Soft multi-stable metamaterials

Abstract

A multi-stable metamaterial includes a plurality of unit cells coupled together. Each unit cell includes a first support portion including a first support segment, a second support portion including a second support segment, and at least two transition supports. Each transition support includes a first end defining a first cross-section and connected to the first support portion, a second end defining a second cross-section and connected to the second support portion, a support length (L) extending between the first end and the second end, and a midsection extending a midsection length (L*) between the first and second ends that is less than the support length. The midsection defines a midsection cross-section that is larger than the first and second cross-sections. Application of an external energy source causes a transition between an initial stable configuration and a transformed stable configuration, which is maintained after removal of the external energy source.

Description

SOFT MULTI-STABLE METAMATERIALSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 663,788, filed June 25, 2024, which is incorporated by reference as if disclosed herein in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0002] This invention was made with government support under R01 EB 032959 and R21 EB 029563, awarded by the National Institutes of Health, and N00014-23- 1-2391, awarded by the Office of Naval Research. The government has certain rights in this invention.TECHNOLOGICAL FIELD

[0003] The following disclosure is directed to embodiments of a multi-stable metamaterial or metamaterials made entirely from soft material and related methods to transform the metamaterial between stable states via an external energy source. In some embodiments, the metamaterial may be comprised of a plurality of unit cells, and the metamaterial’s stability may be programmed by adjusting the geometry of each unit cell. In some embodiments, the metamaterial may be magnetically programmed to enable magnetic field-induced transformation between stable states. The transformed configurations remain stable when the external energy source (e.g., magnetic field) is turned off. In some embodiments, the disclosed inventive metamaterials transform with non-uniform magnetic fields, which may enable selective transformation of metamaterials (e.g., closely spaced metamaterials). In some embodiments, the non-uniform magnetic field actuation may enhance control of the conditions for transformation, where the transformation only occurs with a ‘signature’ field.BACKGROUND

[0004] The wireless actuation of soft materials is of significant interest in the fields of soft robotics and biomedicine. Magnetic fields can safely and efficiently travel through human tissue and have been clinically used, such as in magnetic resonance systems with field strengths up to 8 T. Magnetic fields have been shown to be capable of remotely actuating and controlling magnetic soft biomedical devices within the complex and confined spaces of the human body. Recent advances have demonstrated magnetic-responsive soft architectures for implantable and ingestiblesystems where the rationally designed geometry and magnetic programming enable tailorable deformations, and the soft materials improve the safety and durability by reducing the devicetissue mechanical mismatch. In the field of soft robotics, magnetic soft constructs have been used to achieve locomotion, and as shape morphing micromachines, arms and grippers for robots, miniature soft machines, reconfigurable antennas, and electromagnetic or acoustic filters.

[0005] However, despite the impressive advances, maintaining multiple stable geometrical configurations without sustaining the input energy remains challenging, especially for biomedical devices where mechanical, chemical, and thermal stresses is unpredictable and difficult to control. Previous magnetic soft constructs are not multi-stable and require a sustained magnetic field or temperature / light modulation to maintain the transformed configurations, which inherently constrain the potential applications. While some previous demonstrations have included both magnetic field-induced transformation and multi-stability, they did not demonstrate the ability to maintain stable states under externally applied loads, required relatively rigid materials to achieve the desired boundary conditions, and required stiff plates and sharp features, which are undesirable for biomedical applications.

[0006] Current multi-stable silicone architectures with tilted beams require stiff materials (Young’s modulus, E ~2 GPa) in the supporting segments to maintain stability in the transformed state. However, stiff materials are incompatible with the goals of a soft device and are undesirable for biomedical applications as they increase the device-tissue mechanical mismatch. Moreover, these previous demonstrations are incapable of transformation between stable states by magnetic fields. A majority of previous magnetic soft constructs are not multi-stable and require a sustained magnetic field or temperature / light modulation to maintain the transformed configurations, which inherently constrain the potential applications. For example, in environments where sustaining the input energy would be challenging (e.g., remote settings), in environments where temperature may be challenging to predict or control, and in environments where mechanical, chemical, and thermal stresses can be unpredictable and difficult to control.

[0007] While some previous magnetic soft constructs have included both magnetic field-induced transformation and multi-stability, they did not demonstrate the ability to maintain stable states under externally applied loads, they require relatively rigid materials to achieve the desired boundary conditions, and require stiff plates and sharp features, which are undesirable for biomedical applications. Moreover, many previous magnetic soft constructs require uniform magnetic fields for transformation.

