Bouligand structure and method of forming the same

Abstract

Various embodiments may provide a method of forming a Bouligand structure The method may include mixing an ink composition. The ink composition may include a polymeric resin, fibers and one or more viscosity adjusters. The method may also include depositing the ink composition to form the Bouligand structure using direct ink writing (DIW). The Bouligand structure may include a plurality of layers. The plurality of layers may include a polymer formed from the polymeric resin. The plurality of layers may also include the fibers embedded with different preferred alignment directions in the polymeric resin of different layers of the plurality of layers. The plurality of layers may also include the one or more viscosity adjusters.

Description

BOULIGAND STRUCTURE AND METHOD OF FORMING THE SAMECROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of Singapore application No. 10202302376P filed August 23, 2023, the contents of it being hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] Various embodiments of this disclosure may relate to a Bouligand structure. Various embodiments of this disclosure may relate to a method of forming a Bouligand structure.BACKGROUND

[0003] The microstructural design of reinforced composites significantly influences their mechanical properties, particularly their resistance to catastrophic failure. Researchers have been inspired by the microstructures found in biological materials to create artificial composites with good strength and toughness. One remarkable biological composite is the dactyl club of mantis shrimps, which can withstand impact and cavitation forces of 1501 newtons (N) and 504 N, respectively. Scholars have previously reported that the periodic region in the dactyl club contributes most to its impact resistance due to the helicoidal arrangement of mineral nanorods in a Bouligand structure. In this structure, layers of aligned mineral nanorods are stacked with a small angle turn between each adjacent layer. The pitch angle provides the Bouligand structure shear wave filtering effect and enhances its energy absorption upon fracture.

[0004] One of the strategies used by researchers to reproduce this Bouligand structure involves the manual lay-up procedure of fiber cloths. In this procedure, cut laminates are laid up with a controlled angle between layers to construct a helicoid laminated composite plate that is then cured using the vacuum bagging method. Another strategy to fabricate this type of composites is a brushing-induced assembly of one dimensional (ID) micro / nanofibers on a heated substrate, to fabricate macroscopic ordered two dimensional (2D) films. Specifically, this method includes using a hair brush loaded with a solution containing microfibers. The brush is slid onto a hot (~ 110 °C) planar substrate to deposit the film. After evaporation of the solvent, the microfibers deposited are arranged orderly and unidirectionally, and the processcan be repeated. Another approach to building the Bouligand composites employs a complex magnetically-assisted slip-casting process to align magnetized aluminum oxide (AI2O3) microplatelets into helicoidal Bouligand-like structures in bulk samples. In this process, magnetized AI2O3 micro-platelets coated with superparamagnetic iron oxide nanoparticles are oriented at arbitrarily defined angles using a magnetic field in solution. The solution is cast onto porous gypsum while the magnetic field is programmed to obtain the desired structure. These strategies face limitations in terms of scalability, reproducibility, repeatability, freedom to achieve the desired final three dimensional (3D) shape, and overall efficiency.

[0005] A more rational design in microstructure in macroscopic shapes and a more efficient approach may involve the 3D printing combined with external force e.g., shear force, magnetic or electrical field One typical example involves an electrical field-assisted stereolithographic 3D printing to align the carbon nanotubes (CNTs) in a layer and to control the rotation angles of the container at different layers to obtain CNTs composites with Bouligand structure. Nevertheless, the limited loading of particles within the matrix restricts the extent to which the mechanical properties of the composite can be significantly enhanced. Additionally, the requirement for ultraviolet (UV) light curing of the matrix imposes limitations on the selection of compatible components for the composites. Therefore, extrusion-based 3D printing techniques, where the filament or ink could have high loading of particles are interesting. The particles, like fibers or platelets, will align along the printing direction.

[0006] Fibers such as glass fibers, Kevlar fibers, and carbon fibers, typically used for enhancing the mechanical properties of various polymer matrices have been investigated using extrusion-based 3D printing techniques. Due to the shear force generated at the nozzle, 3D printing of continuous or discontinuous fibers induce their alignment in composites, thereby enhancing their strength and modulus. However, in the fused deposition modeling (FDM) method, the 3D printed fiber-reinforced composite inevitably contains voids between the extruded lines, resulting in weak interfaces. This compromises the strength and modulus of the composites.SUMMARY

[0007] Various embodiments may provide a method of forming a Bouligand structure. The method may include mixing an ink composition. The ink composition may include a polymeric resin, fibers and one or more viscosity adjusters. The method may also include depositing theink composition to form the Bouligand structure using direct ink writing (DIW). The Bouligand structure may include a plurality of layers. The plurality of layers may include a polymer formed from the polymeric resin. The plurality of layers may also include the fibers embedded with different preferred alignment directions in the polymeric resin of different layers of the plurality of layers. The plurality of layers may also include the one or more viscosity adjusters.

[0008] Various embodiments may provide a Bouligand structure. The Bouligand structure may include a plurality of layers. The plurality of layers may include a polymer formed from the polymeric resin, fibers embedded with different preferred alignment directions in the polymeric resin of different layers of the plurality of layers and one or more viscosity adjusters. The Bouligand structure defined by a pitch length and / or a pitch angle may also be varied, and be controlled locally within a three-dimensional (3D) shape defined by the 3D printing technique.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In the drawings, like reference characters generally refer to the same parts throughout the different views. The drawings are not necessarily drawn to scale, emphasis instead generally being placed upon illustrating the principles of various embodiments. In the following description, various embodiments of the invention are described with reference to the following drawings.FIG. 1 shows a general illustration of a method of forming a Bouligand structure according to various embodiments.FIG. 2 shows a general illustration of a Bouligand structure according to various embodiments. FIG. 3A shows a plot of relative frequency (in percent or %) as a function of length (in micrometers) illustrating the distribution of the glass microfibers to be used in the Bouligand structure according to various embodiments.FIG. 3B shows a plot of relative frequency (in percent or %) as a function of diameter (in micrometers) illustrating the distribution of the glass microfibers to be used in the Bouligand structure according to various embodiments.FIG. 3C shows the schematic of three dimensional (3D) printed structures according to various embodiments.FIG. 3D shows a schematic of the setup to conduct the impact test on the samples according to various embodiments.FIG. 4A is a table showing mechanical properties of matrix epoxy, glass fiber and interface from experimental matrix used in simulation modelling according to various embodiments. FIG. 4B is a table showing mechanical properties of another matrix epoxy, glass fiber and interface from “Composite Structures 220 (2019) 460-472”, used in simulation modeling as compared to the experimental matrix according to various embodiments.FIG. 4C is a table showing energy absorption and normalized energy absorption obtained from numerical simulation according to various embodiments.FIG. 5A shows a schematic illustrating the initial finite element (FE) model of the Bouligand structure according to various embodiments for the impact test.FIG. 5B shows a plot of strength (in mega-Pascals or MPa) as a function of strain (in percent or %) illustrating the variation of strength as a function of strain of the matrix without the glass fibers used in the simulation according to various embodiments.FIG. 5C shows a plot of stress (in mega-Pascals or MPa) and Young’s Modulus (in giga-Pascals or GPa) illustrating the tensile stress and Young's Modulus of the matrix without glass fibers used in the simulation.FIG. 5D shows a plot of stress as a function of strain illustrating the stress-strain response of the matrix under uniaxial tension according to various embodiments.FIG. 5E shows a plot of traction as a function of separation illustrating the simulated behavior of the fiber-matrix interface according to various embodiments.FIG. 6A shows a plot of the relative frequency (in percent or %) of the microfibers as a function of the aspect ratio (length (L) / diameter (D)) illustrating the distribution of the aspect ratios of the glass microfibers used for ink preparation according to various embodiments, with the inset being an optical image of the glass microfibers.FIG. 6B shows a plot of viscosity (in Pascals seconds or Pa s) as a function of shear rate (per second or s'1) of the ink composition immediately, 10 mins and 30 mins after adding hardener according to various embodiments.FIG. 6C shows a plot of the shear stress (in Pascals or Pa) as a function of shear rate (per second or s'1) of the ink composition immediately, 10 mins and 30 mins after adding hardener according to various embodiments.FIG. 6D shows a schematic illustrating the orientations of the microfibers at different positions in the nozzle during three dimensional (3D) printing according to various embodiments.FIG. 6E shows a microscopy image of the glass microfibers in an extruded layer according to various embodiments, juxtaposed with a hue-saturation-brightness (HSB) color-coded map that shows the angles of the microfibers in the image.FIG. 6F shows a plot of the distribution of orientation as a function of the orientation (in degrees) of the glass microfibers shown in the image of FIG. 6E according to various embodiments.FIG. 6G is a schematic illustrating a Bouligand structure according to various embodiments.FIG. 6H shows an optical image of a three-dimensional shape printed with a Bouligand structure according to various embodiments.FIG. 7A shows an illustration of the composite structures with microfibers oriented at angles of a = 0°, 45°, and 90° being prepared for the Izod impact test according to various embodiments.FIG. 7B shows a plot of energy absorption Ea(in kilo-Joules per square meter or kJ / tn2) illustrating energy absorption of a control structure (with no microfibers) and composite structures reinforced with microfibers at various angles a according to various embodiments.FIG. 7C shows an image of the fractured composite structures according to various embodiments after impact tests.FIG. 7D shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 0° according to various embodiments.FIG. 7E shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 45° according to various embodiments.FIG. 7F shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 90° according to various embodiments.FIG. 8A shows a plot of impact energy absorption Ea(in kilo-Joules per square meter or kJ / m2) as a function of pitch angle y (in degrees or °) illustrating the impact energy absorption of the Bouligand structures according to various embodiments at various pitch angles.FIG. 8B shows a plot of surface arithmetical mean roughness (in micrometers or pm) / developed interfacial area ratio as a function of pitch angle y (in degrees or °) illustrating the fractured surface roughness values of the Bouligand structures according to various embodiments at various pitch angles.FIG. 8C shows a plot of impact energy absorption Ea(in kilo-Joules per square meter or kJ / m2) as a function of surface arithmetical mean roughness Sa (in micrometers or pm) illustrating theexponential relationship (indicated by the dashed line) between impact energy absorption Eaand surface arithmetical mean roughness Sa of the Bouligand structures according to various embodiments.FIG. 8D shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 10° according to various embodiments. FIG. 8E shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 20° according to various embodiments. FIG. 8F shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 40° according to various embodiments. FIG. 8G shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 60° according to various embodiments. FIG. 8H shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 90° according to various embodiments. FIG. 81 shows scanning electron microscopy (SEM) images of the fractured surfaces of Bouligand structures having pitch angles of 10°, 20°, 60° and 90° according to various embodiments.FIG. 8J shows a plot of porosity (in percent or %) as a function of pitch angle y (in degrees or °) illustrating the variation of total porosities of the Bouligand structures according to various embodiments with pitch angle.FIG. 9A shows a schematic of a specimen including a Bouligand structure according to various embodiments, with images corresponding to different portions (in the XZ plane and in the YZ plane) of the Bouligand structure.FIG. 9B shows scanning electron microscopy (SEM) images of the fractured surfaces indicating crack twisting and crack bridging regions of the Bouligand structure according to various embodiments.FIG. 9C shows a zoomed-in scanning electron microscopy (SEM) image of the crack twisting region of the Bouligand structure according to various embodiments.FIG. 9D shows a zoomed-in scanning electron microscopy (SEM) image of the crack bridging region of the Bouligand structure according to various embodiments.FIG. 10A shows a plot of normalized energy absorption as a function of pitch angle y (in degrees or °) illustrating variation of the normalized energy absorption with pitch angle of the Bouligand structures according to various embodiments under impact at different speeds.FIG. 10B shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 10° according to various embodiments.FIG. 10C shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 40° according to various embodiments.FIG. 10D shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 90° according to various embodiments.FIG. 10E shows snapshots illustrating fracture of a Bouligand structure with a pitch angle y of 40° according to various embodiments after being impacted at an impact speed of 3 m / s from the top right comer.FIG. 10F shows snapshots illustrating fracture of Bouligand structures with pitch angles y of 40° according to various embodiments after being impacted at impact speeds of 2 m / s, 5 m / s and 10 m / s.FIG. 10G shows a plot of normalized energy absorption as a function of pitch angle y (in degrees or °) illustrating the simulated impact performance of Bouligand structures according to various embodiments with higher strength matrixes at impact speeds of 5 m / s and 6 m / s.FIG. 11 A shows a schematic of a three-point bending test on a Bouligand structure according to various embodiments.FIG. 1 1B shows a plot of flexural strength (in mega-Pascals orMPa) / flexural modulus (in gigaPascals or GPa) as a function of pitch angle y (in degrees or °) illustrating the variation of flexural strength and flexural modulus of Bouligand structures according to various embodiments with pitch angle.FIG. 11C shows a plot of flexural strength (in mega-Pascals or MPa) as a function of strain (in percent or %) illustrating the representative stress-strain curves recorded during the flexural tests for Bouligand structures according to various embodiments of different pitch angles.FIG. 1 ID shows a plot of flexural energy absorption Es (in kilo-Joules per square meter or kJ / m2) as a function of pitch angle y (in degrees or °) illustrating variation of flexural energy absorption with pitch angle of the Bouligand structures according to various embodiments.FIG. HE shows optical images of fractured morphologies of the Bouligand structure with a pitch angle of 40° according to various embodiments.FIG. 1 IF shows scanning electron microscopy (SEM) images of fractured morphologies of the Bouligand structure with a pitch angle of 40° according to various embodiments.DESCRIPTION

