Mechanical metamaterial with morphing bistability

Abstract

The present disclosure relates to a mechanical metamaterial with a variable bistable state. The mechanical metamaterial comprises a plurality of metamaterial unit cells connected in sequence in a first direction. Each metamaterial unit cell comprises a connecting head, a variable part and a fixed part connected in sequence in the first direction. The variable part comprises a plurality of variable sheet groups, each variable sheet group comprising two variable sheets, each variable sheet having a top end connected to the connecting head and a bottom end connected to the fixed part, and the width of each variable sheet increasing from the top end to the bottom end. The two variable sheets of each variable sheet group are symmetric about the axis center of the connecting head. The fixed part has a cavity facing the connecting head, and when an axial load is applied to the top of the connecting head, the top end of the variable sheet is bent in the direction of the cavity under the action of the connecting head, and part of the variable sheet and part of the connecting head can be accommodated in the cavity at the top of the fixed part. The mechanical metamaterial of the present disclosure can maintain stable and large deformation and has good band gap regulation ability.

Description

Technical Field

[0001] This disclosure relates to the field of mechanical materials, and more specifically, to a mechanical metamaterial with a deformable bistability. Background Technology

[0002] Vibration characteristics and control of structures are important research areas in dynamics and control. Research on vibration isolation and reduction in engineering structures is crucial for improving the safety of aerospace equipment and large structures. For example, without proper vibration isolation and reduction design in spacecraft, components such as bearings, power supplies, and sensors can be affected, potentially leading to malfunctions. Therefore, suppressing harmful vibrations in structures is essential.

[0003] Mechanical metamaterials are artificially designed mechanical structures that exhibit physical properties not found in natural materials. The use of mechanical metamaterials composed of periodic lattices allows for effective control of elastic wave propagation. Mechanical metamaterials possess bandgap properties, which prevent elastic waves from propagating within certain frequency ranges, thereby enabling vibration control.

[0004] However, in existing technologies, artificially designed mechanical metamaterials have fixed structures, resulting in fixed band gaps and limiting the control of elastic waves within a fixed frequency range. Adjusting the band gap necessitates redesigning the structure of the mechanical metamaterial, thus restricting its applications.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide a mechanical metamaterial with a deformable bistability that can maintain stable and large deformation and has good bandgap control capability.

[0007] Mechanical metamaterials with deformable bistability consist of multiple metamaterial unit cells, which are connected sequentially in the first direction;

[0008] The metamaterial unit cell includes a connector, a deformable part, and a fixed part connected sequentially along a first direction. The deformable part includes multiple deformable plate groups, each deformable plate group includes two deformable plates. The top end of each deformable plate is connected to the connector, and the bottom end of each deformable plate is connected to the fixed part. The width of the deformable plate increases from the top end to the bottom end. The two deformable plates in each deformable plate group are symmetrical about the axis of the connector. The deformable plates are evenly distributed around the axis of the connector.

[0009] The fixing part has a cavity facing the connector. The top of the deformable piece bends toward the cavity as the connector moves toward the fixing part. The cavity is used to accommodate the connector and the deformable piece.

[0010] In one exemplary embodiment of this disclosure, the bottom end of the deformable piece connected to the fixing part is an arc surface, the fixing part has an upper surface, a cavity is disposed on the upper surface, the edge of the upper surface is circular, and the bottom end of the deformable piece is connected to the edge of the upper surface.

[0011] In one exemplary embodiment of this disclosure, the angle between the deformable sheet and the first direction in its free state is... satisfy .

[0012] In one exemplary embodiment of this disclosure, the deformable portion includes two sets of deformable plates, with the apex corners of the deformable plates... satisfy .

[0013] In one exemplary embodiment of this disclosure, the thickness of the deformable sheet Less than 1.5mm.

[0014] In one exemplary embodiment of this disclosure, the deformable piece has no curvature in the direction surrounding the axis of the connector in its free state.