[0008] These are just some of the disadvantages associated with magnetic soft constructs that are currently available.SUMMARY

[0009] Aspects of the following disclosure are directed to embodiments of a multi-stable metamaterial unit cell. In some embodiments, the multi-stable metamaterial unit cell includes a first support portion including one or more first support segments, a second support portion including one or more second support segments, and at least two transition supports. In some embodiments, each transition support includes a first end defining a first cross-section or first cross-section diameter and connected to the first support portion, a second end defining a second cross-section or cross-section diameter and connected to the second support portion, a support length (L) extending between a first end and a second end, and a midsection extending a midsection length (L*) between the first end and the second end that is less than the support length. In some embodiments, the midsection defines a midsection cross-section or cross-section diameter that is larger than the first and second cross-section or cross section diameter. In some embodiments, application of an external energy source is configured to cause a transition between an initial stable configuration and a transformed stable configuration. In some embodiments, the initial stable configuration and the transformed stable configuration are configured to be maintained after removal of the external energy source.

[0010] In some embodiments of the multi-stable metamaterial unit cell, the external energy source is a non-uniform magnetic field. Some embodiments of the multi-stable metamaterial unit cell comprise a Young’s modulus of about 800 kPa. In some embodiments of the multi-stable metamaterial unit cell, the at least two transition supports comprise a reinforcement ratio (R) that is between 0 and 0.625, where R= L* / L. In some embodiments, the multi-stable metamaterial unit cell is comprised of a ferromagnetic composite. In some embodiments of the multi-stable metamaterial unit cell, the ferromagnetic composite comprises a silicone elastomer and magnetic particles. In some embodiments of the multi-stable metamaterial unit cell, the magnetic particles comprise neodymium-iron-boron (NdFeB). In some embodiments, the multi-stable metamaterial unit cell, further includes one or more light-emitting diodes (LEDs) integrated into at least one of: (i) the first support portion; (ii) the second support portions; and (iii) the at least two transition supports. In some embodiments of the multi-stable unit cell, when moved to the initial stable configuration, the at least two transition supports pivot relative to the first and second support portions to increase a distance between the first and second support portions, and when moved tothe transformed stable configuration, the at least two transition supports pivot relative to the first and second support portions to decrease a distance between the first and second support portions.

[0011] Aspects of the following disclosure are directed to embodiments of a multi-stable metamaterial. In some embodiments, the multi-stable metamaterial includes a plurality of unit cells coupled together. In some embodiments, each of the plurality of cell units includes a first support portion including one or more first support segments, a second support portion including one or more second support segments, and at least two transition supports. In some embodiments, each transition support includes a first end defining a first cross-section and connected to the first support portion, a second end defining a second cross-section and connected to the second support portion, a support length (L) extending between a first end and a second end, and a midsection extending a midsection length (L*) between the first end and the second end that is less than the support length. In some embodiments, the midsection defines a midsection cross-section that is larger than the first and second cross-sections. In some embodiments, the application of an external energy source causes a transition between an initial stable configuration and a transformed stable configuration. In some embodiments, the initial stable configuration and the transformed stable configuration are maintained after removal of the external energy source.

[0012] In some embodiments of the multi-stable metamaterial, the external energy source is a non- uniform magnetic field. In some embodiments of the multi-stable metamaterial, the plurality of unit cells is arranged in at least four rows, each of the plurality of the unit cells of a first row is programmed with a first energy barrier, each of the plurality of the unit cells of a second row is programmed with a second energy barrier, each of the plurality of unit cells of a third row is programmed with a third energy barrier, and each of the plurality of unit cells of a fourth row is programmed with a fourth energy barrier. In some embodiments, the first energy barrier, the second energy barrier, the third energy barrier, and the fourth energy barrier are different from each other. In some embodiments, the multi-stable metamaterial further comprises a ferromagnetic composite. In some embodiments of the multi-stable metamaterial, the ferromagnetic composite comprises a silicone elastomer and magnetic particles. In some embodiments of the multi-stable metamaterial, the magnetic particles comprise neodymium-iron- boron (NdFeB). In some embodiments, the multi-stable metamaterial comprises a Young’s modulus of about 800 kPa. In some embodiments, the multi-stable metamaterial includes a conductive trace integrated into at least some of the plurality of unit cells. In some embodiments of the multi-stable metamaterial, when moving to the initial stable configuration, at least two transition supports pivot relative to the first and second support portions to increase the distance between the first and second support portions.

