Engineering heterogeneity structures within a single functional intelligent material for soft actuators and methods of printing such structures

Abstract

Embodiments relate to structures formed from shape memory polymers and methods of making thereof. A structure is formed from at least one UV curable shape memory polymer resin and includes a plurality of domains. Each domain corresponds to a different region of the structure cured via a different UV light exposure time. The structure is configured to transform from a temporary shape to an established shape upon being stimulated by an external stimulus.

Description

ENGINEERING HETEROGENEITY STRUCTURES WITHIN A SINGLE FUNCTIONALINTELLIGENT MATERIAL FOR SOFT ACTUATORS AND METHODS OF PRINTING SUCH STRUCTURESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. Provisional Patent Application No. 63 / 519,573, filed on August 15, 2023. The entirety of this provisional patent application is incorporated by reference herein.FIELD

[0002] Embodiments relate to structures formed from shape memory polymers and methods of forming thereof. In particular, embodiments relate to heterogeneous structures formed from shape memory polymers with tunable mechanical properties and thermal stimuli-responsive behaviors and methods of forming thereof.BACKGROUND

[0003] Intelligent materials have gained extensive utilization in various fields, including soft robotics, smart textiles, biomimetic machines, actuators, and powered exoskeletons. Shape memory polymers (SMPs), one of the most attractive intelligent soft materials, have received intense interest due to their synthetic flexibility and reversible stimuli-responsive properties, allowing for highly deformable behaviors. A wide range of SMPs, including amorphous polymers, semicrystalline polymers, liquid crystalline elastomers (LCE), and hydrogels, have been developed to offer unique properties and functionalities. The SMPs can be programmed to adopt a temporary shape by applying external force when heated above their transitiontemperature (Tg). Once quenched at room temperature, the temporary shape becomes fixed.Remarkably, when the programmed SMPs are subsequently exposed to heat again (e.g., above Tg), they effortlessly recover their original shape. This unique shape-memory effect empowers SMPs to generate programmable movements, including bending, twisting, and contraction, in response to external stimuli.

[0004] For example, fiber-shaped SMPs may enable a lightweight actuator with a superior power-to-mass ratio, extensive strains, and high responsiveness. By applying the twist or coiled structure, the fiber-shaped actuators may function as artificial muscles, exhibiting exceptional work capacity and responsiveness. These actuators can achieve an energy density 50 times higher than natural human muscles, enabling them to lift loads over 600 times their own weight.

[0005] The simultaneous regulation of responsive deformations and mechanical properties is the fundamental challenge for high-performance SMP -based actuators, which requires the utilization of advanced manufacturing and fabrication techniques. For example, various approaches, including electrospinning and wet spinning, can fabricate fiber-shaped SMP actuators.Nevertheless, conventional approaches often possess limited control over material properties, hindering the regulation of robustness and responsiveness in as-fabricated actuators.SUMMARY

[0006] 3D printing has emerged as a promising approach to encode SMPs with spatially regulated material properties and responses. Among the various 3D printing technologies, photo stereolithography stands out by precisely controlling the three-dimensional (3D) geometry of UV-curable polymer precursors while also offering the ability to tune localized material properties through spatial manipulation of light intensity. This approach opens up new avenuesfor tailoring the performance and functionality of SMP-based actuators. By employing spatiotemporal modulation of UV light during the printing process, we can effectively customize both the mechanical properties and the shape memory effect of the fabricated actuators. In this regard, the 3D printing approach offers a promising solution for developing SMP-based actuators with tunable structures, material properties, and responsive behaviors. This innovative technique enables precise control and optimization of the actuator's performance, expanding the possibilities for advanced functional materials and devices.

[0007] We have developed a method utilizing photo-stereolithography-enabled 3D printing technique to fabricate a SMP structure. Specifically, the method involves designing and encoding heterogeneity domains and interfaces, allowing for precise regulation of mechanical properties and stimuli-responsive motions within a single SMP structure. This may be achieved by spatially controlling photo-polymerizations via a grayscale lithography approach, such as by utilizing a dynamic mask. For example, homogeneous SMP fibers may be printed in a layer-by-layer manner, and exposure times of the fibers may be varied to create a tunable elastic modulus. These printed fiber-shaped structures may demonstrate controlled rotation motions and may exhibit different top speeds ranging.

[0008] In an exemplary embodiment, a structure fomied from at least one UV curable shape memory polymer resin comprises a first domain corresponding to a first region of the structure cured via a first UV light exposure time; and a second domain corresponding to a second region of the structure cured via a second UV light exposure time, wherein the first UV light exposure time is different than the second UV light exposure time, wherein the structure is configured totransform from a temporary shape to an established shape upon being stimulated by an external stimulus.

[0009] In some embodiments, the structure further comprises a third domain corresponding to a third region of the structure cured via a third UV light exposure time, wherein the first UV light exposure time is different than the second and third UV light exposure times.

[0010] In some embodiments, the structure further comprises a fourth domain corresponding to a fourth region of the structure cured via a fourth UV light exposure time, wherein the first UV light exposure time is different than the second, third, and fourth UV light exposure times.

[0011] In some embodiments, the external stimulus is a temperature greater than or equal to the glass transition temperature of the at least one UV curable shape memory polymer resin.

[0012] In some embodiments, a value of a mechanical property of the first domain is different than a value of the mechanical property of the second domain.

[0013] In some embodiments, the mechanical property is selected from the group consisting of ultimate tensile strength, Young’s modulus, and toughness.

[0014] In some embodiments, each domain has a Young’s modulus between 524-928 MPa.

[0015] In some embodiments, each domain has a toughness between 0.63 x 106-0.95 x 106 J m- 3.

[0016] In some embodiments, a value of a thermal responsive behavior of the first domain is different than a value of the thermal responsive behavior of the second domain.

[0017] In some embodiments, the thermal responsive behavior is selected from the group consisting of rotation rate, maximum rotation rate, time to reach maximum rotation rate, and turns.

[0018] In some embodiments, the structure has a Young’s modulus ranging from 265-1208 MPa.

[0019] In some embodiments, the structure has a maximum rotation speed ranging from 169-441 rpm.

[0020] In some embodiments, the structure has torsional mechanical energy ranging from 3.9-9. J kg1.

[0021] In an exemplary embodiments, an actuator is formed a structure formed from at least one UV curable shape memory polymer resin comprises a first domain corresponding to a first region of the structure cured via a first UV light exposure time; and a second domain corresponding to a second region of the structure cured via a second UV light exposure time, wherein the first UV light exposure time is different than the second UV light exposure time, wherein the structure is configured to transform from a temporary shape to an established shape upon being stimulated by an external stimulus.

[0022] In an exemplary embodiment, a method of making a structure formed from at least one UV curable shape memory polymer resin comprises printing the structure, wherein the structure comprises a first domain corresponding to a first region of the structure cured via a first UV light exposure time, and a second domain corresponding to a second region of the structure cured via a second UV light exposure time, wherein the first UV light exposure time is different than the second UV light exposure time; heating the structure to a temperature at or above the glass transition temperature of the at least one UV curable shape memory polymer resin; deforming a programmed portion of the structure to a temporary shape via mechanical loading; and cooling the structure to a temperature below the glass transition temperature of the at least one UV curable shape memory polymer resin.

[0023] In some embodiments, printing the structure comprises printing via a grayscale lithography printing process.

[0024] In some embodiments, the grayscale lithography printing process is a fixed height process.

[0025] In some embodiments, the mechanical loading is selected from the group consisting of twisting, bending, rolling, and compressing.