[0015] In one exemplary embodiment of this disclosure, the fixing part further has a base surface facing away from the deformable part, and a transition surface connecting the upper surface and the base surface, the transition surface being a cylindrical surface.

[0016] In one exemplary embodiment of this disclosure,

[0017] The mechanical metamaterial also includes an assembly substrate, which includes multiple mounting base surfaces arranged in an array in the second and third directions. One end of the base surface away from the deformable part has a positioning surface. The metamaterial unit cell is aligned with the mounting base surface through the positioning surface and thus mounted on the assembly substrate.

[0018] Among them, the first direction is perpendicular to the second direction, the first direction is perpendicular to the third direction, and the second direction is also perpendicular to the third direction.

[0019] In one exemplary embodiment of this disclosure, the connector is cylindrical, the positioning surface is circular, the diameter of the connector is equal to that of the positioning surface, and the length of the connector in the first direction is... satisfy The length of the transition surface in the first direction satisfy .

[0020] In one exemplary embodiment of this disclosure, the connector, the deformable portion, and the fixing portion are all made of thermoplastic polyurethane.

[0021] The mechanical metamaterial disclosed herein exhibits a bistable state, consisting of an initial steady state and a compressive steady state. In the compressive steady state, each metamaterial unit cell can maintain stable and large deformation, and the mechanical metamaterial can be switched between the two steady states by applying strain. The metamaterial unit cell of this disclosure can form two band gaps within the computational frequency range, and the band gap range in the initial steady state differs significantly from that in the compressive steady state. Therefore, the mechanical metamaterial of this disclosure has good band gap control capability in the Z direction. Attached Figure Description

[0022] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0023] To better understand this disclosure, reference may be made to the embodiments shown in the following figures. Components in the figures are not necessarily to scale, and related elements may be omitted to emphasize and clearly illustrate the technical features of this disclosure. Additionally, related elements or components may have different arrangements as known in the art. Furthermore, in the figures, the same reference numerals denote the same or similar components in various figures. Wherein:

[0024] Figure 1 This is a schematic diagram of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under the initial steady state.

[0025] Figure 2 This is a top view of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure in the initial steady state.

[0026] Figure 3 This is a schematic diagram from another perspective of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under the initial steady state;

[0027] Figure 4 This is a schematic diagram from another perspective of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under compressive steady state;

[0028] Figure 5 This is a diagram showing the bandgap characteristics in the Z direction of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under initial steady state.

[0029] Figure 6This is a bandgap characteristic diagram in the Z direction of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under compressive steady state.

[0030] Figure 7 This is a schematic diagram showing multiple metamaterial unit cells connected sequentially in the Z direction in an exemplary embodiment of the mechanical metamaterial disclosed herein.

[0031] Figure 8 This is a schematic diagram illustrating the assembly of multiple metamaterial unit cells into one unit via an assembly substrate in one exemplary embodiment of the mechanical metamaterial disclosed herein.

[0032] Figure 9 This is a schematic diagram of the inverted space and Brillouin zone in one exemplary embodiment of the mechanical metamaterial of this disclosure;

[0033] Figure 10 This is a pressure-displacement curve in an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterials of this disclosure;

[0034] Figure 11 This is a bandgap characteristic diagram in the X or Y direction of an exemplary embodiment of a metamaterial unit cell in the mechanical metamaterial of this disclosure under the initial steady state.

[0035] Figure 12 This is a bandgap characteristic diagram in the X or Y direction of an exemplary embodiment of the metamaterial unit cell in the mechanical metamaterial of this disclosure under compressive steady state.

[0036] The annotations in the attached figures are explained as follows:

[0037] 1. Metamaterial unit cell; 11. Connector; 12. Deformable piece; 13. Fixing part; 131. Cavity; 132. Base surface; 133. Transition surface; 134. Positioning surface; 2. Assembly substrate. Detailed Implementation

[0038] The technical solutions of the exemplary embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. The exemplary embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure. Therefore, it should be understood that various modifications and changes can be made to the exemplary embodiments without departing from the scope of protection of this disclosure.