[0013] In some embodiments of the multi-stable metamaterial, when moving to the transformed stable configuration, at least two transition supports pivot relative to the first and second support portions to decrease the distance between the first and second support portions. In some embodiments, the multi-stable metamaterial of claim 10, wherein the plurality of unit cells are formed as a single component. Some aspects of the following disclosure are directed to embodiments of a biomedical device configured to be implanted into a living organism and that is comprised of the multi-stable metamaterial according to the invention. In some embodiments, the biomedical device comprises a Young’s modulus of about 800 kPa.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings show embodiments of the disclosed subject matter for the purpose of illustrating the invention. However, it should be understood that the present application is not limited to the precise arrangements and instrumentalities shown in the drawings, wherein:

[0015] FIG. 1 schematically illustrates a front view of an embodiment of a unit cell base according to some embodiments of the present disclosure;

[0016] FIG. 2 schematically illustrates a front view of an embodiment of a unit cell of a metamaterial according to some embodiments of the present disclosure;

[0017] FIG. 3 schematically illustrates a front view of an embodiment of a unit cell of a metamaterial according to some embodiments of the present disclosure;

[0018] FIG. 4 schematically illustrates a front view of an embodiment of a unit cell of a metamaterial in an initial stable configuration and a transformed stable configuration according to some embodiments of the present disclosure;

[0019] FIG. 5A schematically illustrates an embodiment of a row of unit cells of a metamaterial in an initial stable configuration according to some embodiments of the present disclosure;

[0020] FIG. 5B schematically illustrates the embodiment of FIG. 5 A in a partially transformed or unstable configuration according to some embodiments of the present disclosure;

[0021] FIG. 5C schematically illustrates the embodiment of FIG. 5A in another partially transformed or unstable configuration according to some aspects of the present disclosure;

[0022] FIG. 5D schematically illustrates an embodiment of a row of unit cells of a metamaterial in a transformed stable configuration according to some embodiments of the present disclosure;

[0023] FIG. 6A schematically illustrates an enlarged view of an embodiment of a transition support of a unit cell in an initial stable configuration according to some embodiments of the present disclosure;

[0024] FIG. 6B schematically illustrates an enlarged view of an embodiment of a transition support of a unit cell in a transformed stable configuration according to some embodiments of the present disclosure;

[0025] FIG. 7 illustrates a front view of an embodiment of a metamaterial formed into a cylindrical shape and comprising a plurality of rows of unit cells that are each in an initial stable configuration according to some embodiments of the present disclosure;

[0026] FIG. 8 illustrates a front view of the embodiment of FIG. 7 where each of the unit cells are in a transformed stable configuration according to some embodiments of the present disclosure;

[0027] FIG. 9A illustrates a front view of an embodiment of a metamaterial formed into a cylindrical shape and comprising a plurality of rows of unit cells that are each in a transformed stable configuration according to some embodiments of the present disclosure;

[0028] FIG. 9B illustrates a front view of an embodiment of a metamaterial formed into a cylindrical shape and comprising a plurality of rows of unit cells where some rows of unit cells are in a transformed stable configuration and some rows of unit cells are in an initial stable configuration according to some embodiments of the present disclosure; and

[0029] FIG. 9C illustrates a front view of an embodiment of a metamaterial formed into a cylindrical shape and comprising a plurality of rows of unit cells that are each in an initial stable configuration according to some embodiments of the present disclosure.

[0030] DETAILED DESCRIPTION

[0031] The following discussion relates to various embodiments of soft, multi-stable magnetic- responsive cells (cell(s) or unit cell(s)) 100 and metamaterials 200 comprised of a plurality of said cells 100. The following disclosure further relates to methods of manufacturing and operating soft, multi-stable magnetic-responsive cells 100 and metamaterials 200 comprised of a plurality of said cells 110. The term “soft” as used herein refers to materials having a Young’s modulus between 640 kPa and 1,000 kPa. In some embodiments, the Young’s modulus of the multi-stable metamaterial unit cells and the multi-stable metamaterial is about 800 kPa. It will be understood that the versions described herein are examples that embody certain inventive concepts as detailedherein. To that end, other variations and modifications will be readily apparent to those of sufficient skill. The terms “about” or “approximately” as may be used herein may refer to a range of 80%-125% of the claimed or disclosed value.