[0026] In some embodiments, the structure further comprises an unprogrammed portion, wherein the unprogrammed portion is not subject to deforming via mechanical loading.

[0027] In some embodiments, the method further comprises heating the structure to a temperature greater than or equal to the glass transition temperature of the at least one UV curable shape memory polymer resin to recover an established shape of the programmed portion.

[0028] Further features, aspects, objects, advantages, and possible applications of the present invention will become apparent from a study of the exemplary embodiments and examples described below, in combination with the Figures, and the appended claims.BRIEF DESCRIPTION OF THE FIGURES

[0029] The above and other objects, aspects, features, advantages, and possible applications of the present invention will be more apparent from the following more particular description thereof, presented in conjunction with the following drawings. It should be understood that like reference numbers used in the drawings may identify like components.

[0030] FIG. 1 shows an exemplary method of forming an exemplary heterogeneous structure from SMPs.

[0031] FIG. 2 shows a schematic illustration an of exemplary photo-stereolithography-enabled 3D printing of the SMPs.

[0032] FIG. 3 is a schematic illustration of exposure-time dependent cross-linking density and chemical structures of photosensitive precursors.

[0033] FIG. 4 is a graph showing stress-strain curves of exemplary SMP fibers exposed under different exposure times (e.g., 30, 35, 40, 45, 50 seconds) at room temperature.

[0034] FIG. 5 is a graph showing Young’s modulus and toughness of exemplary SMP fibers versus exposure time.

[0035] FIG. 6 is an optical microscope image of a cross-sectional view of an exemplary SMP fiber.

[0036] FIG. 7 is a graph showing torque required to twist an exemplary SMP exposed under different exposure times (30-50 seconds) at room temperature.

[0037] FIG. 8 is a graph showing shear stress versus shear strain for an exemplary SMP fiber at low twist strains.

[0038] FIG. 9 is a graph showing shear modulus versus exposure time for an exemplary SMP fiber at low twist strains.

[0039] FIG. 10 is a graph showing tan 8 of exemplary SMP fibers with different comonomer IBOA / MA ratios of 0.71 and 0.62 measured from the dynamic mechanical analysis (DMA).

[0040] FIG. 11 is an illustration of the SMP programming process from the twisted state, programmed (fixed) state, to the recovered state.

[0041] FIG. 12 is a graph showing the rotation turns of exemplary SMP fibers versus time.

[0042] FIG. 13 is a graph showing the rotation rate (rpm) of exemplary SMP fibers as a function of time.

[0043] FIG. 14 is a graph showing maximum rotation rate of exemplary SMP fibers and time to reach the top rate versus exposure time.

[0044] FIG. 15 is a graph showing maximum rotation rate versus Young’s modulus of exemplary SMP fibers under 30, 35, 40, 45, and 50 seconds via layer-by-layer printing (from left to right).

[0045] FIG. 16 is a graph showing rotation turns versus time of exemplary SMP fiber-shaped micromotor via layer-by-layer printing at different exposure times (35 and 40 seconds) in response to heat after twisting for 300 turns / m. SMP fibers exposed under 30, 45, and 50 seconds were ruptured under programming 300 tums / m.

[0046] FIG. 17 is a graph showing the rotation rate (rpm) as a function of time obtained from the first derivative of the correlation in FIG. 16.

[0047] FIG. 18 is a graph showing rotation turns versus time of exemplary as-printed fiber (40 seconds exposure time) programming under different temperatures (45, 60, and 75 °C).

[0048] FIG. 19 is a graph showing rotation rate versus time of exemplary SMP fibers under different programming temperatures.

[0049] FIG. 20 is a digital photo demonstrating the compression and recovery of exemplary silicon-graphene composites (4 mg ML-1) at a strain rate of 30 mm min-1to an upper strain limit of 30%.

[0050] FIG. 21 is a graph showing the results of repeatedly programming (5 cycles) SMP fibers at 75 °C.

[0051] FIG. 22 illustrates a 3D model and spatial distribution profile of accumulated exposure time for a first exemplary design of a heterogeneity structure.

[0052] FIG. 23 illustrates a 3D model and spatial distribution profile of accumulated exposure time for a second exemplary design of a heterogeneity structure.

[0053] FIG. 24 illustrates a 3D model and spatial distribution profile of accumulated exposure time for a third exemplary design of a heterogeneity structure.

[0054] FIG. 25 illustrates time-resolved strain mapping via digital image correlation (DIC) analysis under a uniaxial tensile test at room temperature for three exemplary specimens of different heterogeneity designs.

[0055] FIG. 26 is a graph showing a stress-strain curves of representative localized heterogeneity domains obtained from DIC analysis for a first exemplary design.

[0056] FIG. 27 is a graph showing a stress-strain curves of representative localized heterogeneity domains obtained from DIC analysis for a second exemplary design.

[0057] FIG. 28 is a graph showing a stress-strain curves of representative localized heterogeneity domains obtained from DIC analysis for a third exemplary design.

[0058] FIG. 29 is a schematic illustration of three exemplary heterogeneity designs.

[0059] FIG. 30 is a graph showing stress-strain curves of fibers with three exemplary heterogeneity designs.

[0060] FIG. 31 is a graph showing rotation rate (rpm) as a function of time obtained from the first derivative of time-dependent rotation turns tested at 75 °C.

[0061] FIG. 32 is a graph showing a correlation of Young’s modulus and maximum rotation rate for exemplary homogenous (black symbols) and heterogenous fiber-shaped actuators.

[0062] FIG. 33 is an illustration of a three-step process to measure the output torsional mechanical energy: step 1 twist / program the upper region with two ends tethered to store torsional mechanical energy at Tg~75°C; step 2 quench the entire hybrid fiber at room temperature to keep the upper region fixed in a twisted state with only the top end tethered; step 3 tether two ends of the entire fiber and reheat it above Tgto release the stored mechanical energy in the upper region, which can rotate the lower region to overcome the increasing torsional load generated as the lower region is twisted. The red triangle indicates tethered end(s); the red curved arrow indicates programmed rotation direction; the blue curved arrow indicates released rotation direction

[0063] FIG. 34 is a schematic illustration of exemplary hybrid fibers consisting of the upper heterogeneity region as a rotating motor.

[0064] FIG. 35 is a graph showing torque required to twist three exemplary heterogeneous fibers and two exemplary homogenous fibers by 285 turns m-1at Tg(3.5 cm in length).

[0065] FIG. 36 is a graph showing power density versus energy density of rotating motors with three exemplary heterogeneity designs against various torsional loads generated by Homo-fiber 1 (square symbol) and Homo-fiber 2 (triangle symbol).DETAILED DESCRIPTION OF THE INVENTION

[0066] The following description is of an embodiment presently contemplated for carrying out the present invention. This description is not to be taken in a limiting sense but is made merely for the purpose of describing the general principles and features of the present invention. The scope of the present invention should be determined with reference to the claims.

[0067] Shape memory materials, such as shape memory polymers (SMPs), are known for their ability to transform from a temporary shape to an established shape. For example, an SMP can be programmed to embody a temporary shape when in an inactivated state and an established shape when in an activated state. An SMP may transform from its temporary shape to its established shape when stimulated by an external stimulus. The external stimulus can be a condition experienced by the SMP. For instance, such a condition may be a temperature greater than or equal to a critical temperature, such that the SMP is configured to transform from its programmed temporary shape to its established shape once heated to a temperature at or above the critical temperature. The critical temperature may be the glass transition temperature (Tg) of the polymer in some embodiments and such a critical temperature may be dependent on the type of polymer.