[0039] Unless otherwise specified or stated, the term "connection" should be interpreted broadly. For example, "connection" can mean a fixed connection or an integral connection; it can mean a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.

[0040] Furthermore, it should be understood that the directional terms such as "upper," "lower," "inner," and "outer" described in the exemplary embodiments of this disclosure are for convenience only and are used to describe the objects according to the angles shown in the accompanying drawings, and should not be construed as limiting the exemplary embodiments of this disclosure. In the description of this disclosure, directional terms are only used to indicate relative positional relationships, and when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0041] The steady state described in this disclosure, i.e., the stable equilibrium state, refers to other steady states besides the initial steady state that mechanical metamaterials possess. These are states in which the structure may remain in these new stable equilibrium states without automatically returning to its original state when loading or unloading ceases. In this way, the energy input into the structure during loading can be trapped within the metamaterial structure in the form of elastic deformation.

[0042] In related technologies, by rationally designing the structure of metamaterials and altering the geometry, arrangement, and external physical fields of the metamaterial's unit cells, different band gaps can be achieved, enabling vibration control. However, in practical applications, traditional mechanical metamaterials with fixed structures, designed artificially, can only manipulate elastic waves within a fixed frequency range. Achieving band gap modulation requires a complete structural redesign, significantly limiting the engineering applications of mechanical metamaterials. Therefore, developing tunable mechanical metamaterials capable of actively adjusting their operating frequency range is crucial.

[0043] In some related technologies, the band gap of metamaterials can be altered by changing temperature, illumination, or applying strain. Among these methods, applying strain is easier to implement in engineering. However, this method of deforming metamaterials by applying strain to change the band gap has drawbacks: the strain is small, and the structure cannot maintain stable deformation after applying strain, resulting in a limited range of band gap control.

[0044] To address the aforementioned problems, this disclosure provides a bistable mechanical metamaterial, which is described below in conjunction with the appendix. Figures 1 to 12 The specific structure and mechanical properties of the mechanical metamaterial disclosed herein are described in detail.

[0045] To facilitate the explanation of the scheme disclosed herein, the coordinate system used in this disclosure will first be described. In the description of this disclosure, the first direction, the second direction, and the third direction are mutually perpendicular; that is, the first direction is perpendicular to the second direction, the first direction is perpendicular to the third direction, and the second direction is also perpendicular to the third direction, thus forming a Cartesian coordinate system. Taking the Cartesian coordinate system XYZ as an example, the first direction can be regarded as the Z direction, and the second direction and the third direction can be regarded as the X direction and the Y direction, respectively.

[0046] The mechanical metamaterial disclosed herein comprises multiple metamaterial unit cells 1, referenced Figure 7 As shown, multiple metamaterial unit cells 1 are sequentially connected in the Z direction. (Reference) Figure 1 As shown, the metamaterial unit cell 1 includes a connector 11, a deformable part and a fixed part 13 connected sequentially along the Z direction. The deformable part includes multiple deformable plate groups, each deformable plate group includes two deformable plates 12. The top end of each deformable plate 12 is connected to the connector 11, and the bottom end of each deformable plate 12 is connected to the fixed part 13. The width of the deformable plate 12 increases from the top end to the bottom end.

[0047] It should be noted that the connector 11, the deformable part, and the fixing part 13 are connected sequentially in the Z direction, with the deformable part located between the connector 11 and the fixing part 13. The top and bottom ends of the deformable piece 12 described in this disclosure refer to the ends of the deformable piece 12 that are close to the connector 11 in the Z direction and the ends that are close to the fixing part 13 in the Z direction, respectively.