[0032] Referring to FIG. 1, in some embodiments, each unit cell 100 includes a base 110. In some embodiments, the base 110 includes a first support portion 112 and a second support portion 114. In some embodiments, the first support portion 112 is connected to the second support portion 114 via one or more transition supports 116. In some embodiments, the first support portion 112 is connected to the second support portion 114 via two transition supports 116a, 116b.

[0033] Referring to FIGS. 2-4, in some embodiments, the first support portion 112 includes one or more first support segments 122. In some embodiments, the one or more first support segments 122 comprise a trapezoidal shape. In some embodiments, the one or more first support segments comprise at least four (4) sides. In some embodiments, the first support portion 112 and the one or more first support segments 122 are formed as a single component. In some embodiments, the first support portion 112 includes two first support segments 122a, 122b. In some embodiments, the second support portion 114 includes one or more second support segments 124. In some embodiments, the one or more second support segments 124 comprise a trapezoidal shape. In some embodiments, the one or more second support segments comprise at least four (4) sides. In some embodiments, the second support portion 114 and the one or more second support segments 124 are formed as a single component. In some embodiments, the second support portion 114 includes two second support segments 124a, 124b. In some embodiments, the one or more transition supports 116 extend along a support length L from a first end 115 to a second end 117. In some embodiments, the first end 115 is structured to connect to the first support segment 122 and the second end 117 structured to connect to the second support segment 124. In some embodiments, the one or more transition supports 116 include a midsection 126 or mid portion that extends along a midsection length L*. In some embodiments, the support length L greater than the midsection length L*. A reinforcement ratio R is defined as the ratio of the midsection length L* to the support length L (R=L* / L). In some embodiments, the reinforcement ratio R is from 0-0.625. In some embodiments, the support length L comprises a thickness t and the midsection 126 comprises a thickness t*. In some embodiments, the thickness t* of the midsection 126 is greater than the thickness t of the one or more transition supports 116. In some embodiments, modulating t and R is advantageous for configuring or programming a metamaterial 200 comprising a plurality of unit cells 100, as the unit cell width and height of the unit cell 100 are unaffected by these geometric or size changes. In some embodiments, the midsection 126forms an angle 0 relative to the support length L of about 60°. In some embodiments, the angle 0 is not greater than 70°.

[0034] In some embodiments, the unit cell 100 is configured as an entirely soft, multi-stable material (£-800 kPa). In some embodiments, the one or more first support segments 122, the one or more second support segments 124, and the midsection 126 comprise a strategic geometry that is configured to increase the energy barriers of the unit cell 100 by constraining the unit cell’s 100 bending behaviors without changing the unit cell 100 size or the soft material. The increased stability is synergistic for the energy barrier in tension (Etens), which is more challenging to achieve due to the non-zero stresses in state. The one or more first support segments 122, the one or more second support segments 124, and the midsection 126 have a significantly higher Etens than unit cells 100 and metamaterials 200 comprised of a plurality of the unit cells 100 with only some, or none of these features. The higher energy barriers in both loading directions are desirable for maintaining multiple stable configurations in dynamic environments and under external pressure without a continuous input of external energy or modulation of environmental factors (e.g., temperature). In some embodiments, the geometry / size of the first and second support segments 122, 124 and the one or more transition midsections 126 may be changed in order to vary the energy barrier of the unit cell 100. Varying the energy barrier between unit cells 100 acts to “program” the unit cell 100 so that each unit cell 100 selectively responds to a different level of external energy input (e.g., a different magnetic input) in order to transition between stable states. In this manner each of a plurality of unit cells 100 may be individually moved between stable configurations.