[0068] Embodiments may relate to a structure formed from at least one SMP. The structure may therefore be programmed to have a temporary shape and be configured to transform from its temporary shape to an established shape in some embodiments. For example, the structure can beprogrammed to embody a temporary shape when in an inactivated state and an established shape when in an activated state, such as when stimulated by an external stimulus, as described above.

[0069] In exemplary embodiments, the structure may have a programmed portion and optionally an unprogrammed portion. The programmed portion may be programmed with a temporary shape, while the unprogrammed portion may not be programmed with a temporary shape. The programmed portion may be any portion of the structure, such as at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, or 90 vol. % of the structure. In other embodiments, the programmed portion may encompass the entirety of the structure.

[0070] A programmed portion of a structure may be programmed via a thermomechanical cycle. The thermomechanical cycle may include the steps of heating, mechanical loading, and cooling. In particular, the cycle can include heating the programmed portion of the structure to a temperature above the Tgof the SMP. When the temperature of the programmed portion of the structure exceeds the Tgof its SMP, the SMP transforms from a glass / crystalline state to an elastic state, such that the molecular chains in the SMP may be manipulated. The programmed portion of the structure may then be physically manipulated into a temporary shape. Exemplary physical manipulations may include mechanical loading such as, but not limited to, twisting, bending, rolling, compressing, or any other suitable deformation. The loading may depend on a desired temporary shape of the programmed portion of the structure, or on a desired transformation from a temporary shape to the established shape. For example, a programmed portion of a structure may be twisted or wound into a temporary shape such that an untwisting or unwinding motion may occur when the programmed portion of the structure transforms from its temporary shape to its established shape. The structure may then be cooled to a temperaturebelow its Tg(e.g., to room temperature) such that the programmed portion of the structure embodies the temporary shape in an inactivated state. When the structure is reheated, such as to a temperature at or above the Tgof the SMP, the physically manipulated molecular chains of the SMP may revert to its initial shape.

[0071] As described in further detail below, the structures may be formed by a printing process (e.g., a 3D printing process). The established shape of the structure may be defined by the shape or configuration in which an SMP resin is cured / printed. The printing process may therefore be a stereolithography process, such as a grayscale lithography process, that utilizes ultraviolet (UV) light to cure the polymer and form the structure.

[0072] In exemplary embodiments, the SMP resin may comprise any an UV curable resin. In some embodiments, the SMP resin may comprise one or more monomers, a crosslinker, and a photoinitiator. Upon UV light absorption by the resin, the photoinitiator may undergo cleavage and fomi a polymer network. It is therefore contemplated that a longer exposure time may lead to increased absorption of photolytic energy, which may then lead to a higher cross-linking density in the printed SMP.

[0073] In exemplary embodiments, the programmed portion of the structure may comprise a plurality of domains (e.g., regions of the structure), wherein each domain corresponds to a different exposure time. The term exposure time relates to the amount of time in which the polymer is exposed to the UV light during the printing process. The programmed portion may have two domains, three domains, four domains, five domains, or any number domains, wherein each domain corresponds to an exposure time. For example, the first domain may correspond to a first region of the structure cured via a first exposure time, the second domain may correspondto a second region of the structure cured via a second exposure time, a third domain may correspond to a third region of the structure cured via a third exposure time, a fourth domain may correspond to a fourth region of the structure cured via a fourth exposure time, a fifth domain may correspond to a fifth region of the structure cured via a fifth exposure time, etc. However, the number of domains in the programmed portion is not particularly limited, and the programmed portion may include any number of domains. Moreover, exposure times are not particularly limited and may range, for example, from 10-150 seconds, 20-75 seconds, 30-50 seconds, 35-45 seconds, etc. It is therefore completed that the plurality of domains within a single structure may enable heterogenous and localized curing times within the structure.

[0074] The variations in exposure time can enable the regulation of mechanical properties of the structure. For example, as described above, the UV light may trigger a photo-polymerization reaction in the SMP resin, and a longer UV light exposure time may lead to increased absorption of photolytic energy, which may then lead to a higher cross-linking density in the printed SMP. It is therefore contemplated that UV light may be employed to spatially create a plurality of domains in the programmed portion of the structure during the printing process. Accordingly, the employed printing process is preferably one that allows for spatiotemporal control of UV light and / or UV curing time such that a plurality of domains may effectively be installed in the structure. In an exemplary embodiment, the printing process is a grayscale lithography process that allows for such spatiotemporal control.

[0075] Mechanical properties of the structure can be altered by altering the UV light exposure time. As each domain corresponds to a UV light exposure time, it is therefore contemplated that mechanical properties of each domain may be altered by altering the UV light exposure time. Forexample, mechanical properties such as ultimate tensile stress, Young’s modulus, and toughness may be altered by altering the UV light exposure time.

[0076] In exemplary embodiments, Young’s modulus may generally be increased by decreasing the UV light exposure time. For example, the Young’s modulus of a domain with an exposure time of 50 seconds may be lower than the Young’s modulus of a domain with an exposure time of 30 seconds. The Young’s modulus of each domain can range from 524-928 MPa in some embodiments.

[0077] In exemplary embodiments, toughness may be increased by increasing the UV light exposure time. For example, the toughness of a domain with an exposure time of 50 seconds may be higher than the toughness of a domain with an exposure time of 30 seconds. The toughness of each domain may range from 0.63 x 106-0.95 x 106J m-3in some embodiments.

[0078] In exemplary embodiments, the torque required to twist a domain may be increased by increasing the UV light exposure time. For example, the torque required to twist a domain with an exposure time of 50 seconds may be greater than the torque required to twist a domain with an exposure time of 30 seconds. In some embodiments, the torque required to twist domain may range from 0-3.0 N cm, preferably from 1.5-2.75 N cm.

[0079] In exemplary embodiments, the shear modulus of a domain may be increased by increasing the UV light exposure time. We have found that increasing the shear modulus of a domain can allow the domain to sustain higher torque under twist for some embodiments. For example, the shear modulus of a domain with an exposure time of 50 seconds may be greater than the shear modulus of a domain with an exposure time of 30 seconds. In some embodiments, the shear modulus of each domain may range from 1.5-3.5 GPa.

[0080] As can be appreciated from the above, the mechanical properties of a structure may be tuned and controlled by altering the exposure times of the plurality of domains. This can enable control over the mechanical properties exhibited within the domains of a single macroscopic structure. There may also be a tradeoff between some mechanical properties of the structure, such as Young’s modulus and toughness.

[0081] In some embodiments, the mechanical properties of the structure may further or alternatively be tuned and controlled by adjusting the formulation of the SMP resin. For example, by regulating the composition of the one or more monomers, such as the ratio of comonomers that may exhibit different Tg, it may be possible to control the Tgof the resulting SMP resin.

[0082] In some embodiments, the thermal responsive behaviors of the structure can similarly be altered by altering the UV light exposure time. As each domain corresponds to a UV light exposure time, it is therefore contemplated that thermal response behavior of each domain may be altered by altering the UV light exposure time. For example, in embodiments in which a domain is twisted from its established shape to its temporary shape, responsive behaviors such as rotation rate (e.g., unwinding rate), maximum rotation rate, time to reach maximum rotation rate, and turns may be altered based on the UV light exposure time.