[0010] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, logical, and electrical changes may be made without departing from the scope of the invention. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0011] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0012] In the context of various embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements.

[0013] In the context of various embodiments, the term “about” or “approximately” as applied to a numeric value encompasses the exact value and a reasonable variance, e g. within 10% of the specified value.

[0014] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0015] By “comprising” it is meant including, but not limited to, whatever follows the word “comprising”. Thus, use of the term “comprising” indicates that the listed elements are required or mandatory, but that other elements are optional and may or may not be present.

[0016] By “consisting of’ it is meant including, and limited to, whatever follows the phrase “consisting of’. Thus, the phrase “consisting of’ indicates that the listed elements are required or mandatory, and that no other elements may be present.

[0017] Embodiments described in the context of one of the structures are analogously valid for the other structures. Similarly, embodiments described in the context of a method are analogously valid for a structure, and vice versa.

[0018] The direct ink writing (DIW) 3D printing method may be capable of overcoming the limitations of the FDM process. For instance, carbon fibers in epoxy-based inks can be alignedalong the printing direction using shear forces. Lightweight, wood-inspired cellular composites which exhibited Young’s modulus values that are an order of magnitude higher than those obtained by thermoplastics and photocurable resins developed for commercial 3D printing methods, while retaining comparable strength, have been developed. Although extrusion-based 3D printing presents excellent improvement in mechanical performance, only a few works have been carried out using such methods to form unique microstructure designs.

[0019] Various embodiments may relate to the extrusion-based three dimensional (3D) printing of Bouligand structures (also referred to as helicoidal structures) using direct ink writing (DIW). Various embodiments may relate to a Bouligand structure having improved impact resistance achieved through printing. Various embodiments may be simple, sustainable, cost-effective, scalable and shapeable. Various embodiments may allow the local discontinuous fibers, e.g., glass fibers to be aligned along the printing direction during extrusion. Programming the printing angle in each layer may lead to the formation of the helicoidal, Bouligand structure. The impact tests reveal that the energy absorption of the composite structures obtained may be superior to that of composites with unidirectional fiber alignment.

[0020] Impact resistance in fiber composites may be influenced by several factors, such as the shape, dimension, and stiffness of the fibers, the type of matrix, the volume fraction of fibers, the distribution of the fibers, and fibers-matrix interfacial properties. Extrusion-based 3D printing techniques may not only align the fibers at the microscale but may also be capable of printing complex 3D shapes, both of which contribute to the impact resistance of composites. Impact tests may be carried out using pendulum impact Izod test and Charpy test and dropweight impact. Printed continuous glass fiber reinforced Nylon composites, composites with different cellular structures (triangular, hexagonal, rectangular, and solid), and three distinct fiber orientations (0 / 0 / 0 / 0, 0 / 90 / 0 / 90 and 0 / 45 / 90 / -45) have been investigated. The effect of fiber orientation may be very dominant in dictating mechanical properties.

[0021] FIG. 1 shows a general illustration of a method of forming a Bouligand structure according to various embodiments. The method may include, in 102, mixing an ink composition. The ink composition may include a polymeric resin, fibers and one or more viscosity adjusters. The method may also include, in 104, depositing the ink composition to form the Bouligand structure using direct ink writing (DIW). The Bouligand structure may include a plurality of layers. The plurality of layers may include a polymer formed from thepolymeric resin. The plurality of layers may also include the fibers embedded with different preferred alignment directions in respective different layers of the plurality of layers. The plurality of layers may also include the one or more viscosity adjusters.

[0022] Tn other words, the Bouligand structure may be formed by printing using an ink composition (also referred to as “ink”) including a polymeric resin, fibers and one or more viscosity adjusters. After mixing of the ink composition, the ink composition may be transferred to the printer for printing before curing of the polymeric resin.

[0023] During DIW, the ink composition may be deposited (onto a surface) by a nozzle (of a three-dimensional (3D) printer) such that a majority of the fibers (e.g., more than 50%, more than 70%, more than 80%, more than 90% or more than 95%) are aligned along a wall of the nozzle at a tip portion of the nozzle. The nozzle may be chosen to align the fibers along the printing direction. In other words, the nozzle with the appropriate diameter may be chosen such that the majority or all the fibers are aligned along the wall of the nozzle, and that the ink composition can still be deposited (i.e., printed) onto the surface via extrusion. If the nozzle is too large, it may not be possible to align the fibers. On the other hand, if the nozzle is too small, it may not be possible to print at all. In various embodiments, the diameter of the nozzle may, for instance, be selected from a range from 0.5 mm to 1 mm, although in various other embodiments, the diameter of the nozzle may be of any suitable value that is able to align a majority of the fibers and still be able to carry out deposition (i.e., printing). A majority of the fibers included in a printed layer may have a preferred alignment direction based on a printing direction of the layer. The polymeric resin may be cured after the ink composition has been deposited, e.g., on a substrate. In various embodiments, the polymeric resin of one layer may be cured before deposition of the ink composition to form another layer on the cured layer. In various other embodiments, the polymeric resin may be cured after all the layers have been deposited. Careful control of the rheology of the ink composition may allow for the curing of the polymeric resin after all the layers have been deposited or printed. Consequently, a Bouligand structure including different layers with fibers aligned along different preferred alignment directions may be formed via printing layers using different printing directions. The DIW may be carried out by the printer in a layer-by-layer manner such that a first layer of the plurality of layers is (first) printed with fibers in the first layer having a first predefined preferred alignment direction, and a second layer of the plurality of layers is (subsequently) printed on the first layer with fibers in the second layer having a second predefined preferredalignment different from the first predefined preferred alignment direction. In the current context, a layer including fibers with a preferred alignment direction may refer to a layer in which most fibers of the layer (e.g., more than 50%, more than 70%, more than 80%, more than 90% or more than 95%) are aligned within 10° of the preferred alignment direction. For instance, a layer including fibers with a preferred orientation of 45° may have a majority of fibers in that layer (e.g., more than 50%, more than 70%, more than 80%, more than 90% or more than 95% of fibers in that layer) aligned within 35° and 55°. The angle between the preferred alignment direction of the fibers in the first layer and the preferred alignment direction of the fibers in the second layer adjacent to the first layer may be referred to as the “pitch angle”. The “pitch length” may be defined as the distance between the first layer and the adjacent second layer In various embodiments, a pitch length and / or a pitch angle of the Bouligand structure may be varied, and may be controlled locally within a 3D shape defined by the 3D printing technique. In other words, in various embodiments, a pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality of layers may be different. Further, a pitch length between two adjacent layers and a pitch length between two further adjacent layers may be different. In various other embodiments, a pitch length and / or a pitch angle of the Bouligand structure may be constant for the entire structure, i.e., the Bouligand structure may have a constant pitch length and / or a constant pitch angle. A pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality of layers may be equal. Further, a pitch length between two adjacent layers and a pitch length between two further adjacent layers may be equal. The printed Bouligand structure may have a three-dimensional (3D) shape defined by the 3D printing technique.