[0035] As discussed, in some embodiments, the unit cell 100 is comprised of a soft, multi-stable metamaterial. In some embodiments, the soft, multi-stable metamaterial comprises a ferromagnetic composition. In some embodiments, the ferromagnetic composition includes a silicone elastomer and magnetic particles 130. In some embodiments, the magnetic particles 130 comprise microparticles and / or nanoparticles. In some embodiments, the magnetic particles 130 comprise neodymium-iron-boron (NdFeB). In some embodiments, the unit cell 100 includes one or more light-emitting diodes (LEDs) 150 that are connected to a conductive trace or electrical feed 152, such as a wire. In some embodiments, the conductive trace 152 is connected to an energy source 160, such as a battery or other source of electrical power. While FIG. 3 shows one embodiment of the placement of the LEDs 150, the LEDs 150 may be placed at various locations on the unit cell 100 to achieve the desired result. In some embodiments, the one or more LEDs may be in communication with a controller 170 to turn the LEDs 150 on and off, or to program the one or more LEDs 150 such that they turn on and off at certain times and / or such that they mayexhibit a variety of colors. In some embodiments, the controller 170 may be in electrical connected to the energy source 160. In some embodiments, the controller 170 and the energy source 160 may be contained in a common housing 175.

[0036] Operation of the unit cell 100 will now be discussed with general reference to FIGS. 4-5B. In some embodiments, the soft, magnetic-responsive metamaterial of the unit cell 100 transforms between stable configurations when actuated by an external energy source, such as a non-uniform magnetic field. In some embodiments, the unit cell 100 maintains the stable configurations even after the external energy source is removed or turned off due to the geometry of the unit cell 100 and specifically of the one or more first support segments 122, the one or more second support segments 124, and the midsection 126. In some embodiments, the unit cell 100 is configured to transform or move between an initial stable configuration [0] and a transformed stable configuration [1] by loading in the vertical direction in response to application of the external energy source. Referring to FIG. 4, in some embodiments, application of a non-uniform magnetic field may transform the unit cell 100 from the initial stable configuration [0], for example, an expanded state, to the transformed stable configuration [1], for example, a collapsed state as shown in phantom in FIG. 4.

[0037] Referring to FIGS. 4-6B, in some embodiments, transforming from the initial stable configuration [0], such as the expanded state, to the transformed stable configuration [1], such as the collapsed state, is achieved by movement of the one or more transition supports 116 relative to the first support portion 112 and the second support portion 114. In some embodiments, the one or more transition supports 116 are structured to move or position the first support portion 112 away from the second support portion 114 when the unit cell 100 moves to or is in the initial stable configuration [0] shown in FIGS. 2-5 A and 6 A. In some embodiments, the one or more transition supports are structured to move or position the first support portion 112 towards the second support portion 114 when the unit cell 100 moves to or is in the transformed stable configuration [1] shown in FIGS. 5B and 6B. Referring to FIGS. 5A-D, in some embodiments, the unit cell 100 is configured to go through one or more transformative states or configurations (FIGS. 5B and 5C) while moving between the initial stable configuration [0] and the transformed stable configuration [1], In some embodiments, the one or more transformative states are not stable configurations and are not maintained if the external energy source is removed or turned off.

[0038] Referring to FIGS. 7-9C, in some embodiments, a soft multi-stable metamaterial (metamaterial) 200 is comprised of a plurality of individual unit cells 100. In some embodiments, the metamaterial 200 is magnetically responsive due to the unit cells 100 being formed from aferromagnetic material as previously described. In some embodiments, the plurality of unit cells 100 are arranged in stacked rows. In some embodiments, the metamaterial 200 may be formed in any shape that is desired. As shown in the embodiments of FIGS. 7-9C, the metamaterial 200 is formed into a cylindrical shape. In some embodiments, the cylindrical shape is about 2 cm x 8 cm when in the initial stable configuration [0], In some embodiments, the cylindrical shape is about 4 cm x 8 cm when in the initial stable configuration [0], As previously discussed, in some embodiments, the metamaterial 200 may be in an expanded state when each of the unit cells 100 are at the initial stable configuration [0] as shown in FIGS. 7 and 9C. As previously discussed, in some embodiments, the metamaterial 200 moves to the collapsed state when each of the unit cells 100 move to the transformed stable configuration [1] as shown in FIGS. 8 and 9 A. In some embodiments, such as shown in FIG. 7, each stacked row is programmed differently such that each row of the metamaterial 200 responds to a different external energy input (e.g., magnetic input) so that it may be actuated individually. In some embodiments, each row of unit cells 100 may be programmed with a range of energy barriers (e.g., R= 0.6, 0.4, 0.25, 0) to enable full expansions and collapsing of the metamaterial 200.