[0048] In an exemplary embodiment of this disclosure, the two deformable pieces 12 of each deformable piece group are symmetrical about the axis of the connector 11, that is, the two deformable pieces 12 belonging to the same deformable piece group are rotationally symmetrical about 180°. The connector 11 is also arranged along the Z-axis. For ease of describing the structure of other parts of the metamaterial unit cell 1, the axis of the connector 11 can be regarded as coaxial with the Z-axis. All deformable pieces 12 of each deformable piece group are evenly distributed around the Z-axis.

[0049] refer to Figure 3 As shown, the fixing part 13 has a cavity 131 facing the connector 11. When a Z-direction load is applied to the top of the connector 11, the deformable part is composed of deformable plates 12 and has elasticity within a certain range, while the fixing part 13 can be considered as a rigid body. Therefore, under the load, the connector 11 will move towards the fixing part 13 and gradually approach the fixing part 13. During this process, refer to... Figure 4 As shown, the top of the deformable piece 12 bends toward the cavity 131 under the action of the connector 11, and the part of the deformable piece 12 near the top and part of the connector 11 can be accommodated in the cavity 131 at the top of the fixing part 13.

[0050] Since each metamaterial unit cell 1 has the same structure and is connected sequentially along the Z direction, and the direction of the external load is also Z, we can take only one metamaterial unit cell 1 as the research object and analyze its force-displacement relationship under pressure, thereby obtaining the state when multiple metamaterial unit cells 1 are connected in series.

[0051] In its initial state, i.e., when the connector 11 is in a free state without being subjected to an external load in the Z direction, the metamaterial unit cell 1 is in an initial steady state with zero deformation. The self-weight of each metamaterial unit cell 1 is relatively small compared to the external load experienced by the connector 11 during the deformation of the deformable plate 12, and therefore can be ignored. A vertically downward Z-direction pressure is applied to the top of the connector 11 of the metamaterial unit cell 1 in the initial steady state. During the deformation process, reference... Figure 10 The force-displacement curves shown have strain on the horizontal axis and pressure on the vertical axis. The presence of negative pressure indicates that metamaterial unit cell 1 exhibits negative stiffness, suggesting that the metamaterial unit cell 1 of this disclosure possesses bistable characteristics during compression. When the downward pressure returns to 0 from its negative value, the potential energy of metamaterial unit cell 1 reaches an extremely low point, representing a different steady state from the initial steady state, termed the compressive steady state.

[0052] It can be seen that the mechanical metamaterial disclosed herein has a bistable state of initial steady state and compressive steady state. Under the compressive steady state, each metamaterial unit cell 1 can maintain a stable and large deformation, and the mechanical metamaterial can be switched between the two steady states by applying strain to it.

[0053] Furthermore, the bandgap characteristics of the disclosed mechanical metamaterial under initial and compressive steady-state conditions are analyzed using finite element numerical simulation. Periodic boundary conditions are applied to metamaterial unit cell 1, and the bandgap along the Z-direction of metamaterial unit cell 1 under initial and compressive steady-state conditions is calculated along the irreducible Brillouin zone boundary, respectively. The band structure curves of the disclosed metamaterial unit cell 1 under initial and compressive steady-state conditions are obtained, with reference to... Figure 5 and Figure 6 As shown. The metamaterial unit cell 1 of this disclosure can form two band gaps within the computational frequency range, and the band gap range in the initial steady state differs significantly from that in the compressive steady state. Therefore, the mechanical metamaterial of this disclosure has good band gap control capability in the Z direction.

[0054] In one exemplary embodiment of this disclosure, reference is made to Figure 3 As shown, cavity 131 is provided on the upper surface of fixing part 13, that is, the surface of fixing part 13 near the bottom end of deformable piece 12. And the edge of the upper surface of fixing part 13 is round. The bottom end of deformable piece 12 for connecting with fixing part 13 is arc surface, and the bottom end of deformable piece 12 is connected to the edge of the upper surface of fixing part 13.