[0083] In exemplary embodiments, the rotation rate (e.g., unwinding rate) of a domain may be increased by increasing the UV light exposure time to a time up to and including 40 seconds. However, the rotation rate of a domain may be decreased by increasing the UV light exposure time over 40 seconds. The rotation rate of each domain may range from 100-315 rpm for some embodiments. Similarly, the maximum rotation rate (of a domain may be increased by increasingthe UV light exposure time to a time up to and including 40 seconds, but the rotation rate of a domain may be decreased by increasing the UV light exposure time over 40 seconds. For some embodiments, the maximum rotation rate of each domain may range from 100-350 rpm.

[0084] In exemplary embodiments, the time to reach maximum rotation rate of a domain may be decreased by increasing the UV light exposure time to a time up to and including 40 seconds. However, the time to reach maximum rotation rate of a domain may be increased by increasing the UV light exposure time over 40 seconds. The time to reach maximum rotation rate of each domain may range from 4-9 seconds for some embodiments.

[0085] As can be appreciated from the above, the thermal response behaviors of a structure may be tuned and controlled by altering the exposure times of the plurality of domains. This enables control over the thermal responsive behaviors exhibited within the domains of a single macroscopic structure. The responsive behaviors of the structure may further or alternatively be tuned by adjusting the external stimulus temperature. For example, lower external stimulus temperatures may lead to lower rotation rates.

[0086] In some embodiments, the plurality of domains may form a domain profile within the programmed portion of the structure. The term domain profile relates to the manner in which the plurality of domains are spatially positioned, sized, shaped, and configured within the programmed portion of the structure via fixed-height grayscale lithography. The domain profile may therefore be manipulated by changing the position, size, shape, etc. of the domains and / or the exposure times of different domains. The interactions between the plurality of domains may affect the overall performance of the structure, such that the domain profile may alter the mechanical characteristics and the thermal responsive behaviors of the structure itself. Inexemplary embodiments, the domain profile may be configured such that the structure has aYoung’s modulus ranging from 265-1208 MPa, a maximum rotation speed ranging from 169- 441 rpm, and a torsional mechanical energy ranging from 3.9-9.5 J kg-1.

[0087] A structure may have any domain profile, and possible domain profiles are not particularly limited. For example, a first exemplary domain profile may include a gradual increase in curing time over predefined equal intervals in the longitudinal direction of the printed structure (see, e.g., FIG. 22), leading to a plurality of similarly sized domains along the length of the structure. As second exemplary domain profile may include a sequential, alternative change from a first curing time to a second curing time over predefined equal intervals in the longitudinal direction of the printed structure (see, e.g., FIG. 23), leading to two alternating domains along the length of the structure.

[0088] In exemplary embodiments, the structure’s transformation between an established shape and a temporary shape may be repeatable. For example, the structure may maintain a shape recovery ratio at or near 100%.

[0089] Embodiments may further relate to a method of forming structure from at least one SMP. The method may comprise designing a domain profile of the structure including a plurality of domains, as described above. For example, in some embodiments the domain profile and the structure itself may be designed using computer-aided design software. The method may further comprise printing the structure with heterogeneous domains via a fixed-height lithography in accordance with the design. As seen in FIGS. 2A and 2B, a grayscale lithography process may be used to print the structure. For example, the grayscale lithography process may be used to control the spatial distribution profile of localized UV exposure times, enabling multipledomains in a single structure. Grayscale lithography may be realized using a fixed-height UV curable system in a photo-stereolithography-based liquid crystal display (LCD) 3D printer. The fixed-heigh system refers to the method of layer building, wherein each layer is printed at a predetemiined height.

[0090] As detailed above, the method may further comprise programming the structure, or a programmed portion of the structure, via a thermomechanical cycle (e.g., heating, mechanical loading, and cooling).

[0091] In exemplary uses, a programmed structure may be used as an actuator. An actuator may be any component, such as a component of a machine, that may produce force, torque, and / or displacement in a controlled way and in response to some input (e.g., stimulus). For example, the programmed structure may be used a micro actuator or a micro motor. However, it should be understood that the above are only exemplary uses for the described structures, and uses and applications of the structures are not limited to these listed examples.EXAMPLES

[0092] Below are examples of specific embodiments for carrying out the present application.The examples are offered for illustrative purposes only, and are not intended to limit the scope of the present application in any way. Efforts have been made to ensure accuracy with respect to numbers used (e.g., amounts, temperatures, etc.), but some experimental error and deviation should, of course, be allowed for.

[0093] Experimental Methods - Material Preparation: Methyl acrylate (MA), isobornyl acrylate (IBOA), 1,6-hexanediol diacrylate (HDDA), Bis(2,4,6- trimethylbenzoyl)- phenylphosphineoxide (Irgacure 819), methanol, and ethyl acetate were obtained from Sigma-Aldrich (USA) and used as purchased. MA (56.9 mol%) and IBOA (40.3 mol%) as comonomers,HDDA (2.8 mol%) as a crosslinker, and Irgacure819 (0.5 wt%) as the photoinitiator were mixed at room temperature and stirred for 6 hours to create the printing precursor. The precursor was stored away from light before printing to prevent property deterioration.

[0094] Experimental Methods - Printing System Setup and Printing Procedure of SMPFibers: The layer-by-layer 3D printing of homogeneous SMP fibers was first used as a fundamental study, and was achieved using a liquid crystal display 3D printer (Anycubic Photon Mono X 6K, Shenzhen, China). A fixed-height digital light curing system using a liquid crystal display 3D printer was also developed for grayscale lithography to print heterogeneous SMP fibers with designed domains. A closed printing cell was constructed using a vat, two fixed- height cover glasses (height: 0.6-0.9 mm), and a large cover glass on top (Figure S7). CAD software (Solidworks) was employed for designing the printing models. The curing thickness of the specimen is fixed during this fixed- height printing process. The various thicknesses indicated in the printing models do not represent the dimensions of the printing samples. Instead, they signify the number of repeated curing times (25 seconds for each unit exposure), which can tune the material properties by varying the accumulated doses of UV exposure. For instance, within the same fixed height, a region with a 150 seconds curing time required six-unit UV exposures (6 x 25 seconds per layer = 150 seconds), while a region with a 50 seconds curing time needed to be exposed twice (2 x 25 seconds per layer = 50 seconds).

[0095] To fabricate the SMP fibers for torsional rotation demonstration, the printing precursor was injected into the closed cell and cured by the LCD printer, resulting in fibers with dimensions of 0.9 x 0.9 x 120 mm. Smaller dimensions (e.g., 0.6 x 0.6 x 35 mm) of the printedfibers were obtained for measuring the stored and released mechanical energy. Following the printing process, a post-printing washing step was conducted using a solvent mixture of ethyl acetate and methanol (ratio 1:1) to remove any excess unreacted monomers present in the printed samples. Subsequently, the samples were heated in an oven at 100°C for 30 minutes.

[0096] Experimental Methods - Characterizations and Measurements: The glass transition temperature of the as-printed fibers from layer-by-layer printing was determined using a dynamic mechanical analyzer (DMA, Q800 TA Instruments) (temperature range: 20°C - 100°C; heating rate: 5°C min-1; frequency: 1 Hz). DMA was also employed to measure the torque, storage modulus, loss modulus, and tan 3 at specific temperatures. DMA (Anton Paar MCR 702e) was used for the measurement of transition temperature (Tg) of homogenous and heterogenous SMP fibers (dimension: 0.6 x 0.6 x 35mm) (temperature: 30 to 100°C; heating rate: 2 °C min-1; frequency: 1Hz; oscillating amplitude: 0.01% strain).