[0039] In some embodiments, such as shown in FIG. 7, the varying geometry of the transition supports 116 / midsection 126 may be seen in each row. In some embodiments, the transition supports 116 / midsection 126 may have a larger cross-section or cross-section diameter in lower rows as compared to transition supports 116 / midsections 126 in unit cell rows closer to the top of the metamaterial 200. In some embodiments, the first support segments 122 and / or the second support segments 124 of unit cell rows may comprise geometric or size changes at various locations on the metamaterial 200. In some embodiments, the metamaterial 200 is unable to fully expand if each row of unit cells 100 is programmed with the same energy barrier (e.g., R=0.6). Accordingly, programming one or more rows of unit cells 100 in the metamaterial 200 differently from each other may better enable a controlled and / or a transition between a totally expanded state and a totally collapsed state. In some embodiments, transition between fully collapsed and fully expanded states of the metamaterial may be completed in less than 1 second. In some embodiments, transition between fully collapsed and fully expanded states of the metamaterial may be completed in less than 0.5 seconds. In some embodiments, transition between fully collapsed and fully expanded states of the metamaterial may be completed in less than 0.2 seconds. In some embodiments, transition between fully collapsed and fully expanded states of the metamaterial may be completed in about 0.15 seconds

[0040] In some embodiments, such as when the metamaterial 200 is in the cylindrical shape, each row of unit cells 100 may be actuated separately so that the one or more dimensions may beprecisely controlled. As shown in FIGS. 7-9C, in some embodiments, the height dimension of the metamaterial 200 may be adjusted between the transformed stable configuration [1] having a height Hl to the initial stable configuration [0] having a height HO. In some embodiments, a height Hn corresponds to a scenario where some of the cells are in transformed stable configuration [1] and some of the unit cells 100 are in the initial stable configuration [0], Accordingly, in some embodiments, one or more different heights Hn may be achieved between HO and Hl depending on the number of rows of unit cells 100 comprising the metamaterial 200. In some embodiments, the metamaterial 200 remains stable at HO, Hn, and Hl even after the magnetic input is removed.

[0041] In some embodiments, the metamaterial 200 may be formed into a biomedical implant that is configured to be inserted or implanted into a living organism (e.g., human or animal) in one configuration and then exposed to an external energy source, such as a non-uniform magnetic field, to transform the biomedical implant into another configuration. For example, in some embodiments, the medical implant may be implanted in the collapsed state and then transformed after implantation. In some embodiments, the metamaterial 200 is comprised of a soft material which, in addition to its ability to transform after implantation, improves the safety of biomedical devices comprised of the metamaterial 200. In some embodiments, the metamaterial 200 comprises a deployable instrument that includes a conductive trace 152 and one or more electronic components, such as a processor. In some embodiments, the deployable instrument comprises an antenna.

[0042] In some embodiments, the metamaterial 200 is capable of changing between stable configurations (e.g., between the initial stable configuration and the transformed stable configuration) and maintaining the stable configuration across a temperature range of -20°C- 100°C without any external energy input. Accordingly, the metamaterial 200 is able to transform and maintain stable states in environments where temperature may be challenging to predict and / or control. Some embodiments, the metamaterial 200 is structured to maintain stable states in the presence of a wide range of environmental stressors, such as air current (6.6 m / s), a water vortex (150 rpm), and waterjets (vertical and at 45° with flow rates of 97 and 84 mL / s, respectively). In some embodiments, the metamaterial 200 can effectively achieve geometrical transformation without requiring stiff materials in the supporting segments 112, 114, 116, 122, 124, 126, which reduces susceptibility to fracture, plastic deformation at relatively low strains, material degradation, and failure at material interfaces. In some embodiments, the metamaterial 200 is configured to recover its functionality (i.e., preserving its multi-stability and transformation abilities) under extreme forces and physical damage. In some embodiments, the extreme forces include blunt impact with a force of about 87 kN. In some embodiments, the metamaterial 200retains its functionality after prolonged chemical exposure. In some embodiments, the prolonged chemical exposure includes immersion in a solution of simulated gastric fluid for about seven (7) days at room temperature (18°C-25°C) while being agitated at 120 RPM in a shaker. In some embodiments, prolonged chemical exposure results in a <15% impact to the programmed energy barrier of the metamaterial 200.