[0024] The Bouligand structure may alternatively be referred to as a Bouligand composite structure, or simply a Bouligand composite. Various embodiments may form a structure with mechanical properties, e.g., impact resistance, that are superior compared to structures formed by other 3D printing methods, such as FDM. In various embodiments, the process may generate some internal microvoids between the different layers Nevertheless, various embodiments may form Bouligand structures that have much less microvoids compared to structures formed from prior methods. Various other embodiments may form Bouligand structures that have nomicrovoids. Various embodiments may also form structures that have lower porosity and / or good interface binding between fibers Various embodiments may have enhanced impact resistance by controlling the pitch angle.

[0025] Tn various embodiments, the Bouligand structure may be configured such that a fractured surface roughness of the Bouligand structure increases with the pitch angle up to a threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°. The Bouligand structure is further configured such that the fractured surface roughness of the Bouligand structure may decrease with the pitch angle when the pitch angle is above the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°.

[0026] In various embodiments, the Bouligand structure may be configured such that an impact energy absorption of the Bouligand structure increases with a pitch angle up to the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°. The Bouligand structure may be further configured such that the impact energy absorption of the Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°.

[0027] In various embodiments, the Bouligand structure may have a maximum energy absorption of 2.0 kJ / m2or more, e.g., 2.4 kJ / m2or more for a different polymer composite system. In various other embodiments, the Bouligand structure may have a maximum energy absorption of any suitable value.

[0028] In various embodiments, the Bouligand structure may have a maximum flexural strength of 30 MPa or more, e.g., 36.9 MPa or more. In various other embodiments, the Bouligand structure may have a maximum flexural strength of any suitable value.

[0029] In various embodiments, the Bouligand structure may have a stiffness of 2.0 GPa or more, e.g., 2.26 GPa or more. In various other embodiments, the Bouligand structure may have a stiffness of any suitable value.

[0030] In various embodiments, the one or more viscosity adjusters may include carbon black or carbon nanotubes.

[0031] In various embodiments, a hardener may be mixed with the polymeric resin, the fibers and the one or more viscosity adjusters to form the ink composition. The hardener may assist in the cross-linking of the polymeric resin (i.e., curing of the polymeric resin) to form the polymer. In various embodiments, the polymeric resin may be cured at any suitable temperature, e.g., any temperature selected from a range from 20 °C to 25 °C. In variousembodiments, the polymeric resin may be configured to be cured upon application of an external trigger, such as a particular range of temperature or application of ultraviolet (UV) light. In various embodiments, the ink composition may include one or more additional functional elements for inducing one or more functional properties, such as electrical conductivity, thermal conductivity, color, etc. The one or more functional elements may be molecules or particles. For instance, the ink composition may include dye molecules so that the resultant Bouligand structure may be of a certain color or may include electrically conductive particles in sufficient concentration to induce electrical conductivity.

[0032] In various embodiments, the fibers included in the ink composition may be at least 35%, e.g., at least 50% by weight relative to the polymeric resin. In other words, in various embodiments, a weight of the fibers to a weight of the polymeric resin may at least be 35 : 100, e.g., 50 : 100. By having a high weight ratio of the fibers to the polymeric resin, various embodiments may have improved properties, such as impact resistance and fractured surface roughness.

[0033] In various embodiments, the fibers may be inorganic fibers such as glass fibers, Kevlar fibers, or carbon fibers In various other embodiments, the fibers may include a hydroxyapatite mineral or silicon carbide (SiC). In yet various other embodiments, the fibers may be organic fibers, e.g., wood fibers In various embodiments, the fibers may be microfibers, e.g., glass microfibers. The fibers may be short. For instance, the fibers may each have a length selected from a range from 25 pm to 300 pm. e.g. 50 pm. In various embodiments, an aspect ratio (i.e., ratio of the length to the diameter) of each of the fibers may be of a value selected from a range from 2 to 30, e.g., 5.

[0034] In various embodiments, the plurality of layers may include a coupling agent, e.g. a silane coupling agent. The surfaces of the fibers may be modified by the coupling agent to improve interface compatibility with the polymer

[0035] In various embodiments, the polymer may be a thermoset polymer, e g., cured epoxy, silicone, poly methylmethacrylate (PMMA) or polyurethane.

[0036] FIG. 2 shows a general illustration of a Bouligand structure according to various embodiments. The Bouligand structure may include a plurality of layers 202a, 202b. The plurality of layers 202a, 202b may include a polymer 204 formed from the polymeric resin, fibers 206a, 206b embedded with different preferred alignment directions in respective different layers of the plurality of layers 202a, 202b, and one or more viscosity adjusters 208.

[0037] In other words, the method may relate to forming a Bouligand structure by forming a plurality of layers 202a, 202b with fibers 206a, 206b having different preferred alignment directions. For instance, the layer 202a may include fibers 206a having a first preferred alignment direction, while the layer 202b may include fibers 206b having a second preferred alignment direction different from the first preferred alignment direction. The layers 202a, 202b may include a matrix including the polymer 204 and the one or more viscosity adjusters 208.

[0038] For avoidance of doubt, FIG. 2 seeks to provide a general illustration of some features according to various embodiments and is not intended to limit the number, orientation, arrangement, size, shape etc. of the features. For instance, while FIG. 2 shows two layers 202a, 202b, various embodiments may relate to a structure having any suitable number of layers, e.g. 2, 3, 5, 10 etc. In addition, while FIG. 2 shows a certain number of fibers 206a, 206b in each layer, various embodiments may relate to a structure with layers including any suitable number of fibers 206a, 206b. For sake of clarity and to avoid clutter, not all the fibers in FIG. 2 have been labelled. Further, while FIG. 2 shows fibers 206a aligned laterally, and fibers 206b aligned diagonally, various embodiments may relate to a structure having one layer with fibers aligned in any one suitable direction, and another layer with fibers aligned in another suitable direction.

[0039] While FIG. 2 shows the fibers 206a aligned perfectly in one direction and fibers 206b aligned perfectly in another direction, various embodiments may relate to a Bouligand structure having a layer in which most fibers 206a (or 206b) of one layer 202a (or 202b), e.g., more than 50%, more than 70%, more than 80%, more than 90% or more than 95%, are arranged within 10° of the preferred alignment direction (i.e. ±10°). In the current context, a layer including fibers with a preferred alignment direction may relate to a layer in which most fibers of the layer (e.g., more than 50%, more than 70%, more than 80%, more than 90% or more than 95%) are aligned within 10° of the preferred alignment direction.

[0040] In various embodiments, the one or more viscosity adjusters 208 may include carbon black or carbon nanotubes.

[0041] In various embodiments, the fibers 206a, 206b may be inorganic fibers such as glass fibers, Kevlar fibers, or carbon fibers. In various embodiments, the plurality of fibers 206a, 206b may include a hydroxyapatite mineral or silicon carbide (SiC). In various other embodiments, the fibers 206a, 206b may be organic fibers, e.g., wood fibers. In various embodiments, the fibers 206a, 206b may be glass microfibers.

[0042] In various embodiments, the polymer 204 may be a thermoset polymer, e.g., cured epoxy, silicone, poly methylmethacrylate (PMMA) or polyurethane.

[0043] In various embodiments, a pitch length and / or a pitch angle of the Bouligand structure may be varied In other words, in various embodiments, a pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality of layers may be different. Further, a pitch length between two adjacent layers and a pitch length between two further adjacent layers may be different. In various other embodiments, the pitch length and / or the pitch angle of the Bouligand structure may be constant for the entire structure, i.e., the Bouligand structure may have a constant pitch length and / or a constant pitch angle. A pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality of layers may be equal. Further, a pitch length between two adjacent layers and a pitch length between two further adjacent layers may be equal. The printed Bouligand structure may have a three-dimensional (3D) shape defined by the 3D printing technique. In various embodiments, the Bouligand structure may have a three-dimensional (3D) shape defined by three-dimensional printing. In various embodiments, the Bouligand structure may be configured such that a fractured surface roughness of the Bouligand structure increases with a pitch angle up to a threshold pitch angle of 40°. The fractured surface roughness of the Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold pitch angle of 40°.

[0044] In various embodiments, the Bouligand structure may be configured such that a fractured surface roughness of the Bouligand structure increases with the pitch angle up to a threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°. The Bouligand structure is further configured such that the fractured surface roughness of the Bouligand structure may decrease with the pitch angle when the pitch angle is above the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°.