[0055] It should be noted that, in this exemplary embodiment, for ease of understanding, the deformable sheet 12 can be approximately regarded as a fan shape, with its width increasing from the top to the bottom, and the bottom being an arc surface, as shown in the reference. Figure 2As shown. However, in reality, the deformable piece 12 is not strictly fan-shaped. For example, the top of the deformable piece 12 is connected to the connector 11. If the connector 11 can be a cuboid, then the top of the deformable piece 12 can be a plane; if the connector 11 can be a cylinder, then the top of the deformable piece 12 can be an arc surface. In one exemplary embodiment, the deformable piece 12 has no curvature in the direction surrounding the axis of the connector 11 in its free state. That is, the deformable piece 12 is flat in its free state. The bottom end of the deformable piece 12 is used to connect with the edge of the upper surface of the fixing part 13. Therefore, the arc surface of the bottom end of the deformable piece 12 is not an arc surface, but a free curved surface adapted to the arc of the upper surface edge of the fixing part 13 and the degree of inclination of the deformable piece 12 relative to the XY plane.

[0056] The curvature of the circumferential direction around the Z-axis is perpendicular to the direction of deformation of the deformable piece 12. Therefore, the deformable piece 12 is an inclined straight plate in the free state. Compared with the curvature of the deformable piece 12 in the circumferential direction around the Z-axis, it is more conducive to ensuring the deformation stability of the deformable piece 12.

[0057] Since the deformable pieces 12 are distributed around the axis of the connector 11, according to geometric relationships, the sum of the tilt angle of the deformable piece 12 relative to the XY plane and the tilt angle relative to the Z direction in its free state is 90°. The tilt angle relative to a certain direction described in this disclosure is calculated as the acute angle between the deformable piece 12 and that direction. In an exemplary embodiment, refer to... Figure 1 As shown, the angle between the deformable piece 12 and the Z-axis in the free state satisfy .

[0058] Keeping other conditions unchanged, for different Compression tests were conducted on metamaterial unit cell 1 under certain conditions, and force-displacement curves were plotted. It can be found that... Different values ​​of will affect the minimum pressure during deformation. Based on the aforementioned analysis, when the minimum pressure is negative, the metamaterial unit cell 1 exhibits bistable characteristics during compression. The specific value affecting the minimum pressure, and thus the strain of metamaterial unit cell 1 under compressive steady state. By... By controlling the angle between 70° and 75°, the metamaterial unit cell 1 can achieve a relatively stable bistable state during compression, and there is a significant difference between the initial steady state and the compression steady state. The compression steady state has a strong ability to maintain stability.

[0059] Furthermore, keeping other conditions constant, compression tests were conducted on the metamaterial unit cell 1 under different thicknesses of the deformable sheet 12, and force-displacement curves were plotted. It can be found that... It also affects the minimum pressure during deformation and the strain corresponding to the compressive steady state. The inventors discovered that by... By controlling the thickness to less than 1.5 mm, the metamaterial unit cell 1 can achieve a relatively stable bistable state during compression, and there is a significant difference between the initial steady state and the compression steady state. The compression steady state has a strong ability to maintain stability.

[0060] The deformable portion includes multiple deformable piece groups, each deformable piece group including two deformable pieces 12. For example, the deformable portion may include two deformable piece groups, that is, the deformable portion includes a total of four deformable pieces 12; or, the deformable portion may include three deformable piece groups, that is, the deformable portion includes a total of six deformable pieces 12. The deformable portion may also include more deformable piece groups, which will not be elaborated here. In an exemplary embodiment, refer to... Figure 2 As shown, the deformable part includes two sets of deformable plates, namely four deformable plates 12, each of which has a apex angle of 12. Keeping other conditions unchanged, for different Compression tests were conducted on the metamaterial unit cell 1 under certain conditions, and force-displacement curves were plotted. It can be observed that the apex angle of the deformable plate 12... It will affect the bandgap of metamaterial unit cell 1 in both the initial steady state and the compressive steady state, and will also affect the difference in the bandgap range of metamaterial unit cell 1 in the above two steady states.