[0043] In some embodiments, the metamaterial 200 is configured to retain structure and multistability in the presence of extreme thermal stress. In some embodiments, the extreme thermal stress includes engulfing the metamaterial 200 in flames for a period of time. In some embodiments, the extreme thermal stress includes engulfing the metamaterial 200 in flames for about or at least 15 seconds. In some embodiments, the metamaterial 200 can maintain its multistability (with energy barriers changing by -18% to +21%) and recover its ability to transform via the external energy source after exposure to extreme thermal stress. In some embodiments, reprogramming of the magnetic domain after an extreme thermal event is needed to fully restore the transformation abilities if large portions of the metamaterial 200 exceed the Curie temperature (Tc = 360 °C) of the magnetic particles 130, which causes demagnetization. In some embodiments, the entirely soft configuration enables the metamaterial 200 to preserve its robust multi-stability, which is critical to maintaining transformed stable states and is in stark contrast to prior art metamaterials that are irreversibly damaged when exposed to fire.

[0044] In some embodiments, the metamaterial 200 is structured to achieve complex motions and functionalities that leverage the selective actuation capabilities of the non-uniform magnetic fields. In some embodiments, the metamaterial 200 is structured to produce bending motions by selectively actuating the closely-spaced unit cells 100 of a tilt stage. In some embodiments, the metamaterial 200 may be structured to produce more complex (e.g., twisting) and coupled (e.g., bending and extension) actuation by strategically assembling metamaterial unit cells 100. In some embodiments, the metamaterial may be structured to robustly achieve the rapid and coordinated motions of a wirelessly-controlled valve and peristaltic pump, using the selective transformation of individual segments of the metamaterial 200 and / or individual unit cells 100 by leveraging the non-uniform magnetic field and maintain transformed configurations even against the fluid pressure during pumping. The ability the metamaterial 200 to achieve complex motions and robustly maintain stability is in stark contrast to prior art multi-stable metamaterials that are unable to achieve the remote and selective actuation and prior art soft constructs that are incapable of maintaining the stable configurations without a continuously applied energy source or temperature change for applications such as fluid pumping.

[0045] In some embodiments, the multi-stable metamaterials 200 may be fabricated from silicone elastomers in a casting process using 3D printed molds. In some embodiments, the metamaterial 200 may be formed by combining the silicone part A (e.g., Dragon Skin 30, Smooth-On) with a cure accelerator ( e.g., Plat-Cat, Smooth-On) at 2-8 wt.% of part A, mixing for 60 seconds (AR- 100, Thinky USA), adding silicone part B at 1 : 1 ratio (A: B, by weight) along with pigment if desired, then mixing all components for 60 seconds followed by 30 seconds of defoaming. In some embodiments, magnetic particles are added to the silicone elastomers at a 1 : 1 : 1.5 ratio (A:B: magnetic microparticles, by weight) and mixed for 45 seconds. In some embodiments, after mixing, the silicone may be cast in the molds after the mixing process, cured for a curing time, and then demolded. In some embodiments, magnetic metamaterials may be post-cured for about 60 minutes at about 60 °C. In some embodiments, magnetic programming of the metamaterial 200 may be performed by deforming the specimen into state [1], then programming with an impulse magnetizer at 2 T.

[0046] In some embodiments, magnetic actuation of the metamaterial 200 may be performed by manually controlling a permanent magnet below the metamaterial 200. In some embodiments, more than one magnet may be used to actuate the metamaterial 200, for example, in instances where the metamaterial 200 is used for a peristaltic pump to coordinate the opening and closing motions. In some embodiments, the one or more magnets may be automatically controlled.

[0047] In summary, the ability of the soft multi-stable metamaterial to selectively transform between multiple programmed stable configurations with an external energy source, such as a non- uniform magnetic field, can lead to a myriad of applications in soft robotics and biomedical devices.

[0048] Although the invention has been described and illustrated with respect to exemplary embodiments thereof, it should be understood by those skilled in the art that the foregoing and various other changes, omissions and additions may be made therein and thereto, without parting from the spirit and scope of the present invention.

Claims

CLAIMSWhat is claimed is:

1. A multi-stable metamaterial unit cell, comprising: a first support portion comprising one or more first support segments; a second support portion comprising one or more second support segments; and at least two transition supports, comprising, a first end defining a first cross-section and connected to the first support portion, a second end defining a second cross-section and connected to the second support portion, a support length (L) extending between a first end and a second end, and a midsection extending a midsection length (L*) between the first end and the second end that is less than the support length, wherein the midsection defines a midsection cross-section that is larger than the first and second cross-section, wherein application of an external energy source is configured to cause a transition between an initial stable configuration and a transformed stable configuration, and wherein the initial stable configuration and the transformed stable configuration are configured to be maintained after removal of the external energy source.

