning the print material from a fluid to a solid or semi-solid state at the location where the print material is deposited to form the foam; and removing at least a portion of the support material to release the foam from the support material, wherein (i) the print material comprises a thermoset material, (ii) the foam comprises the thermoset material defining a nonstochastic, regular packing of a plurality of voids, (iii) a plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the surface of the extrusion, and (iv) a volume of the thermoset material comprises an elastic modulus lower than an elastic modulus of an equivalent volume of the thermoset material without voids.

42. The method of claim 41, wherein the thermoset material comprises at least one material selected from the group consisting of polyoxybenzylmethylenglycolanhydride, benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea-formaldehyde resin, vinyl ester resin, and a fiber reinforced thermoset resin.

43. The method of claim 41 wherein a pattern in which the print material is suspended determines a distribution of the voids in the thermoset material.

44. The method of claim 41, wherein a pattern in which the print material is suspended determines at least one of an aspect ratio, volume, axes of symmetry, orientation, surface area, or Hausdorff dimension of the voids.

45. The method of claim 41, wherein at least one void is occupied by support material.

46. The method of claim 41, wherein the support material comprises a hydrophobic non-

Newtonian fluid.

47. The method of claim 41, wherein the support material comprises a mixture of oil, water, polyacrylic acid, lanolin, and surfactant.

48. The method of claim 41, wherein the support material comprises a gelatin slurry.

49. The method of claim 41, wherein the support material comprises a mixture of oil, surfactant, and water.

50. A method for fabricating a nonstochastic foam, the method comprising the steps of: providing a support material within which the foam is fabricated; depositing, into the support material, a print material comprising a plurality of adjacent extrusions, with contacting surfaces of pairs of adjacent extrusions defining striations therebetween, wherein depositing comprises: mechanically supporting at least a portion of the print material by the support material during the depositing to prevent deformation of the print material during deposition; suspending print material in the support material at a location where the print material is deposited; and transitioning the print material from a fluid to a solid or semi-solid state at the location where the print material is deposited to form the foam; and removing at least a portion of the support material to release the foam from the support material, wherein (i) the print material comprises a thermoset material, (ii) the foam comprises the thermoset material defining a void, a sidewall of the void comprising a triply periodic minimal surface of the thermoset material, (iii) a plurality of molecules in each extrusion are aligned in a direction parallel to a striation defined by the extrusion, and (iv) a volume of the thermoset material comprises an elastic modulus lower than an elastic modulus of an equivalent volume of the thermoset material without voids.

51. The method of claim 50, wherein the thermoset material comprises at least one material selected from the group consisting of polyoxybenzylmethylenglycolanhydride, benzoxazine resin, chloroprene resin, cyanate ester resin, diallyl-phthalate resin, epoxy resin, furan resin, isoprene rubber resin, maleimide resin, melamine resin, phenol resin, polyester resin, polyimide resin, polysulfide resin, polyurea resin, polyurethane resin, silicone resin, urea-formaldehyde resin, vinyl ester resin, and a fiber reinforced thermoset resin.

52. The method of claim 50 wherein a pattern in which the print material is suspended determines a distribution of the voids in the thermoset material.

53. The method of claim 50, wherein a pattern in which the print material is suspended determines at least one of an aspect ratio, volume, axes of symmetry, orientation, surface area, or Hausdorff dimension of the voids.

54. The method of claim 50, wherein the support material comprises a hydrophobic non- Newtonian fluid.

55. The method of claim 50, wherein the support material comprises a mixture of oil, water, polyacrylic acid, lanolin, and surfactant.

56. The method of claim 50, wherein the support material comprises a gelatin slurry.

57. The method of claim 50, wherein the support material comprises a mixture of oil, surfactant, and water.