[0097] The mechanical properties, including Young’s modulus, strain at break, ultimate tensile stress, and yield point, were obtained using a mechanical tester (CS2-1100 Series, Chatillon) through the tensile test. Young’s modulus values were calculated from the slope of each stress- strain curve, ultimate tensile stress values were obtained from the maximum value in each stress- strain curve. The yield points were obtained from the interception among the 0.2% offset lines and the stress- strain curves. Tensile toughness can be calculated using the area underneath the stress-strain curve. Dog-bone specimens (with a middle cross-sectional area: 0.5 x 2.5 mm) printed using the same SMP were stretched at a constant strain rate of 2 mm min-1at room temperature.

[0098] A custom-built torsion tester (M7I, Mark- 10) was utilized to measure the torque at room temperature and demonstrate the stimuli-responsive rotation motion and work capacity at Tg. The test platform consists of a programmable step motor, a sensor, a heating band, and a temperature controller. This comprehensive setup allows for the generation of rotation motion, torque measurement, and precise control of the environmental temperature surrounding the tested samples. For the torque measurements, the printed fiber (dimension: 1.5mm x 1.5mm x 120mm) was rotating with one end tethered and connected to the torque sensor, and the other end driven by a step motor. To calculate the shear modulus of the SMP fibers, the shear strain and shear stress are given by Equations (1) and (2), respectively:

[0099] where Rsis the radius of fiber, Lsis its length. The torque Γ and twisted angle θ were directly measured through twisting tests. From the curves of shear stress versus shear strain at small twist angles (strain < 0.02), the shear modulus can be derived from the slope for each curve. For the rotation demonstration, a SMP fiber was tethered between two grippers and then subjected to heat using the heating band, reaching the desired temperature. The fiber could be programmatically twisted to different degrees or turns during this process. Subsequently, the SMP fiber was quenched to room temperature, fixing its twisted state. By raising the temperature above its transition temperature (Tg), the fiber could revert to its original untwisted state. A 1.5 g load was subjected to one end of the fiber.

[0100] DMA (Anton Paar MCR 702e) was employed to measure the torque (three heterogeneous fibers as rotating motors and two homogeneous motors as loads), as well as the work capacity of heterogeneity fibers in a two-part hybrid fiber (total length: 7 cm). The upper region (3.5 cm in length) serves as a rotating motor, while the lower region (3.5 cm in length), acts as a torsional load. The upper motor can rotate and overcome the increasing torsional load generated by the lower region as it continues to be twisted, thereby delivering work capacity. The number of turns and rotating speed of the lower load region, driven by the upper motor region, were determined through frame-by-frame video recording. The released mechanical energy of the rotating motor was obtained by integrating the torque-angle curves using Equation (3):

[0101] where Γ and θ represent the measured torque and rotation angle of the torsional load part, respectively. The power of the motor part was calculated using Equation (4):

[0102] The mass of the load part was 0.02 g, allowing for the calculation of specific energy density and specific power density.

[0103] Digital image correlation (DIC) analysis was used as a non-contact, non- interferometric method to measure the complete information of deformation or strain mapping of SMP samples. This technique utilizes a stereoscopic camera setup to capture a series of digital images of the deforming surface during the tensile test. The surface strain can be determined through correlation analysis by comparing the measured surface contour with the resolved displacement from the image sequence. To perform DIC analysis, a reference image of theundeformed surface is acquired before the test. Random patterns are applied to the measuring surface, serving as markers for correlation. These patterns are tracked and compared with those in the reference state to calculate the displacement and strain. In this study, graphene oxide powders with a size range of 15-20 pm were mixed with the precursor resin before printing, allowing them to act as markers for DIC. The tensile tests were conducted at a frequency of 2 Hz, and the time-resolved optical images were captured using ARAMIS 12M sensor. The strain mappings and associated analysis were obtained from GOM Correlate software.

[0104] EXAMPLE 1 - Effect of UV Curing Time on Mechanical Properties of SMPFibers via Layer-by-Layer Printing: In FIG. 2A, a “bottom-up” configuration of a photo- stereolithography-based LCD 3D printing technique is presented, which employs UV light to spatially trigger the photo-polymerization reaction in a layer-by-layer manner. Specifically, the photosensitive SMP resins consist of methyl acrylate (MA 56.9 mol%), isobomyl acrylate (IBOA 40.3 mol%) as comonomers, 1 ,6-hexanediol diacrylate (HDDA 2.8 mol%) as a crosslinker, and bis (2,4,6-trimethyl benzoyl)- phenylphosphineoxide (Irgacure819 0.5 wt%) as a photoinitiator. Upon UV light absorption by the precursor, the photoinitiator may undergo cleavage, forming the polymer network. At this stage, a longer exposure time may correspond to increased absorption of photolytic energy, leading to a higher cross-linking density in the as- printed polymers (FIG. 3). To further investigate the properties of homogeneous SMP fibers dependent on exposure time, we conducted a series of layer-by-layer printing using five different exposure times (30, 35, 40, 45, and 50 seconds). The printing dimensions are summarized inTable 1.Table 1: Printing dimensions of SMP fibers exposed under different curing times (e.g., 30, 35,40, 45, 50 seconds) with the printing error via layer-by-layer printing method

[0105] Quantitative mechanical characterizations were performed by measuring the stress required to stretch and the torque needed to twist the fibers at room temperature. The stress-strain curves of the as-printed SMP fibers under various exposure times were obtained through uniaxial tensile tests, revealing variations in ultimate stress and strain at the point offailure based on the exposure time (FIG. 4). For instance, the fiber printed with an exposure time of 30 seconds exhibited ultimate stress of 8 MPa, which monotonically increased to 18 MPa as the exposure time increased to 50 seconds. A similar variation was observed for Young’s modulus, obtained from the slope of the linear region of stress-strain curves, ranging from 524 to 928 MPa, as the exposure time varied from 30 to 50 seconds. To elucidate the trade-off between high modulus and high toughness, we plotted Young’s modulus and toughness of the SMP fibers at various exposure times (FIGg. 5). The fiber with the shortest exposure time of 30 seconds displayed the highest toughness of 0.95 x 106 J m-3but the lowest Young’s modulus of 524 MPa. As the exposure time increased to the maximum exposure time of 50 seconds, the toughness decreased to 0.63 x 106 J m-3, while Young’s modulus reached its maximum value of 928 MPa. These findings provide insight into the relationship among exposure time, Young’s modulus, and toughness in the layer-by-layer printed SMP fibers.

[0106] The optical microscope image in FIG. 6 illustrates the cross-sectional view of the as-printed fiber and indicates a layered texture attributed to layer-by-layer printing. The thickness of each layer is consistent with the printing layer thickness (~50 pm). A single fiber (dimension: 1 ,5mm x 1 ,5mm x 120mm) requires greater torque to twist when printed under a longer curing time per layer, as seen from the torsion test results in FIG. 7. Assuming SMP fibers as non-coiled cylinders, the shear strain and shear stress are given by Equations (1) and (2), respectively. From the curves of shear stress versus shear strain at small twist angles (strain < 0.02), the shear modulus can be derived from the slope for each curve, as shown in FIG. 8. Increasing the exposure time may also boost the shear modulus of SMP fibers, allowing them to sustain a higher torque under twist, as demonstrated in FIG. 9. Therefore, the mechanicalproperties of the 3D-printed SMP fibers can be widely tuned by varying the curing time during layer-by-layer 3D printing.