[0045] In various embodiments, the Bouligand structure may be configured such that an impact energy absorption of the Bouligand structure increases with a pitch angle up to the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°. The Bouligand structure may be further configured such that the impact energy absorption ofthe Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold angle of a value selected from a range from about 39° to about 41°, e.g., about 40°.

[0046] In various embodiments, the Bouligand structure may have a maximum energy absorption of 2.0 kJ / m2or more, e.g,, 2.4 kJ / m2or more. Tn various other embodiments, the Bouligand structure may have a maximum energy absorption of any suitable value.

[0047] In various embodiments, the Bouligand structure may have a maximum flexural strength of 30 MPa or more, e.g., 36.9 MPa or more. In various other embodiments, the Bouligand structure may have a maximum flexural strength of any suitable value.

[0048] In various embodiments, the Bouligand structure may have a stiffness of 2.0 GPa or more, e.g., 2.26 GPa or more. In various other embodiments, the Bouligand structure may have a stiffness of any suitable value.

[0049] Various embodiments may relate to a Bouligand structure formed by any one method as described herein. Various embodiments may relate to an ink composition.

[0050] To create Bouligand composites, one strategy may include manually laying-up long fiber reinforced polymer laminates with a controlled angle between each layer. However, the use of continuous long fibers poses drastic constraints on the shapes In contrast, the use of short fibers allows the creation of liquid inks or pastes that can be used in additive manufacturing processes. For instance, Bouligand composites have been produced by brush- induced assembly of short micro / nanofibers on a heated substrate. In other works, adjusting the pH, aspect ratio and concentration of chitin whiskers in a solution could trigger their selfassembly into a Bouligand structure. However, these strategies still face limitations in terms of scalability, control of the Bouligand pitch angle, freedom to achieve complex three- dimensional (3D) shapes and overall efficiency. Having a fabrication method that can tailor the structural parameters, such as the pitch angle, can allow rational design and optimization of the Bouligand structure for high impact resistance in fiber-reinforced composites.

[0051] To enable such rational structural design, an efficient fabrication approach is 3D printing. To align microfibers at any desired angles, 3D printing has been combined with external fields. For example, stereolithographic 3D printing has been combined with electric fields to align carbon nanotubes (CNTs) within each deposited layer. However, stereolithography requires a liquid resin that cures using ultraviolet (UV), which limits the loading in CNTs and the mechanical properties of CNTs. In contrast, extrusion-based 3D printing techniques such as fused deposition modelling (FDM) and direct ink writing (DIW)do not have these limitations. In FDM, thermoplastic filaments are melted, extruded, and deposited on a cool substrate, whereas DIW involves pushing viscous inks with shear-thinning and thixotropic properties through a nozzle on a substrate. Due to the extrusion at the nozzle in both methods, shear can cause alignment along the printing direction of the microfibers distributed in the filaments or in the ink. To form Bouligand structures, it may therefore be sufficient to control the direction in which the nozzle is moving in each layer to set the orientation of microfibers present in the extruded material. Using FDM, Bouligand structures have been manufactured, showing improvements in their specific impact energies. However, delamination of the composite occurs during failure, likely due to the inevitable voids between the extruded lines that resulted in weak interfaces. In addition, FDM also has constraints on the achievable fiber concentration, and thus on the achievable mechanical properties. These issues are serious for future practical and commercial applications. In turn, DIW has been shown to be capable of 3D printing a wide variety of compositions, including viscous inks with high concentrations in reinforcing particles. Using DIW to 3D print Bouligand structures can potentially overcome the limitations of FDM and achieve improved mechanical properties, while enabling fine control over the microstructure to test and understand energy-dissipating mechanisms during fracture.

[0052] Various embodiments may relate to epoxy composites reinforced with glass microfibers assembled into Bouligand structures with controllable pitch angles 3D printed using DIW. The impact resistance and flexural properties of the composites may also be tested. Numerical simulations are conducted to support the experimental results to study the fracture mechanisms. First, the rheological properties of a viscous ink containing glass microfibers are optimized to yield an ink printable using DIW and allowing alignment of the glass microfibers along the printing direction. Subsequently, Izod impact tests are conducted on notched 3D printed composites to compare the energy absorption of unidirectional and Bouligand structures. The fractured specimens are inspected using scanning electron microscopy (SEM), laser microscopy, and micro computed tomography (micro-CT), which allow the characterization of the surface morphology, porosity, and cracking mechanisms. The flexural properties of the composites are also tested to compare the dynamic with the quasi-static fracture behaviors. The findings from this study provide insights into 3D printed, lightweight, and impact-resistant reinforced composites for potential applications in the aerospace, automotive, and defense industries, among others.

[0053] Materials

[0054] Carbon black was obtained from PRINTEX® XE 2-B and multi-walled CNTs (MWCNTs) were obtained from Graphi strength® Arkena Innovative Chemistry. E-Glass fibers (milled glass microfibers) were sourced from Japan’s Nippon Electric Glass Co. The lengths and diameters of the microfibers ranged 20 pm - 300 pm and 7 pm -14 pm, respectively, with average values of 50 pm and 10 pm. FIG. 3A shows a plot of relative frequency (in percent or %) as a function of length (in micrometers) illustrating the distribution of the glass microfibers to be used in the Bouligand structure according to various embodiments. FIG. 3B shows a plot of relative frequency (in percent or %) as a function of diameter (in micrometers) illustrating the distribution of the glass microfibers to be used in the Bouligand structure according to various embodiments Commercial epoxy resin and epoxy hardener (Casting Resin MS 1000) were purchased from WEICON South East Asia Pte Ltd.

[0055] Ink Preparation

[0056] Multi-wall carbon nanotubes (MWCNTs) (0.15 g) and carbon black (0.03 g) were dispersed into 7.98 g of epoxy resin using a Thinky Mixer (THINKY ARE-250, Japan) for 5 minutes at 2,000 revolutions per minute (rpm). Subsequently, the glass microfibers (5.25 g) were added to the above mixture and mixed for 5 minutes at 1000 rpm using an overhead mixer (Base Hei-TORQUE VALUE 400, Heidoph Instruments GmbH & Co. KG, Germany). Afterward, 1.59 g of epoxy harder was introduced and mixed using the same overhead mixer for 5 minutes at 500 rpm at a cold temperature (in an ice bath). The slow speed of the mixing and the use of the ice bath reduced the heat generated from the mixing and slowed down the epoxy reaction and the consolidation of the mixture, which was the ink for direct ink writing (DIW).

[0057] DIW of Bouligand Composites

[0058] The three-dimensional (3D) printing set-up (3D Potter Micro 8, 3D Potter Inc USA) consisted of a vertical nozzle with a mechanical piston to extrude the ink through the nozzle. The 3D models were created using a computer-aided design software (Rhinoceros 7). IdeaMaker was used to slice the designs into layers for the printing. Unidirectional microfibers orientation at angles a = 0°, 45°, and 90° within all the layers, and Bouligand structures with various pitch angles y = 10°, 20°, 40°, 60°, and 90° were designed. To realize these, the 3D printer deposited a layer with aligned glass fibers and then deposited another layer with aprinting direction twisted at the certain angle, the pitch angle, to obtain the Bouligand structure in composites

[0059] The following printing parameters may be used: a diameter nozzle of 0.8 mm, printing speed of 8 mm / s, layer thickness of 0.4 mm, and flow rate of 50%. At least six specimens of each design were printed for each test. The length, width, and depth values of the printed specimens were 64 mm, 6 mm and 12.8 mm, respectively. For these dimensions, 32 layers were deposited on top of each other. Since the total number of layers was fixed and the pitch angle y was varied, the period of the helicoidal assembly increased as the pitch angle increased: period ^ . (1)

[0060] Therefore, the periods of the Bouligand structures with y = 10°, 20°, 40°, 60°, and 90° were 1.8, 3.5, 7.1, 10.7 and 16, respectively. FIG. 3C shows the schematic of three dimensional (3D) printed structures according to various embodiments.

[0061] Impact Tests and Characterization

[0062] Izod impact tests were conducted using the Tinius Olsen impact machine (Willow Grove, PA, U.S.A.) following the ASTM standard D256. A V-notch of 2 mm depth was cut using a sample notch tool (DS-93). The dimensions of the impacted samples were as follows: 64 mm (length, / ), 12 mm (width, bx) and 4 mm (thickness, h). The applied pendular energy was 3.3669 J. The impact speed rate was 3.5 m / s. FIG. 3D shows a schematic of the setup to conduct the impact test on the samples according to various embodiments. The impact energy absorption Eaexpressed in kJ / m2was calculated using the following equation:103, (2)7where Ecis the corrected energy absorbed by the specimen (in joules); h is the thickness of the specimen (in mm); and b is the remaining width (in mm) of the specimen after testing. The specimens were polished using silicon carbide (SiC) papers before impact testing.

[0063] The size distribution of glass fibers was captured from the optical microscope and SEM images. The size of 100 glass microfibers was quantified to establish the size distribution using ImageJ software and plotted by Origin 2018 software. The quantitative orientation measurement of microfibers in the matrix was conducted on ImageJ within the Orientation! plugin. The rheological properties of the inks were measured at room temperature using a Rheometer (Bohlin, Malvern Instruments) with 15 mm serrated plates and a gap of 500 pm.Amplitude sweeps were carried out from 0.1 to 1000 Pa using oscillation mode at 1 Hz. The viscometry mode measurements were carried out for shear rates from 0.001 s'1to 100 s’1. All measurements were repeated at least three times. Electron microscopy was carried out on samples coated with 10 nm gold using a SEM (JSM-7600 F and JSM-5600 LV, JEOL, Japan).X-ray micro-CT analysis (Broker Skyscan 1173) was utilized to characterize the distribution of the glass microfibers in the epoxy matrix. The scanning was performed at 80 kV and 65 pA with a pixel size of 6.7 pm and a detector averaging 4 frames. Then, the ImageJ software was used to collect the 2D image projections and to merge them into a 3D volumetric representation of the specimen. The density and porosity of the samples were determined using Archimedes method and the following formulas:where p is the density of the sample, pwis the density of water (0.997 g / mL), pTis the theoretical density of the sample (1.39 g / mL), Ptis the total porosity of the sample, WAis the dried weight of the sample and WIAand W!ware the weights of the impregnated sample measured in air and water, respectively. At least 3 specimens were tested for each composite.