2. The multi-stable metamaterial unit cell of claim 1, wherein the external energy source is a non-uniform magnetic field.

3. The multi-stable metamaterial unit cell of claim 1, further comprising a Young’s modulus of about 800 kPa.

4. The multi-stable metamaterial unit cell of claim 1, wherein the at least two transition supports comprise a reinforcement ratio (R) that is between 0 and 0.625, where R= L* / L.

5. The multi-stable metamaterial unit cell of claim 1, comprised of a ferromagnetic composite.

6. The multi-stable metamaterial unit cell of claim 5, wherein the ferromagnetic composite comprises a silicone elastomer and magnetic particles.

7. The multi-stable metamaterial unit cell of claim 6, wherein the magnetic particles comprise neodymium-iron-boron (NdFeB).

8. The multi-stable metamaterial unit cell of claim 1, further comprising one or more lightemitting diodes (LEDs) integrated into at least one of: (i) the first support portion; (ii) the second support portions; and (iii) the at least two transition supports.

9. The multi-stable unit cell of claim 1, wherein in the initial stable configuration, the at least two transition supports pivot relative to the first and second support portions to increase a distance between the first and second support portions, and wherein in the transformed stable configuration, the at least two transition supports pivot relative to the first and second support portions to decrease a distance between the first and second support portions.

10. A multi-stable metamaterial, comprising: a plurality of unit cells coupled together, each of the plurality of cell units comprises, a first support portion comprising one or more first support segments; a second support portion comprising one or more second support segments; and at least two transition supports, comprising, a first end defining a first cross-section and connected to the first support portion, a second end defining a second cross-section and connected to the second support portion,a support length (L) extending between a first end and a second end, and a midsection extending a midsection length (L*) between the first end and the second end that is less than the support length, wherein the midsection defines a midsection cross-section that is larger than the first and second cross-section, wherein application of an external energy source is configured to cause a transition between an initial stable configuration and a transformed stable configuration, and wherein the initial stable configuration and the transformed stable configuration are configured to be maintained after removal of the external energy source.

11. The multi-stable metamaterial of claim 10, wherein the external energy source is a non- uniform magnetic field.

12. The multi-stable metamaterial of claim 10, wherein: the plurality of unit cells are arranged in two or more rows; a plurality of the unit cells of one of the two or more rows are programmed with a first energy barrier; a plurality of the unit cells of another of the two or more rows are programmed with a second energy barrier; and the first energy barrier is different than the second energy barrier.

13. The multi-stable metamaterial of claim 10, further comprising a ferromagnetic composite.

14. The multi-stable metamaterial of claim 13, wherein the ferromagnetic composite comprises a silicone elastomer and magnetic particles.

15. The multi-stable metamaterial of claim 14, wherein the magnetic particles comprise neodymium-iron-boron (NdFeB).

16. The multi-stable metamaterial of claim 10, further comprising a Young’s modulus of about 800 kPa.

17. The multi-stable metamaterial of claim 10, wherein: the plurality of unit cells are arranged in four (4) rows; each of the plurality of unit cells in a first row is programmed with a first energy barrier; each of the plurality of unit cells in a second row is programmed with a second energy barrier; each of the plurality of unit cells in a third row is programmed with a third energy barrier; each of the plurality of unit cells in a fourth row is programmed with a fourth energy barrier; and the first energy barrier, the second energy barrier, the third energy barrier, and the fourth energy barrier are different from each other.

18. The multi-stable metamaterial of claim 10, wherein in the initial stable configuration, the at least two transition supports pivot relative to the first and second support portions to increase a distance between the first and second support portions, and wherein in the transformed stable configuration, the at least two transition supports pivot relative to the first and second support portions to decrease a distance between the first and second support portions.

19. The multi-stable metamaterial of claim 10, wherein the plurality of unit cells are formed as a single component.

20. A biomedical device configured to be implanted into a living organism and comprised of the multi-stable metamaterial of claim 10.

21. The biomedical device of claim 20, further comprising a Young’s modulus of about 800 kPa.

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