[0061] For example, in one exemplary embodiment of this disclosure... It is 60°, for reference. Figure 5 As shown, the bandgap of metamaterial unit cell 1 in the initial steady state ranges from 99 to 169 Hz. Figure 6 As shown, the bandgap range of metamaterial unit cell 1 under compressive steady state is 65-161 Hz. It can be seen that the bandgap range of metamaterial unit cell 1 changes significantly from the initial steady state to the compressive steady state.

[0062] By different The bandgap characteristics of metamaterial unit cell 1 under the condition of [condition] are analyzed. This allows for a significant difference in the bandgap range of the metamaterial unit cell 1 under the two steady states, thereby enabling the mechanical metamaterial of this disclosure to regulate vibrations over a wide range in the Z direction under compressive steady state. Furthermore, maintaining a spacing of at least 10° between the four deformable plates 12 reduces the difficulty of fabricating the metamaterial unit cell 1 and avoids defects such as adhesion caused by excessively close spacing between the deformable plates 12 during manufacturing, thus affecting the overall bandgap characteristics of the mechanical metamaterial.

[0063] Of course, in other exemplary embodiments, changes can also be made. This alters the bandgap range of metamaterial unit cell 1 under initial and compressive steady states, and reduces the difference in bandgap range between the two steady states, ensuring that its bandgap range meets the needs of practical engineering. For example, it makes... <60° to match more precise bandgap range differences.

[0064] It should be noted that the "apex angle of deformable piece 12" mentioned above refers to the included angle between the two sides of deformable piece 12. Specifically, since the width of deformable piece 12 increases from the top to the bottom, the included angle formed by the intersection of the two sides of deformable piece 12 along the direction from the bottom to the top is less than 180°. .

[0065] In the embodiments of this disclosure described above, the edge of the upper surface of the fixing part 13 is circular, that is, the fixing part 13 can be approximately regarded as a cone with the bottom on top and the top on the bottom, and the cavity 131 is provided at the bottom of the cone, and the cavity 131 can also be conical. Thus, the metamaterial unit cell 1 of this disclosure also has a band gap in the X and Y directions, which can isolate vibrations within a certain frequency range in the horizontal X and Y directions.

[0066] Furthermore, in one exemplary embodiment of this disclosure, reference is made to... Figure 1 As shown, the fixing part 13 has a base surface 132 facing away from the deformable part, i.e., the aforementioned outer conical surface. The fixing part 13 also has a transition surface 133 connecting the upper surface and the base surface 132. The transition surface 133 is a cylindrical surface. Since the deformable piece 12 has a certain thickness, the transition surface 133 is beneficial in two ways: firstly, it facilitates the connection between the bottom end of the deformable piece 12 and the edge of the upper surface of the fixing part 13, i.e., the bottom end of the deformable piece 12 is connected to the edge of the upper surface of the transition surface 133; secondly, it also helps to give the metamaterial unit cell 1 a certain impact resistance in the X and Y directions and a suitable band gap range.

[0067] For example, the length of the transition surface 133 in the Z direction is , .

[0068] In one exemplary embodiment of this disclosure, reference is made to Figure 7 As shown, the connector 11 is cylindrical, and the base surface 132 of the fixing part 13 has a positioning surface 134 at one end opposite to the deformable part. When multiple metamaterial unit cells 1 are connected sequentially in the Z direction, they are connected by the top surface of the connector 11 of the next metamaterial unit cell 1 to the bottom positioning surface 134 of the previous metamaterial unit cell 1, and the axes of the connectors 11 of each metamaterial unit cell 1 connected sequentially in the Z direction are coaxial. Preferably, the positioning surface 134 is also circular, and the diameter of the positioning surface 134 is the same as the diameter of the connector 11. For example, the diameter of the positioning surface 134 and the diameter of the connector 11 are both 8 mm.