[0064] Topographical analysis of the fractured surfaces was conducted using a laser microscope (Keyence VK-X1000) over the entire fractured area for each composite after impact test. The topographical results were evaluated quantitatively using roughness parameters. The arithmetical mean roughness (Sa) was calculated following:where A represents the projected area of the surface in the X-Y plane and z(x,y) the heights in the topographical image. The developed interfacial area ratio (Sdr) was calculated as the percentage of the area’s additional surface area due to the roughness as compared to the planar surface area (the Sdr of a completely levelled surface is 0), following the equation:dz x y) where — is the gradient associated with the point located at the place x, y along the x axis, dz(x,y) . , , i l l i i— is the gradient associated with the point located at the place x, y along the y-axis.

[0065] Flexural strength and modulus values were obtained using 3-point bending in a mechanical testing machine (Mark- 10 Corporation, USA, model F305) equipped with a 250 Nload cell. The span of the jig was L= 32 mm. The size of the samples was 55 * 12 * 4 mm3. The measurements were carried out by loading the specimens at a constant displacement rate of 1 mm.min '. All specimens were polished before testing. At least 5 specimens were tested for each microstructure. The flexural stiffness Sr was obtained using the equation:> ml3f 4bh.3(7) where m is the slope of the secant of the load-displacement curve in the elastic region, A is the span, and b and h are the sample's width and thickness. The flexural energy absorption Esin the bending test, which approximates the toughness, was calculated using the equation:where F is the load in N, d is the displacement in m and x0is the displacement at failure. The flexural strength (cr) was calculated using: o- =32Pbmh2L' (9) where Pmis the peak load during the test. The maximum strain e was calculated following:

[0066] Finite Element Modeling

[0067] Finite element (FE) analysis was conducted using Abaqus 2020. The model was composed of glass microfibers (length: 25 pm, diameter: 5 pm, and aspect ratio: 5) assembled into Bouligand structures with the desired pitch angle y and surrounded by a matrix meshed with solid elements C3D4. The fiber-matrix interface was simulated with cohesive elements. The simulated samples had representative geometric dimensions of 325 pm x 810 pm x 214 pm (length x width x depth). The volume content of the microfibers (20 vol%) used in the numerical simulation was the same as that in the experiment.

[0068] FIG. 4A is a table showing mechanical properties of matrix epoxy, glass fiber and interface from experimental matrix used in simulation modelling according to various embodiments. FIG. 4B is a table showing mechanical properties of another matrix epoxy, glass fiber and interface from “Composite Structures 220 (2019) 460-472”, used in simulation modeling as compared to the experimental matrix according to various embodiments. FIG. 4C is a table showing energy absorption and normalized energy absorption obtained from numerical simulation according to various embodiments.

[0069] FIG. 5A shows a schematic illustrating the initial finite element (FE) model of the Bouligand structure according to various embodiments for the impact test. Only the elastic behavior is considered for the glass fibers. Continuum damage mechanics is used to describe the progressive damage in the matrix. The discrete cohesive zone method is adopted to model the traction-separation behavior at the fiber-matrix interface. The sample below notch at the left, bottom and right sides are fully constrained by the fixed boundaries. Besides, a cuboid block was set as a rigid body with a reference point (RP) using an initial high velocity v to strike toward the sample. The ‘penalty contact’ formulation involving friction coefficient is utilized for the general contact during whole impact process.

[0070] The tensile stress-strain response of the pure matrix without glass microfibers was measured experimentally FIG. 5B shows a plot of strength (in mega-Pascals or MPa) as a function of strain (in percent or %) illustrating the variation of strength as a function of strain of the matrix without the glass fibers used in the simulation according to various embodiments. FIG. 5C shows a plot of stress (in mega-Pascals or MPa) and Young’s Modulus (in giga-Pascals or GPa) illustrating the tensile stress and Young's Modulus of the matrix without glass fibers used in the simulation.

[0071] FIG. 5D shows a plot of stress as a function of strain illustrating the stress-strain response of the matrix under uniaxial tension according to various embodiments.

[0072] FIG. 5D presents the stress-strain curve obtained from uniaxial tension tests in FIGS. 5 A-B, assuming the matrix exhibits isotropic and elastoplastic constitutive behavior. The linear elastic phase is characterized by the elastic modulus Em. Upon reaching the yield strength Oy the Johnson-Cook constitutive model is employed to describe the yielding behavior of the matrix.

[0073] FIG. 5E shows a plot of traction as a function of separation illustrating the simulated behavior of the fiber-matrix interface according to various embodiments.

[0074] Results

[0075] To enable the design and fabrication of the Bouligand structures using 3D printing, the concentration of glass microfibers in the epoxy resin had to be adjusted to ensure printability. The ink was required to have a high viscosity and a high yield stress to allow extrusion and shape retention, respectively, and the possibility to print multiple layers without the collapse of the structure. Glass microfibers (50 pm in length and 10 pm in diameter on average) were used for the reinforcements. These glass microfibers were similar in chemistryto those used in continuous long fiber composites, but the short lengths were necessary to permit the creation of complex shapes with good resolution via 3D printing. The dimensions of the microfibers may be important since they bore a significant percentage of the applied load Here, the aspect ratio of the microfibers ranged from 2 to 30, with an average value of 5. FIG. 6A shows a plot of the relative frequency (in percent or %) of the microfibers as a function of the aspect ratio (length (L) / diameter (D)) illustrating the distribution of the aspect ratios of the glass microfibers used for ink preparation according to various embodiments, with the inset being an optical image of the glass microfibers. To meet the rheological requirements for DIW, carbon black and MWCNTs were introduced in the ink. These additional nanomaterials may enhance the final mechanical performance. The ink may be optimized to efficiently enable the homogeneous dispersion of the constituents and the removal of the air bubbles. FIG. 6B shows a plot of viscosity (in Pascals seconds or Pa s) as a function of shear rate (per second or s'1) of the ink composition immediately, 10 mins and 30 mins after adding hardener according to various embodiments. FIG. 6C shows a plot of the shear stress (in Pascals or Pa) as a function of shear rate (per second or s'1) of the ink composition immediately, 10 mins and 30 mins after adding hardener according to various embodiments. The finalized optimized ink contained 35 wt. % (weight percent) glass microfibers and had a viscosity at rest of 1000 Pa s and a yield stress of 500 Pa., which allowed 3D printing As shown in FIG. 6B, the viscosity of the ink may increase from 1000 Pa s to 7000 Pa s in half an hour.

[0076] After the ink was mixed, it was immediately transferred into the 3D printing syringe before the epoxy matrix was cured. The variation of viscosity as a function of time may be seen in FIG. 6B. In practice, the curing reaction may be slowed by using an epoxy matrix that crosslinked upon application of an external trigger, such as a low temperature. In this study, the resin and its curing time were chosen arbitrarily.

[0077] FIG. 6D shows a schematic illustrating the orientations of the microfibers 606 at different positions in the nozzle 612 during three dimensional (3D) printing according to various embodiments. To avoid clutter and to improve clarity, not all microfibers 606 have been labeled in FIG. 6D. During DIW, the glass microfibers 606 transitioned from a random orientation behind the tip of the nozzle 612 (position (i)) to an aligned orientation along the walls of the nozzle 612 at the tip portion (position (ii)). After extrusion and deposition, the microfibers 606 maintained their orientation, which was further fixed by the increase in viscosity due to the curing of the resin (position (iii)). FIG. 6D shows a first layer 602a beingformed on a substrate 610. This orientation of the microfibers 606 after 3D printing was verified by optical microscopy FIG. 6E shows a microscopy image of the glass microfibers in an extruded layer according to various embodiments, juxtaposed with a hue-saturation-brightness (HSB) color-coded map that shows the angles of the microfibers in the image. FIG. 6F shows a plot of the distribution of orientation as a function of the orientation (in degrees) of the glass microfibers shown in the image of FIG. 6E according to various embodiments. The precise alignment of the glass microfibers could therefore be combined with complex 3D shapes. FIG. 6G is a schematic illustrating a Bouligand structure according to various embodiments. The Bouligand structure may be formed after the deposition process shown in FIG. 6D, and may have multiple layers 602a - q. Each layer may include a plurality of fibers, which are not labeled in FIG. 6G to avoid clutter and improve clarity. The fibers in each layer are aligned along a preferred alignment direction. As seen from FIG. 6G, the fibers in adjacent or neighboring layers may be aligned in different preferred alignment directions, and the difference between the preferred alignment directions is the pitch angle. The Bouligand structure may be formed over the substrate 610.

[0078] FIG. 6H shows an optical image of a three-dimensional shape printed with a Bouligand structure according to various embodiments. The 3D microstructures in printed parts of complex shapes could be resolved using micro computed tomography (micro-CT). After curing, the printed reinforced composites retained their shape and microstructure and had a low density of 1.4 g / mL.