[0107] We have found that the material behaviors of the SMPs can be tuned not only through the exposure time but also by adjusting the formulation of the resin. By regulating the ratio of comonomers MA and IBOA, which exhibit similar acrylate-based reactivities but different transition temperatures (Tgof MA: 9°C, Tg of IBOA: 85°C), it becomes possible to control the transition temperature of the resulting SMP. For instance, adjusting the molar ratio to 0.71 (IBOA / MA) allows for the regulation of the as-printed SMP’s transition temperature to approximately 72°C, as determined by dynamic mechanical analysis (DMA) (FIG. 10).Similarly, modifying the ratio to 0.62 (IBOA / MA) decreases the transition temperature to 50°C (FIG. 10).

[0108] EXAMPLE 2 - Thermal Responsive Rotation Behaviors of Fiber-ShapedActuators via Layer-by-Layer Printing: Furthermore, we assessed the shape memory effect through a rotational motion to evaluate the performance of SMP fibers as soft micro-motors in response to heat stimuli. The key parameters characterizing the rotation motion, such as rotation turns, and rate, were used for this purpose. A custom-built platform integrating a stepper motor, a torque / force sensor, a heating band, and a temperature controller was employed (FIG. 11). This setup allowed us to generate rotation motion, measure torque, and control the environmental temperature surrounding the tested samples. When the temperature exceeded the transition temperature Tg(72°C), the SMP fibers transitioned from a glass state to a highly elastic state. Under external force, the randomly wound molecular chains in the SMP could be deformed. To initiate the experiment, the as-printed fibers were first twisted at a temperature above Tg, for 200turns per meter (e.g., 20 turns for 10-cm SMP fiber), and their torsional mechanical energy was stored upon quenching back to room temperature (FIG. 11). Upon reheating to a temperature above Tg, the melting of the crystalline phase resulted in the softening of the SMP materials, causing the deformed molecular chains to revert to their original winding structure.Consequently, the twisted fibers underwent untwisting, producing a rotation motion akin to a motor. During the untwisting motion, all SMP fibers were subjected to a 1.5 g weighted load, which is 30 times the weight of the fiber. The time-resolved free rotation, specifically the untwisting motion, of the SMP fibers was measured (FIG. 12). The rotation rate (rpm) was calculated based on the first derivative of the correlation between rotation turns and time, plotted as a function of time (FIG. 13).

[0109] During the untwisting process of the twisted fiber, the rotation rate initially increased and reached a peak value within a few seconds before gradually decreasing to zero. The behavior of fiber- shaped motors closely correlates with the mechanical properties regulated by the UV-curable printing process. Specifically, as the UV curing time was extended from 30 to 40 seconds, the as-printed fibers exhibited an increase in the rotation rate. However, when the exposure time was further increased to 50 seconds, the rotation rate showed a decreasing trend. The fiber cured for 40 seconds achieved the highest top rotating speed of 314 rpm and the shortest acceleration / recovery time (FIG. 14), indicating a favorable balance between high modulus and high toughness. In contrast, the fiber cured for the longest time (50 seconds) attained a lower top speed of 109 rpm, despite having the maximum modulus of the fiber material (FIG. 15). Thus, with the co-regulation of the modulus and toughness, our fiber-shape soft motor enables enhanced programmable rotation motions, offering a potential solution fordesigning high-performance SMP actuators. The best-performing SMP fiber (cured for 40 seconds) demonstrated increased mechanical energy stored, allowing it to withstand more twists (e.g., 300 turns m-1) and achieve a higher maximum rotation rate (e.g., 350 rpm) (FIGS. 16-17).

[0110] In addition to the dependence on printing time, we explored the impact of temperature on the torsional twist behavior of our fiber-shaped motors. FIGS. 18 and 19 present the untwisting rotation performance of SMP fibers at three different temperatures (45, 60, and 75°C). At temperatures below the transition temperature (Tg), the twisted SMP fibers exhibited slower rotation motions, with reduced maximum rates of 50 rpm at 60°C and 25 rpm at 45°C, compared to the fiber tested at 75°C, which achieved a top speed of 300 rpm. The fibers tested at low temperatures also took longer to recover to their original state. Furthermore, the fibers tested at lower temperatures only achieved recoveries of 170 turns m-1at 60°C and 140 turns m-1at 45°C, resulting in relatively lower shape recovery ratios of 85% and 70%, respectively (Table 2), compared to 100% shape recovery ratio for the fiber tested at 75°C with the same twisted rotation turns (e.g., 200 turns m-1). We also demonstrated the reversibility of our SMP fiber motors through five sequential programming / reprogramming cycles (FIG. 20), showing a slight decrease in the maximum rotation rate while maintaining a nearly 100% shape recovery ratio (FIG. 21).Table 2: Shape fixity ratio, shape recovery ratio, and maximum rotation speed for SMP fiber with 40 seconds exposure time under different programming temperatures (45°C, 60°C, 75°C).

[0111] EXAMPLE 3 - Grayscale Lithography-Regulated Heterogeneity Designs: To achieve control over the responsive behaviors exhibited within a single macroscopic actuator, we employed a grayscale lithography technique to introduce heterogeneous domains into our SMPs. By controlling the spatial distribution profde of the localized curing times, we could regulate the overall mechanical properties and stimuli- responsive deformation of the fibers. The grayscale lithography was realizing using a fixed-height UV curable system in a photo-stereolithography- based LCD 3D printer. FIGS. 2A and 2B illustrate the basic configuration, which involves a closed secondary cell constructed inside the resin vat with spacers to control the height of the printing samples (0.6-0.9 mm). We printed three dog-bone specimens with different heterogeneity designs, as depicted by their 3D models in FIGS. 22-24, along with the corresponding distribution profiles of accumulated UV curing time shown in FIGS. 22-24. It is important to note that the curing thickness of the specimen is fixed during our fixed-height printing process. The various thicknesses indicated in the printing models do not represent thedimensions of the printing samples. Instead, they signify the number of repeated curing times (25 seconds for each unit exposure), which can tune the material properties by varying the accumulated doses of UV exposure. To this end, we employed a series of dynamic masks to spatially control the UV curing during the fixed-height printing, as shown in FIGS. 22-24. To gain a deeper understanding of the mechanical behaviors influenced by the heterogeneous domains, we conducted a time-resolved strain mapping analysis using digital image correlation (DIC) during uniaxial tensile tests on the three dog-bone specimens with different heterogeneity designs (FIG. 25). We derived localized stress-strain curves at representative heterogeneity domains by combining the strain mapping data from the DIC analysis with the corresponding stress obtained from the tensile test (FIGS. 26-28).

[0112] Regarding the designs, (1) Hetero-t1-t5: exposure time gradually increasing from t1 to t5 along the longitudinal direction ( t1 = 50 seconds, t2 = 75 seconds, t3 = 100 seconds, t4 = 125 seconds, t5 = 150 seconds); (2) Hetero-t5@t1-h: exposure time alternatively changing between t1 and t5 along the longitudinal direction; and (3)Hetero-t5@t1-v: exposure time alternatively changing between t1 and ts along the lateral direction. In our study, we incorporated three different heterogeneity designs into our dog-bone specimens. The first heterogeneity design (Design 1: Hetero-t1-t5) involved a gradual increase in curing time, ranging from the shortest exposure time of 50 seconds to the maximum exposure time of 150 seconds, with intervals of 25 seconds. This resulted in a longitudinal stiffness gradient distributed between soft and stiff domains (FIGS. 22-24). The second design (Design 2: Hetero-t5@t1-h) included only the minimum (t1 = 50 seconds) and maximum exposure times (t5 = 150 seconds), alternatively changing along the longitudinal direction, creating sharp interfaces between stiff and softdomains (FIGS. 22-24). In the third design (Design 3: Hetero-t5@t1-v), we investigated the effect of domain orientation by aligning the heterogeneity structures from Design 2, with the stiff domains oriented vertically in the same direction as the tensile stretch (FIGS. 22-24). These SMPs with grayscale lithography-regulated heterogeneity domains illustrated slightly different transition temperatures, as determined by DMA.