[0069] In one exemplary embodiment of this disclosure, reference is made to Figure 8As shown, the mechanical metamaterial also includes an assembly substrate 2, which is arranged along the XY plane. The assembly substrate 2 includes multiple mounting bases arranged in an array in the X and Y directions. The metamaterial unit cell 1 is aligned with the mounting bases through its bottom positioning surface 134, thereby being mounted on the assembly substrate 2. That is, multiple metamaterial unit cells 1 are coaxially connected end to end in a row in the Z direction, and are mounted on the assembly substrate 2 through the positioning surface 134 at the bottom of the lowest metamaterial unit cell 1 aligned with the mounting bases; each row of metamaterial unit cells 1 is arranged in an array on the assembly substrate 2 in a one-to-one correspondence. The mechanical metamaterial of this disclosure assembles the metamaterial unit cells 1 into a whole through the assembly substrate 2. The axes of all the connectors 11 of the metamaterial unit cells 1 are arranged in the Z direction perpendicular to the assembly substrate 2. In the X and Y directions, the metamaterial unit cells 1 are not directly connected, but their positional relationship is indirectly determined by the assembly substrate 2, thereby having relatively definite and stable bandgap characteristics in the X and Y directions.

[0070] In one exemplary embodiment, the connector 11, the deformable portion, and the fixing portion 13 can all be made of thermoplastic polyurethane (TPU). The structure of the metamaterial unit cell 1 disclosed herein allows the deformable sheet 12 to deform within the linear elastic range, thereby ensuring that the deformation of the metamaterial unit cell 1 is recoverable and repeatable. Although the fixing portion 13 can be made of the same elastic material TPU as the deformable portion, the fixing portion 13 has a high structural stiffness and is approximately a rigid body under pressure. This makes it easier for the combination of the deformable portion and the fixing portion 13 to achieve Bragg scattering and local resonance, which is beneficial for the emergence of band gaps in the X, Y, and Z directions. Since the connector 11, the deformable portion, and the fixing portion 13 can be made of the same material, the metamaterial unit cell 1 of the exemplary embodiment of this disclosure can be 3D printed. The metamaterial unit cell 1 can also be 3D printed onto the assembly base surface of the assembly substrate 2.

[0071] For example, the height h of the deformable part in the Z direction is not less than 10 mm and not more than 14 mm, and the length of the connector 11 in the first direction is... The length of the transition surface 133 in the first direction is not less than 8 mm and not more than 10 mm. Not less than 6 mm and not more than 10 mm. A brief description of the method for calculating the band structure of the mechanical metamaterial of this disclosure in the Z direction and in the X or Y direction is provided:

[0072] The band structure in the Z direction is calculated:

[0073] refer to Figure 9 As shown, a triangular prism For the Brillouin zone in the inverted space of the metamaterial unit cell, where, , and Let be the basis vectors in the reciprocal space. To calculate the band structure of metamaterial unit cell 1 along the Z direction, the irreducible Brillouin zone is... Divide the path into a sufficient number of parts and sweep the dividing points. In the finite element software COMSOL, the band structure of the metamaterial unit cell 1 in the vertical Z-direction during the initial and compressive steady states, i.e., the relationship between the wave vector and the characteristic frequency, can be calculated. Figure 5 , Figure 6 As shown in the figure. The horizontal axis represents the wave vector, and the vertical axis represents the frequency, in Hz. From... Figure 5 As can be seen, in the initial steady state, the bandgap range is 99-169 Hz, and the bandgap width is 70 Hz; from Figure 6 As can be seen, under compression steady state, the band gap ranges from 65 to 161 Hz, and the band gap width is 96 Hz.