[0079] Impact Energy Absorption

[0080] The control of the microstructure during 3D printing was convenient for studying the effects of microstructural design on impact resistance. Firstly, composites with unidirectional microfiber orientations were designed and fabricated. To observe the effect of fiber orientation on crack propagation, the composites were purposely printed and tested at various microfiber angles a with respect to the impact direction (e.g., a = 0°, 45°, and 90°) were successfully 3D printed, notched, and submitted to the Izod impact test. FIG. 7A shows an illustration of the composite structures with microfibers oriented at angles of a = 0°, 45°, and 90° being prepared for the Izod impact test according to various embodiments. FIG. 7B shows a plot of energy absorption Ea(in kilo-Joules per square meter or kJ / m2) illustrating energy absorption of a control structure (with no microfibers) and composite structures reinforced with microfibers at various angles a according to various embodiments. As shownin FIG. 7B, the energy absorption of all unidirectional composites was higher than that of the control structure without glass microfibers. Increasing a increased the impact energy absorption of the composites from 0.514 kJ / m2for a = 0° to 1.1 kJ / m2for a = 90°. To explore the toughening mechanisms, the morphology of the fractured surface was captured for each microstructure. FIG. 7C shows an image of the fractured composite structures according to various embodiments after impact tests. FIG. 7D shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 0° according to various embodiments. FIG. 7E shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 45° according to various embodiments. FIG. 7F shows scanning electron microscopy (SEM) images of the composite structure with fibers having unidirectional orientation of a = 90° according to various embodiments. White arrows indicate river-like structures with hackles and ribbons. Dark arrows indicate the pull-out and breakage of the glass microfibers. The control structure presented a straight crack along the notched direction. The addition of microfibers with an a = 0° orientation showed a very straight crack along the notched direction, which was parallel to the microfibers. From the electron micrographs in FIG. 7D, crack slippage along the microfibers resulted in river-like structures with hackles and ribbons at the fractured surface, which contributed to increasing the energy absorption relative to the control composites. These types of white marks are typical of ductile deformation of the matrix in the presence of reinforcements. As there was no increase in crack tortuosity between the control structure and the composites with a = 0°, the difference in energy absorption was negligible. However, increasing the orientation angle to a = 45° deviated the crack from the notch direction following the microfiber orientations, extending the crack length and increasing the energy absorption. Additionally, it could be observed that some glass microfibers were removed from the matrix (dark arrows in FIG 7E) This phenomenon, along with crack slippage, may contribute to these composites exhibiting higher energy absorption levels than the composites with a = 0°. Upon further increasing the orientation angle to a = 90°, the fractured surface morphology appeared increasingly rough. Electron micrographs showed that most microfibers were pulled out and broken during impact, indicating the presence of a crack bridging mechanism (FIG. 7F). Crack deflection led to increased tortuosity, and the presence of microfibers perpendicular to the notch and crack propagation directions increased the energy dissipation. Overall, these series of experiments provided insights into the modes of fracturepropagation in the microfiber-reinforced composite structures. At angles below 45°, the crack tended to propagate along the microfibers with a minor increase in the total energy absorption. Increasing the orientation angle to 90° resulted in a relatively great degree of crack deflection and energy absorption with increasing microfiber fracture. From a = 0° to 90°, a transition between two fracture mechanisms was observed with slippage at low angles and pull-out and broken fiber at relatively high angles. Furthermore, there was some correlation between an increased impact energy absorption and an increased surface roughness. How the surface morphology and topography reflected the failure behavior has been reported in several studies. Therefore, tailoring the microstructure to significantly enhance the surface roughness could be expected to further amplify the energy absorption during fracture.

[0081] To demonstrate that the Bouligand structures could create rough fractured surfaces and increase energy absorption, 3D Bouligand structure are printed with pitch angles of y = 0°, 10°, 20°, 40°, 60° and 90°. By conducting the same impact tests as for unidirectional composites, increased energy absorption was recorded for all pitch angles. FIG. 8A shows a plot of impact energy absorption Ea(in kilo-Joules per square meter or kJ / rn2) as a function of pitch angle y (in degrees or °) illustrating the impact energy absorption of the Bouligand structures according to various embodiments at various pitch angles. The dashed lines serve as visual guides. The minimum energy absorption level of the Bouligand structures was obtained at y = 10°, with a value of 1.5 kJ / m2. By increasing the pitch angle to y = 40°, a maximum energy absorption of 2.48 kJ / m2was obtained. Beyond y = 40°, the composite structures exhibited relatively low impact resistance of 1.6 kJ / m2at y = 90°. The excellent energy absorption levels of the Bouligand structures relative to the unidirectional composites were attributed to the Bouligand structures, revealing an optimum pitch angle at which the energy absorption is at a maximum value. From FIG. 8A, the angle 40° may provide the best properties for the Bouligand structures. This phenomenon was different from Bouligand structures made from other materials, which showed a maximum toughness at a highly reduced pitch angle of approximately 9.47°. This result likely occurred due to the differences in chemical composition and microfiber size. Indeed, it has been reported that the aspect ratio of the microfiber drastically modified the responses of the composites. To better understand the performance of the Bouligand structure according to various embodiments, and to verify the importance of the pitch angle, the fractured surfaces were carefully analyzed. Precisely, the surface topographies of the fractured surfaces were measured, and the surface arithmetical mean roughness Sa valuesand the developed interfacial area ratio Sdr values were quantified. FIG. 8B shows a plot of surface arithmetical mean roughness (in micrometers or pm) / developed interfacial area ratio as a function of pitch angle y (in degrees or °) illustrating the fractured surface roughness values of the Bouligand structures according to various embodiments at various pitch angles. The dashed lines serve as visual guides. As depicted in FIG. 8B, increasing the pitch angle increased Sa and Sdr from 180 pm and 1.3, respectively, at y = 10° to the maximum values of 600 pm and 1.9, respectively, at y = 40°. At high pitch angles, Sa and Sdr decreased again to 190 pm and 1.4, respectively, at y = 90°. Interestingly, the impact energy absorption Ea was found to vary exponentially with Sa with a coefficient of correlation R2= 0.99. FIG. 8C shows a plot of impact energy absorption Ea(in kilo-Joules per square meter or kJ / m2) as a function of surface arithmetical mean roughness Sa (in micrometers or pm) illustrating the exponential relationship (indicated by the dashed line) between impact energy absorption Eaand surface arithmetical mean roughness Sa of the Bouligand structures according to various embodiments. Such an exponential correlation between roughness and energy absorption was analogous to the exponential correlation between roughness and flexural toughness reported elsewhere. Furthermore, the morphologies of the entire fractured surfaces were obtained through reconstructed 3D views. FIG. 8D shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 10° according to various embodiments. FIG. 8E shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 20° according to various embodiments. FIG. 8F shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 40° according to various embodiments. FIG. 8G shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 60° according to various embodiments. FIG. 8H shows a reconstructed three dimensional (3D) view of the topology of the fractured surface of the Bouligand structure with a pitch angle of 90° according to various embodiments.

[0082] FIG. 81 shows scanning electron microscopy (SEM) images of the fractured surfaces of Bouligand structures having pitch angles of 10°, 20°, 60° and 90° according to various embodiments.

[0083] In the Bouligand structure with y = 10° (FIG. 8D), the fractured surface was relatively smooth, and the crack slipped along the microfibers, which indicated crack twistingas the dominant fracture mechanism. The fractured surface of the structure with y = 20° (FIG. 8E) displayed two mountain-like features that were the result of crack deflections along the microfiber orientations. The peaks of the mountains likely correspond to the areas where the microfibers were at 90°. Within the scanned area, there were four structural periods, and it was expected that the microfibers reached orientations of 90° four times, but only two mountainlike features were observed. One probable reason for this discrepancy was that the fracture of the structure was a complex process that could not be predicted with 100% accuracy, particularly in the fabricated samples, where defects such as bubbles and misalignments may be present. Nevertheless, the trends observed experimentally correlated well with the microstructures. Apart from the two mountain-like regions, the rest of the fractured surface was relatively smooth. As the pitch angle increased further to y = 40° (FIG. 8F), the surface roughness of the fracture surface increased with further fracture of the microfibers and with large crack deflection events. Beyond y = 40° (FIGS. 8G-H), the topographies of the fractured surfaces appeared relatively smooth with continuous crack paths. Overall, the cracking mechanisms in the Bouligand composites included crack twisting and crack bridging. When both mechanisms occurred, the fracture surface area was amplified, resulting in increased energy absorption. The transition from the predominantly crack twisting mode at small pitch angles to the predominantly crack bridging mode at higher pitch angles has been reported in other works, but at relatively small pitch angles. In Bouligand structures with a small pitch angle, the dominant mechanism may be the crack-twisting mode. With an increase in pitch angle, the dominant crack mode may transition from crack twisting to crack bridging, which may result in more fibers being pulled out. The results here demonstrated that by carefully tuning the pitch angle by 3D printing, it was possible to tailor the fractured surface roughness to achieve maximum energy absorption. This enhancement in the impact resistance came despite the presence of certain defects, such as gaps, bubbles, and misalignment, that could not be avoided. A small amount of porosity may be measured in the Bouligand structures, which could contribute positively to the energy absorption. FIG. 8J shows a plot of porosity (in percent or %) as a function of pitch angle y (in degrees or °) illustrating the variation of total porosities of the Bouligand structures according to various embodiments with pitch angle. The voids that may be present close to the crack tip expand and tend to coalesce, which trigger plastic deformation in the surrounding matrix. Accordingly, the collapse of voids and associated microcracking before the main fracture may also contribute to the impact resistanceof the composite. Overall, the impact resistance achieved in the 3D printed Bouligand structures was quite remarkable.