[0113] We conducted strain mapping using DIC analysis to gain further insight into the localized mechanical properties of the designed heterogeneous structures. Representative regions were selected to track the heterogeneous behaviors in the three designed specimens. Figure 3D shows that relatively stiffer regions exhibit more minor localized deformations and strains compared to the relatively softer regions. For instance, in Design 1, we can easily differentiate the strains at representative stiff (point 3), soft (point 1), and intermediate regions (point 2) by observing the time-resolved variations of colors. The localized stress-strain curves for the three selected regions derived from the DIC analysis are shown in FIG. 26. These curves demonstrate a gradual increase in modulus (e.g., El < E2 < E3) ranging from 623 to 982 MPa and a decrease in strain to failure (e.g., ε1 > ε2 > ε3), indicating that the heterogeneity domains are encoded into the specimen with a modulus gradient. Design 2, on the other hand, exhibits a sharp transition between soft and stiff regions, as evidenced by the pronounced strain differences between the selected point 1 and point 2 ε1 > ε2), indicating a sharp interface feature. However, for Design 3, no noticeable differences in stress-strain behaviors were observed at different regions. This is because the encoded stiff domains arc aligned in the same direction as the tensile stretch, resulting in the stiff regions carrying most of the stress. Consequently, similar modulus values (e.g., 1083, 1057, 1042 MPa) are obtained in the three different localized regions, regardless ofstiff and soft domains. Additionally, the specimen with vertically aligned stiff domains exhibits a higher ultimate strength than the other two heterogeneity designs (e.g., 16 versus 14 or 9 MPa).

[0114] EXAMPLE 4 - Engineering Heterogeneities for Simultaneous Regulation ofResponsive Rotations and Mechanical Properties:

[0115] Furthermore, we replicated three heterogeneity designs to encode our fiber-shaped micromotors with a dimension of 0.9 mm x 0.9 mm x 120 mm (FIG. 29 and Table 3).Table 3: Printing dimensions of three designed fibers with heterogeneous domains by a fixed- height printing method.

[0116] Initially, we fabricated five homogeneous fibers with different curing times (Homo-t1: 50 seconds, Homo-t2: 75 seconds, Homo-t3:: 100 seconds, Homo-t4: 125 seconds, and Homo-t5: 150 seconds) as control samples, all having the same designed dimensions (Table 4).The increase in curing time from 50 to 150 seconds resulted in a more than four- fold increase inYoung’s modulus, ranging from 265 to 1208 MPa for the homogeneous fibers printed using the fixed-height method (FIG. 30). Meanwhile, the maximum rotation rate of these fibers also varied, starting from 196 rpm (Homo-ti: 50 seconds curing time) with a relatively longer acceleration time, reaching a peak value of 366 rpm ( Homo-t3: 100 seconds curing time) with the shortest time to reach the top rate, and eventually decreasing to 169 rpm (Homo-t5: 150 seconds) with prolonged acceleration time (FIG. 31). This trend follows a similar variation pattern observed in the layer-by-layer printing approach (FIG. 32).Table 4: Printing dimensions of homogeneous SMP fibers cured under different exposure times (t1 = 50 seconds, t2 = 75 seconds, t3 = 100 seconds, t4= 125 seconds, t5 = 150 seconds) by fixed-height printing method. 1

[0117] Compared to homogeneous fibers, our designed heterogeneous fibers exhibit simultaneous regulations of mechanical properties and stimuli-responsive performance. Here, the programming temperature of 75°C was selected based on the glass transition temperature of thethree heterogeneous fibers. By incorporating various stiff (e.g., 150 seconds) and soft domains(e.g., 50 seconds) into our fiber-shaped actuators, the three heterogeneity-designed fibers demonstrate a tunable modulus ranging from 885 to 1063 MPa while controlling the rotation motion. Specifically, the Hetero-t5@t1-h fiber, which features sharp stiff-soft interfaces along the transverse direction (Design 2), shows an improved maximum rotation rate of 258 rpm compared to both the Homo-t1 fiber (196 rpm) with a lower modulus (e.g., 265 MPa) and the Homo-t5 fiber (169 rpm) with a higher modulus (e.g., 1208 MPa). The sharp variation at the interfaces between the stiff and soft domains enhances the stimuli-responsive performance by achieving a good balance between modulus and toughness. The stiff domains, indicated by a steeper slope in region 2 (FIG. 27), provide robust mechanical support during the rotation motion, while the soft domains, represented by higher strain in region 1 (FIG. 27), have potential to store more mechanical energy during the programmable rotation motion.

[0118] Furthermore, the orientation of the heterogeneity domains plays a significant role in the rotation performance of the fiber-shaped motor. The Hetero-t5@t1-v fiber, featuring reinforced stiff domains along the longitudinal direction, exhibits a much higher rotation rate with a top speed of 374 rpm and a shorter time of 5.72 seconds to reach the maximum rate compared to the Hetero-t5@t1-h fiber. This enhanced performance might probably be attributed to the higher ultimate strength and toughness (FIG. 28). Interestingly, the Hetero-t1-t5 fiber, which incorporates a gradient of stiffness modulus or strain through spatial heterogeneity designs (e.g., t2-t3-t4) between the stiffest and softest domains, achieves an even higher maximum rotation rate of 441 rpm (Movie S7) compared to the other two heterogeneity-designed fibers and the best-performing homogeneous fiber (e.g., Homo-t3). This improvement can be attributed tothe gradient feature between the stiff and soft domains, which synergizes the complementary properties between neighboring domains. Therefore, engineering heterogeneity domains within a single fiber-shape actuator presents a new effective strategy for simultaneously co-regulating the overall mechanical properties and stimuli-responsive behaviors.

[0119] EXAMPLE 5 - Regulated Mechanical Energy of Torsional Actuators with Heterogeneity Designs: To further investigate the stored and released mechanical energy of our torsional actuators as rotating motors, we fabricated a hybrid fiber consisting of two regions with a total length of 7.0 cm, as shown in FIG. 33. The upper region, which is 3.5 cm long, serves as a rotating motor, while the lower region, also 3.5 cm in length, acts as a torsional load (FIG. 34). In the first step, we tethered only the two ends of the upper motor region as indicated by the red triangles (FIG. 33). Then, the upper region was programmed to store torsional mechanical energy by twisting it with 10 turns at Tg~75°C. Subsequently, the hybrid fiber was quenched at room temperature, keeping the upper motor region fixed in a twisted state, while the lower end remained untethered (step 2). Upon reheating the entire hybrid fiber, which was tethered at both ends (step 3), the stored torsional mechanical energy in the upper region was released, enabling it to function as a rotating motor. The motor could rotate and overcome the increasing torsional load generated by the lower region as it continued to be twisted, thus delivering work capacity.