[0074] Calculations are performed on the band structure in the X or Y direction:

[0075] Similar to the method for calculating the band structure in the Z direction, this is achieved by considering the irreducible Brillouin zone. The path is scanned, and the band structure of the metamaterial unit cell 1 in the horizontal X or Y direction can be calculated in COMSOL under initial steady state and compressive steady state. After the calculation, the in-plane and out-of-plane polarization formulas are used. Out-of-plane bandgap characteristics were selected. In the formula, p is the polarization factor, and (u, v, w) is the displacement field within metamaterial unit cell 1. If p is close to 1, the calculated modes can be considered out-of-plane modes. Modes with p > 0.9 were selected as out-of-plane modes, and the out-of-plane bandgap characteristics of metamaterial unit cell 1 under initial steady state and compressive steady state were obtained as follows: Figure 11 , Figure 12 As shown in the figure, the shaded area represents the bandgap of metamaterial unit cell 1. Comparing the bandgap under the initial steady state and the compressed steady state, it can be found that the bandgap range of metamaterial unit cell 1 remains constant between 32-47 Hz and does not change with the steady state. Therefore, the metamaterial unit cell 1 of this disclosure can isolate out-of-plane wave propagation of the same frequency in the horizontal X or Y direction under different steady states.

[0076] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

[0077] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of protection of this disclosure is limited only by the appended claims.

Claims

1. A mechanical metamaterial exhibiting deformation bistable state, characterized in that, The mechanical metamaterial comprises multiple metamaterial unit cells, which are sequentially connected in a first direction. The metamaterial unit cell includes a connector, a deformable portion, and a fixed portion connected sequentially along the first direction. The deformable part includes multiple deformable piece groups, each deformable piece group includes two deformable pieces, the top end of each deformable piece is connected to the connector, the bottom end of each deformable piece is connected to the fixing part, and the width of the deformable piece increases from the top end to the bottom end. The two deformable pieces in each deformable piece group are symmetrical about the axis of the connector, and the deformable pieces are evenly distributed around the axis of the connector. The fixing part has a base surface facing away from the deformable part. The base surface is a conical surface that is wider at the top and narrower at the bottom. The fixing part has a cavity facing the connector. During the movement of the connector towards the fixing part, the deformable piece deforms and bends within the linear elastic range, and the shape of the fixing part is fixed. The top end of the deformable piece bends towards the cavity, and the cavity is used to accommodate the connector and the deformable piece. The fixing part also has a transition surface connecting the bottom end of the deformable piece and the base surface. The transition surface is a cylindrical surface.

2. The mechanical metamaterial with deformable bistable state according to claim 1, characterized in that, The angle between the deformable piece and the first direction in its free state satisfy .

3. The mechanical metamaterial with deformable bistable state according to claim 1, characterized in that, The deformable part includes two sets of deformable plates, and the apex corners of the deformable plates... satisfy .

4. The mechanical metamaterial with deformable bistable state according to claim 1, characterized in that, The thickness of the deformable sheet Less than 1.5mm.

5. The mechanical metamaterial with deformable bistable state according to claim 1, characterized in that, The deformable piece has no curvature in its free state along the axis surrounding the connector.

6. The mechanical metamaterial with deformable bistable state according to claim 1, characterized in that, The mechanical metamaterial also includes an assembly substrate, which includes multiple mounting base surfaces arranged in an array in the second and third directions. The end of the base surface facing away from the deformable part has a positioning surface. The metamaterial unit cell is aligned with the mounting base surface through the positioning surface, thereby being mounted on the assembly substrate. Wherein, the first direction is perpendicular to the second direction, the first direction is perpendicular to the third direction, and the second direction is also perpendicular to the third direction.

7. The mechanical metamaterial with deformable bistable state according to claim 6, characterized in that, The connector is cylindrical, the positioning surface is circular, the diameter of the connector is equal to the diameter of the positioning surface, and the length of the connector in the first direction is... satisfy The length of the transition surface in the first direction satisfy .

8. The mechanical metamaterial with deformable bistable state according to any one of claims 1 to 7, characterized in that, The connector, the deformable part, and the fixed part are all made of thermoplastic polyurethane.

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