[0084] The Bouligand composites with a pitch angle of 40° exhibited the highest energy absorption during impact. A closer look at the topography of the fracture surface further confirmed the fracture mechanisms discussed above. FIG. 9A shows a schematic of a specimen including a Bouligand structure according to various embodiments, with images corresponding to different portions (in the XZ plane and in the YZ plane) of the Bouligand structure. High crack tortuosity along the impact direction (in the XZ plane) likely resulted from a combination of crack twisting and crack bridging. The straight crack path in the YZ plane at the back of the Bouligand structure suggested that the crack propagated along the direction of the microfibers within each aligned layer. FIG. 9B shows scanning electron microscopy (SEM) images of the fractured surfaces indicating crack twisting and crack bridging regions of the Bouligand structure according to various embodiments. The top region presented a smooth fracture surface topography because the crack propagated along the microfiber orientation. This phenomenon was confirmed by the image at a high resolution shown in FIG. 9C. FIG. 9C shows a zoomed-in scanning electron microscopy (SEM) image of the crack twisting region of the Bouligand structure according to various embodiments. In contrast, the bottom region framed by the white dotted lines showed a relatively rough surface topography, and many glass microfibers were pulled out and broken, which were confirmed by the high resolution image shown in FIG. 9D. FIG. 9D shows a zoomed-in scanning electron microscopy (SEM) image of the crack bridging region of the Bouligand structure according to various embodiments. Therefore, the combined crack twisting and bridging mechanisms contributed to the high impact energy absorption levels in Bouligand composites with a pitch angle of 40°.

[0085] Numerical Simulation Analysis

[0086] To confirm the experimental results, numerical simulations were conducted using the finite element method. The mechanical properties of the matrix were obtained experimentally (see FIG. 4 A). The Johnson-Cook constitutive model parameters of the matrix were obtained by fitting the experimental stress-strain curves. The simulation model used the optimal alignment of glass microfibers with a length of 25 pm, diameter of 5 pm, and aspect ratio of 5 in structures without porosity While other input parameters, such as the cohesive behaviors for interface properties and the continuum damage model for the epoxy matrix, were sourced from the literature, these parameters were proven to be successful in epoxy andmicrofiber systems in finite element modeling (FEM) simulations. Given that the simulation model relied on the ideal parameters, the resulting value of energy absorption could not be directly compared with the experimental results. Therefore, the value was substituted with the normalized energy absorption. The simulation of the impact tests of the Bouligand structures with pitch angles from 10° to 90° revealed a maximum energy absorption at 40°, confirming the experimental results (FIGS. 4C, 10A). FIG. 10A shows a plot of normalized energy absorption as a function of pitch angle y (in degrees or °) illustrating variation of the normalized energy absorption with pitch angle of the Bouligand structures according to various embodiments under impact at different speeds. With increasing impact speed, the maximum value was still obtained at a pitch angle of 40° for all speeds. This finding indicated that the impact speed did not affect the optimum pitch angle Furthermore, the impact speed (strain rate) influenced the continuum damage of the epoxy matrix, thereby playing a role in the energy absorption of the composites. However, the value was lower than those of Bouligand structures, as shown in FIG. 4C. Therefore, the increased energy absorption of the composites as the impact speed increased was attributed to the Bouligand structure. This phenomenon, wherein a high impact speed resulted in additional energy absorption during failure, was confirmed in laminated structures.

[0087] After impact failure, the fracture morphologies presented crack propagation features similar to those in the experiments. FIG. 10B shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 10° according to various embodiments. FIG. 10C shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 40° according to various embodiments. FIG. 10D shows the fracture morphology of the fractured Bouligand structure with a pitch angle y of 90° according to various embodiments. In Bouligand structures with y of 10°, the crack propagated along the microfibers, revealing crack twisting as the dominant fracture mode. Upon increasing y to 40°, crack twisting and crack bridging along the microfiber orientation were observed. In the Bouligand structure with y of 90°, the crack twisted when the microfibers were parallel to the notch direction, while crack bridging occurred when the microfibers were perpendicular to the notch direction. Therefore, the transition from crack twisting to crack bridging at an optimum pitch angle of 40° may be confirmed. In addition, the numerical simulations provided information on the mode by which the composite fractured during impact.

[0088] FIG. 10E shows snapshots illustrating fracture of a Bouligand structure with a pitch angle y of 40° according to various embodiments after being impacted at an impact speed of 3 m / s from the top right comer. The color code represents the local tensile stresses. Before impact, the sample was relaxed, and no stress was observed at its surface. Once the pendulum struck, stresses quickly accumulated at the notch tip and in the opposite region near the clamp holder. These stress concentrations led to cracking at these regions, which then propagated and eventually met each other.

[0089] FIG. 10F shows snapshots illustrating fracture of Bouligand structures with pitch angles y of 40° according to various embodiments after being impacted at impact speeds of 2 m / s, 5 m / s and 10 m / s. When examining the Bouligand structures with y = 40° at a low impact speed of 2 m / s, there was a negligible difference in fracture behavior relative to the Bouligand structure at an impact speed of 3 m / s. This slight difference was indicative of a minor enhancement in energy absorption. However, with an increase in impact speed of 5 m / s, the Bouligand structure with y = 40° revealed additional crack tortuosity and fracture roughness therefore resulting in further energy absorption. With a further increase in the impact speed to 10 m / s, the Bouligand structure was destroyed at the impact location, as marked by the arrows in FIG. 10F, and it was difficult to estimate the energy absorption and the fracture mechanism. Therefore, the Bouligand structures being impacted under high impact speeds beyond 10 m / s from the simulation could not be compared with those being impacted under lower impact speeds (e.g., 2, 3, and 5 m / s).

[0090] Likewise, the use of a matrix with a high mechanical strength and an increased impact speed could increase the energy absorption values without changing the optimum pitch angle. FIG. 10G shows a plot of normalized energy absorption as a function of pitch angle y (in degrees or °) illustrating the simulated impact performance of Bouligand structures according to various embodiments with higher strength matrixes at impact speeds of 5 m / s and 6 m / s. The parameters of the matrix are based on those shown in FIG. 4B.

[0091] Quasistatic Bending Test

[0092] The simulated results indicated the limited effect of the impact speed on the optimum pitch angle. This point is important since in practical applications, the Bouligand structures undergo various types of loadings. Furthermore, other scholars have tested the quasistatic fracture of Bouligand composites with other compositions. Therefore, 3-point bending tests may be performed to estimate the flexural performance of the Bouligand structures accordingto various embodiments at various pitch angles. FIG. 11A shows a schematic of a three-point bending test on a Bouligand structure according to various embodiments. FIG. 1 IB shows a plot of flexural strength (in mega-Pascals or MPa) / flexural modulus (in giga-Pascals or GPa) as a function of pitch angle y (in degrees or °) illustrating the variation of flexural strength and flexural modulus of Bouligand structures according to various embodiments with pitch angle. All Bouligand structures exhibited a flexural strength between 20 and 40 MPa and a flexural modulus between 1.6 and 2.4 GPa, which were relatively high strengths and moduli for 3D printed fiber-reinforced polymers. These values could be optimized by choosing a stronger resin or other constituents in the ink. Interestingly, the Bouligand composites with a pitch angle of 40° exhibited the highest flexural strength and modulus, with values of 37 MPa and 2.26 GPa, respectively. These values were 48% and 28% greater than those of the Bouligand structures with pitch angles of 10° and 90°, respectively. In contrast, the Bouligand structures with a pitch angle of less than 40° exhibited a relatively high strain at fracture. For instance, the composites with a pitch angle of 10° broke at 4% strain, whereas composites with a pitch angle of 90° broke at 2% strain. FIG. 11C shows a plot of flexural strength (in mega-Pascals or MPa) as a function of strain (in percent or %) illustrating the representative stress-strain curves recorded during the flexural tests for Bouligand structures according to various embodiments of different pitch angles. The structures with small pitch angles showed crack twisting and a large fracture surface area, resulting in increased strain at failure, whereas composites with high pitch angles showed crack bridging and straight cracks, resulting in decreased flexural strain at failure. Furthermore, calculation of the flexural energy absorption Esby integrating the force- displacement curves yielded an estimate of the quasistatic toughness of the composites. FIG. 1 ID shows a plot of flexural energy absorption Es(in kiloJoules per square meter or kJ / m2) as a function of pitch angle y (in degrees or °) illustrating variation of flexural energy absorption with pitch angle of the Bouligand structures according to various embodiments. When plotting Esas a function of the pitch angle, 40° was still the pitch angle yielding the highest value. Esincreased linearly from y = 10° to 40°, reaching a maximum value of 8 kJ / m2at y = 40°. However, beyond a 40° pitch angle, Eslargely decreased to 4 kJ / m2at y = 90°. Finally, the crack path in the Bouligand structures with y = 40° showed high tortuosity, which likely contributed mostly to the energy absorption during testing. FIG. 1 IE shows optical images of fractured morphologies of the Bouligand structure with a pitch angle of 40° according to various embodiments. FIG. 1 IF shows scanning electron microscopy(SEM) images of fractured morphologies of the Bouligand structure with a pitch angle of 40° according to various embodiments The electron micrographs of the fractured surface displayed the combined fracture mechanisms with crack twisting and crack bridging. These results confirmed the limited influence of impact speed according to the simulations.