[0120] To ensure the proper integration of a motor and load in a hybrid fiber, we measured and compared the torques required to twist three heterogeneous fibers and two homogenous fibers by 285 turns m1at Tg(FIG. 35). Consistent with our findings on rotation motions (FIG. 31), the Hetero-t1-t5 fiber, featuring a heterogeneous gradient between the stiffest and softest domains, exhibited the highest torque deliveries with the twisted angles (FIG. 35).Notably, all three heterogeneous fibers showed higher torques than the two homogeneous fibersFurthermore, programming and untwisting the fiber to store and release energy demonstrated a highly reversible behavior, as evident from the torque-angle curves.

[0121] To determine the stored and released mechanical energies of these fibers, we integrated the torque- angle curves using Equation (3). Upon programming 285 turns m-1, the three heterogeneous fibers stored torsional energies of 69, 59.5, and 41.5 J kg-1for designs 1-3, respectively, surpassing the stored energies of the two homogeneous fibers (e.g., 34.5 J kg-1for Homo-fiber 1 and 19 J kg-1for Homo- fiber 2) (Table 5).Table 5: Total stored mechanical energy, released energy, and released-to-stored energy ratio for three designed SMP fibers with heterogeneous domains (e.g., Design 1: Hctcro-ti-ty Design 2: Hetero-t5@t1-h; Design 3: Hetero-t5@t1-v).

[0122] Given their relatively high torques and mechanical energies, we selected three heterogeneous fibers to incorporate into the upper region of the hybrid fiber for storing and releasing torsional energies as rotating motors, while the two homogeneous fibers were integrated into the lower region to serve as various torsional loads. As an example, the Hetero-t1- t5 incorporated in the upper region of the hybrid fiber enables various energy outputs when rotating the relatively high load for 5 turns (Homo-fiber 1) and relatively low load for 6.5 turns (Homo- fiber 2) against increasing torque as the load continued to be twisted. The mechanical energy (work capacity) generated from the Hetero-t1-t5 rotating motor in the upper region (0.02 g) was calculated to be 9.5 J kg-1(power density: 0.45 W kg-1) when subjected to high load twisting (Homo-fiber 1) (FIG. 36). Against the low load (Homo-fiber 2), the motor delivered a work capacity of 8.0 J kg-1(power density: 0.42 W kg-1). The other two heterogeneous rotating motors exhibited slightly lower energy and power outputs (e.g., Hetero-t5@t1-h: 8.0 / 6.6 J kg-1for high / low load; Hetero-t5@t1-v: 6.0 / 3.9 J kg-1for high / low load). Moreover, the ratio of released energy to stored energy for the Hetero-tl-t5 fiber was calculated to be 13.76%, indicating a high output energy efficiency, which surpasses that of other comparative torsional fiber actuators (Table 6).Table 6: Comparisons of actuation performance for different rotation motors.

[0123] It should be understood that the disclosure of a range of values is a disclosure of every numerical value within that range, including the end points. It should also be appreciated that some components, features, and / or configurations may be described in connection with only one particular embodiment, but these same components, features, and / or configurations can be applied or used with many other embodiments and should be considered applicable to the other embodiments, unless stated otherwise or unless such a component, feature, and / or configuration is technically impossible to use with the other embodiment. Thus, the components, features, and / or configurations of the various embodiments can be combined together in any manner and such combinations arc expressly contemplated and disclosed by this statement.

[0124] It will be apparent to those skilled in the art that numerous modifications and variations of the described examples and embodiments are possible considering the above teachings of thedisclosure. The disclosed examples and embodiments are presented for purposes of illustration only. Other alternate embodiments may include some or all of the features disclosed herein. Therefore, it is the intent to cover all such modifications and alternate embodiments as may come within the true scope of this invention, which is to be given the full breadth thereof.

[0125] It should be understood that modifications to the embodiments disclosed herein can be made to meet a particular set of design criteria. Therefore, while certain exemplary embodiments of the apparatus and methods of using and making the same disclosed herein have been discussed and illustrated, it is to be distinctly understood that the invention is not limited thereto but may be otherwise variously embodied and practiced within the scope of the following claims.

Claims

WHAT IS CLAIMED IS:

1. A structure formed from at least one UV curable shape memory polymer resin, the structure comprising: a first domain corresponding to a first region of the structure cured via a first UV light exposure time; and a second domain corresponding to a second region of the structure cured via a second UV light exposure time, wherein the first UV light exposure time is different than the second UV light exposure time, wherein the structure is configured to transform from a temporary shape to an established shape upon being stimulated by an external stimulus.

2. The structure of claim 1, wherein the structure further comprises: a third domain corresponding to a third region of the structure cured via a third UV light exposure time, wherein the first UV light exposure time is different than the second and third UV light exposure times.

3. The structure of claim 2, wherein the structure further comprises: a fourth domain corresponding to a fourth region of the structure cured via a fourth UV light exposure time, wherein the first UV light exposure time is different than the second, third, and fourth UV light exposure times.

4. The structure of claim 1, wherein the external stimulus is a temperature greater than or equal to the glass transition temperature of the at least one UV curable shape memory polymer resin.

5. The structure of claim 1 , wherein a value of a mechanical property of the first domain is different than a value of the mechanical property of the second domain.

6. The structure of claim 5, wherein the mechanical property is selected from the group consisting of ultimate tensile strength, Young’s modulus, and toughness.

7. The structure of claim 5, wherein each domain has a Young’s modulus between 524-928 MPa.

8. The structure of claim 5, wherein each domain has a toughness between 0.63 x 106-0.95 x 106 J m-3.

10. The structure of claim 1, wherein a value of a thermal responsive behavior of the first domain is different than a value of the thermal responsive behavior of the second domain.

11. The structure of claim 5, wherein the thermal responsive behavior is selected from the group consisting of rotation rate, maximum rotation rate, time to reach maximum rotation rate, and turns.

12. The structure of claim 1, wherein the structure has a Young’s modulus ranging from 265- 1208 MPa.

13. The structure of claim 1, wherein the structure has a maximum rotation speed ranging from 169-441 rpm.

14. The structure of claim 1, wherein the structure has torsional mechanical energy ranging from 3.9-9.5 J kg-1.

15. An actuator formed from the structure of claim 1.

16. A method of making a structure formed from at least one UV curable shape memory polymer resin, the method comprising: printing the structure, wherein the structure comprises: a first domain corresponding to a first region of the structure cured via a first UV light exposure time, and a second domain corresponding to a second region of the structure cured via a second UV light exposure time, wherein the first UV light exposure time is different than the second UV light exposure time; heating the structure to a temperature at or above the glass transition temperature of the at least one UV curable shape memory polymer resin;deforming a programmed portion of the structure to a temporary shape via mechanical loading; and cooling the structure to a temperature below the glass transition temperature of the at least one UV curable shape memory polymer resin.

17. The method of claim 16, wherein printing the structure comprises printing via a grayscale lithography printing process.

18. The method of claim 17, wherein the grayscale lithography printing process is a fixed height process.

19. The method of claim 16, wherein the mechanical loading is selected from the group consisting of twisting, bending, rolling, and compressing.

20. The method of claim 16, wherein the structure further comprises an unprogrammed portion, wherein the unprogrammed portion is not subject to deforming via mechanical loading.

21. The method of claim 16, further comprising: heating the structure to a temperature greater than or equal to the glass transition temperature of the at least one UV curable shape memory polymer resin to recover an established shape of the programmed portion.

22. A structure formed from at least one UV curable shape memory polymer resin, the structure formed via the method of claim 16, claim 17, claim 18, claim 19, claim 20, or claim 21.

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