[0093] Various embodiments may relate to discontinuous glass microfiber composites with controlled microstructures 3D printed using D1W. Composites with unidirectional orientation may possess a maximum energy absorption of 1.1 kJ / m2at a = 90°, where the microfibers are perpendicular to the impact direction. By building Bouligand composites with microfibers at a = 90°, increased impact energy absorption may be obtained at a pitch angle of y = 40° with values reaching 2.5 kJ / m2, representing a 140% increase relative to the unidirectional composites. Moreover, a strong correlation between surface roughness and energy absorption in Bouligand composites is revealed. The surface roughness can be used to estimate the impact resistance performance of Bouligand composites in the future. From the fracture morphologies, hybrid fracture mechanisms with crack twisting and crack bridging models may be observed in the Bouligand composites during low-velocity impact in the experiment (3.5 m / s) and in the numerical simulation (2-5 m / s). As the pitch angle increases, the fracture surface morphologies transition from crack twisting-dominated patterns to crack bridging-dominated patterns. In addition to dynamic impact, the flexural strength and modulus values of the Bouligand composites at y = 40° may exhibit maximum values of 37 MPa and 2.26 GPa, respectively.

[0094] Due to the use of D1W as the 3D printing process, it is found that the absence of microvoids, the low porosity and the good interface binding between each deposited may prevent macroscopic delamination under impact loading relative to the reported results in FDM composites. Furthermore, previous scholars have reported that the increase in microfiber loading results in additional microfiber slippage and pull-out, enabling increased impact energy absorption According to various embodiments, microfiber concentrations exceeding 35 wt. % in the ink may be prepared by adjusting the contents of carbon black and CNTs. Therefore, the impact performance may be improved by using a high concentration of glass fibers in Bouligand composites based on practical applications. Furthermore, surface modification of glass microfibers using small molecules, such as silane coupling agents, to improve the interface compatibility with the matrix may be an option to enhance the performance of the Bouligand composites. The higher aspect ratio of the fibers may decrease the critical pitch angle and may further enhance the energy absorption levels. In various embodiments, theaspect ratio of glass fibers may be 2-30, which is shorter than the fibers in the beetle exoskeleton (aspect ratio of 50). To properly increase the aspect ratio of fibers and avoid clogging at the tip of the nozzle, thin commercial glass fibers and carbon fibers can be employed in the fabrication of Bouligand composites Moreover, biomaterials, such as hydroxyapatite mineral microfibers and silicon carbide (SiC) whiskers, can be introduced in this ink to extend their applications. Although the fracture mechanism is observed at low- velocity impact herein, determining the fracture performance values of the Bouligand composite under high-velocity or even hyper-velocity impact conditions may be an interesting topic for future investigations.

[0095] Various embodiments may provide technique that allows simultaneous microstructure and macroscopic shape design to enhance the mechanical properties, particularly the impact resistance, and to extend the practical applications of fiber composites in the aerospace, automotive, and defense industries, among others.

[0096] Various embodiments may have advantages over conventional methods / structures. Compared to the conventional lay-up procedure, the brushing self-assembly approach, various embodiments based on ink direct writing (DIW) may be efficient, simple, sustainable, cost- effective, potentially scalable to centimeters or meters, and may provide complex 3D shapes. In DIW, the viscous “ink” may be extruded out from the small nozzle under a controlled flow rate and may be deposited along digitally defined paths. DIW may therefore print 3D structures layer-by-layer where the fibers distributed in the ink are aligned along the printing direction under the shear force at the nozzle. Programming the printing angle at each layer may lead to the formation of the helicoidal Bouligand structure.

[0097] Compared to the electrical field assisted stereolithographic 3D printing used to align carbon nanotubes (CNTs) to obtain Bouligand CNTs composites, various embodiments may provide a simple and highly efficient 3D printing process with a high concentration of fibers in ink. The fibers according to various embodiments may not be required to have high electrical conductivity. The printed composites may be cured at room temperature.

[0098] Compared to the FDM 3D printing process, various embodiments may not generate voids between deposited filaments. There may not be weak interfaces between deposited filaments, which may prevent delamination under applied force. Various embodiments may be carried out at room temperature and may not need high-temperature treatment. The concentration of fiber in filaments used in FDM may be relatively low up to 27 wt. % due tothe high viscosity of the thermoplastic resin. However, according to various embodiments, the fiber concentration in the ink composition may be higher than 50 wt. %.

[0099] In terms of the impact resistance compared to existing continuous fiber composites with Bouligand structure, various embodiments may not exhibit delamination when the composites are impacted and may present high energy absorption in addition to the other benefits from 3D printing.

[0100] Compared to conventional cement composites with Bouligand structure, various embodiments may have low weight, low porosity, high strength, and high impact resistance. The polymer used may be replaced by a polymer that can be recycled and may be sustainable.

Claims

CLAIMS1. A method of forming a Bouligand structure, the method compnsing: mixing an ink composition comprising: a polymeric resin; fibers: and one or more viscosity adjusters; and depositing the ink composition to form the Bouligand structure using direct ink writing (DIW); wherein the Bouligand structure comprises a plurality of layers, the plurality of layer comprising: a polymer formed from the polymeric resin; the fibers embedded with different preferred alignment directions in the polymeric resin of different layers of the plurality of layers; and the one or more viscosity adjusters.

2. The method according to claim 1, wherein the one or more viscosity adjusters comprise carbon black or carbon nanotubes.

3. The method according to claim 1 or claim 2, wherein a hardener is mixed with the polymeric resin, the fibers and the one or more viscosity adjusters to form the ink composition.

4. The method according to any one of claims 1 to 3, wherein the fibers comprised in the ink composition are at least 35% by weight relative to the polymeric resin.

5. The method according to any one of claims 1 to 4, wherein the fibers comprised in the ink composition are at least 50% by weight relative to the polymeric resin.

6. The method according to any one of claims 1 to 5, wherein the fibers are glass fibers, Kevlar fibers, or carbon fibers.

7. The method according to any one of claims 1 to 6, wherein the polymer is a thermoset polymer.

8. The method according to claim 7, wherein the polymer is cured epoxy.

9. The method according to any one of claims 1 to 8, wherein the ink composition is deposited by a nozzle such that a majority of the fibers are aligned along a wall of the nozzle at a tip portion of the nozzle.

10. The method according to any one of claims 1 to 9, wherein the direct ink writing (DIW) is carried out by a printer in a layer-by-layer manner such that a first layer of the plurality' of layers is printed with fibers in the first layer having a first predefined preferred alignment direction, and a second layer of the plurality of layers is printed on the first layer with fibers in the second layer having a second predefined preferred alignment different from the first predefined preferred alignment direction.

11. The method according to any one of claims 1 to 10, wherein a pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality of layers are different.

12. The method according to any one of claims 1 to 10, wherein a pitch angle between preferred alignment directions of two adjacent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality' of layers are equal.

13. The method according to claim 12, wherein the Bouligand structure is configured such that a fractured surface roughness of the Bouligand structure increases with the pitch angle up to a threshold angle of 40°; andwherein the Bouligand structure is further configured such that the fractured surface roughness of the Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold angle of 40°.

14. The method according to claim 12 or claim 13, wherein the Bouligand structure is configured such that an impact energy absorption of the Bouligand structure increases with a pitch angle up to the threshold angle of 40°; and wherein the Bouligand structure is further configured such that the impact energy absorption of the Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold angle of 40°.

15. The method according to any one of claims 1 to 14, wherein the ink composition further comprises one or more additional functional elements for inducing one or more functional properties.

16. The method according to any one of claims 1 to 15, wherein the Bouligand structure has a three-dimensional (3D) shape defined by three- dimensional printing.

17. A Bouligand structure comprising: a plurality of layers, the plurality of layers comprising: a polymer formed from a polymeric resin: fibers embedded with different preferred alignment directions in the polymeric resin of different layers of the plurality of layers: and one or more viscosity adjusters.

18. The Bouligand structure according to claim 17, wherein the one or more viscosity adjusters comprise carbon black or carbon nanotubes.

19. The Bouligand structure according to claim 17 or claim 18, wherein the fibers arc glass fibers, Kevlar fibers, or carbon fibers.

20. The Bouligand structure according to any one of claims 17 to 19,wherein the polymer is a thermoset polymer.

21. The Bouligand structure according to claim 20, wherein the polymer is cured epoxy.

22. The Bouligand structure according to any one of claims 17 to 21, wherein a pitch angle between preferred alignment directions of two adj cent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality' of layers are different.

23. Tire Bouligand structure according to any one of claims 17 to 21 , wherein a pitch angle between preferred alignment directions of two adj cent layers of the plurality of layers and a further pitch angle between preferred alignment directions of two further adjacent layers of the plurality’ of layers are equal.

24. The Bouligand structure according to claim 23, wherein the Bouligand structure is configured such that a fractured surface roughness of the Bouligand stmeture increases with the pitch angle up to a threshold pitch angle of 40°; and wherein the Bouligand stmeture is further configured such that the fractured surface roughness of the Bouligand structure decreases with the pitch angle when the pitch angle is above the threshold pitch angle of 40°.

25. The Bouligand structure according to claim 23 or claim 24, wherein the Bouligand stmeture is configured such that an impact energy absorption of the Bouligand structure increases with the pitch angle up to the threshold angle of 40°; and wherein the Bouligand stmeture is further configured such that the impact energy absorption of the Bouligand stmeture decreases with the pitch angle when the pitch angle is above the threshold pitch angle of 40°.

26. The Bouligand stmeture according to any one of claims 17 to 25, wherein the Bouligand stmeture has a maximum energy absorption of 2.4 kJ / m2or more.

27. The Bouligand structure according to any one of claims 17 to 26, wherein the Bouligand structure has a maximum flexural strength of 36.9 MPa or more.

28. The Bouligand structure according to any one of claims 17 to 27, wherein the Bouligand structure has a stiffness of 2.26 GPa or more.

29. The Bouligand structure according to one any of claims 17 to 28, wherein the Bouligand structure has a three-dimensional (3D) shape defined by three- dimensional printing.

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