A method for designing a multi-stable metamaterial with desired energy absorption characteristics

Abstract

The application belongs to the field of computer aided design, and discloses a multi-stable metamaterial design method with ideal energy absorption characteristics, which firstly carries out theoretical analysis on a buckle to establish a mathematical model. Then, according to the theoretical solution of the buckle structure stiffness value, reverse topology optimization design is carried out on a curved beam to make the force displacement curve of the curved beam have negative stiffness and peak force corresponding to the buckle. The buckle structure and the optimized and customized curved beam are assembled through a functional component, and then a multi-stable metamaterial unit cell with ideal energy absorption characteristics can be obtained. The unit cell is programmed and designed, and then the required metamaterial can be constructed to meet the energy absorption requirements under complex loads. The technical scheme is widely applicable to the fields of aerospace, automobile industry and building protection, and can improve the impact resistance of equipment while avoiding excessive rebound of impact energy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of mechanical metamaterial design, and relates to a design method of a multi-stable metamaterial with ideal energy absorption characteristics. The method is suitable for achieving ideal energy absorption efficiency in a variety of impact environments, and locking the structure when the energy absorption is completed to protect equipment and personnel, such as an energy absorption system for a whole satellite, to achieve secondary load satellite impact protection. BACKGROUND

[0002] Impact load is extremely common in industrial production and daily life, and often causes irreversible damage to the precision, operating life and safety of instruments. Considering the urgent need for safety, research and development of structures that can resist impact have become the focus, especially in the protection of precision instruments and critical equipment. Traditional energy absorption structures, such as tubular structures, composite structures, honeycomb structures, foam structures and flat plate structures, have been thoroughly discussed in previous studies, but their performance still needs to be optimized. In order to make up for the shortcomings of traditional design, researchers and engineers have begun to develop a variety of advanced structures, including metamaterials. Energy absorption metamaterials / structures usually exhibit significant nonlinear behavior based on their cleverly designed microstructures, which gives them unique advantages in energy absorption and cushioning. A common energy absorption metamaterial is a multi-stable metamaterial with negative stiffness characteristics, which is usually achieved by a pre-set structural deformation mode, such as the buckling of a flexible rod or shell, or the sliding of a buckle. These designs make the multi-stable metamaterials intentionally "collapse" or "deform" when subjected to impact or compression, rather than contract or resist, thereby achieving effective absorption and buffering of impact energy at the stable state transition. However, the ideal energy absorption metamaterial force-displacement curve should be rectangular and have a wide and flat force platform. This can help maintain a relatively constant stress level during deformation, which not only helps to improve energy absorption efficiency, but also provides effective cushioning under impact load, reducing the transmission of impact force to the protected object.

[0003] Inverse Design of Energy-absorbing Metamaterials by Topology Optimization, Advanced Science, 10 (2023) 1–10). However, the permanent plastic deformation caused by the nonlinear behavior makes the metamaterials damaged after impact, which is difficult to reuse. Moreover, compared with the multi-stable metamaterials, the force plateau characteristics of the energy-absorbing metamaterials improve the energy-absorbing efficiency, but they do not have the ability to control the energy rebound, which leads to the possibility of secondary impact when the impact energy is released. Therefore, the ideal energy-absorbing material should not only have a force plateau, but also have a bistable characteristic to lock the absorbed energy and prevent the occurrence of secondary collision.

[0004] A crashworthiness design method of a high-speed train bamboo-like anti-climbing energy-absorbing device is disclosed in Chinese patent application CN118070625A. The invention is inspired by the characteristics of bamboo, such as lightweight, high specific energy absorption, strong bending and torsional resistance, etc. It provides a high-speed train bamboo-like anti-climbing energy-absorbing device and its crashworthiness design method to enhance the crashworthiness and axial crushing stability of the anti-climbing energy-absorbing device and fully utilize its energy dissipation capacity in limited space. However, this structure often generates a large reaction force during impact, causing stress concentration or local damage to the protected object. SUMMARY

[0005] The technical problem solved by the present invention is to overcome the problem of limited energy-absorbing capacity and inability to control energy rebound of traditional impact-resistant structures. The present invention proposes a multi-stable metamaterial design method with ideal energy-absorbing capacity, which utilizes its nonlinear mechanical properties to achieve multi-stage energy absorption and dissipation, effectively reducing the initial impact force and maintaining the overall stability and integrity while significantly reducing the rebound energy.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A multi-stable metamaterial design method with ideal energy absorption characteristics, the design method is designed by combining custom curved beams and buckle structures with each other, thereby giving the metamaterial rich programmability, making it have the ability to adjust flexibly. When compressing these metamaterials, the curved beams customized by topology optimization first provide an initial energy barrier and absorb part of the energy. Then the buckle structure gradually activates to ensure that the force-displacement curve presents an ideal rectangle and locks the system state when the energy absorption is completed. The invention verifies the energy absorption capacity and multi-stable characteristics of the metamaterial through additive manufacturing and experimental characterization. The error between the force platform of the designed metamaterial unit cell and the theoretical force platform is less than 6%, and the stable state conversion occurs. In addition, the impact test also proves the impact resistance and protection ability of the designed metamaterial. This phased energy absorption mechanism not only effectively improves the energy absorption efficiency, but also avoids the excessive rebound of impact energy by precisely controlling the deformation process of the metamaterial, ensuring the stability and controllability of the protected structure after impact.

[0008] The proposed design method solves the fusion problem of traditional energy absorption metamaterials in complex nonlinear mechanical behavior, providing new possibilities for developing efficient, stable and controllable energy absorption systems. Specifically, the following steps are included:

[0009] S1: Design and theoretical analysis of buckle structure in metamaterial unit cell: The buckle structure is composed of vertical beams with cantilever hooks and sliding grooves with inclination angles, which are symmetrically arranged. Considering the assembly of the buckle structure and the curved beam, a boss with a length of is set at the bottom of the buckle structure. Other known parameters include: the inclination angle of the sliding groove , the height and the width of the lower end . The thickness and height of the vertical beam are and respectively. In order to obtain the relationship between the vertical force and the vertical displacement , the vertical beam is assumed to be an elastic beam and is fixed at the bottom. When the sliding groove can only move vertically, the vertical beam will bend due to horizontal compression and increase the friction force, so that the overall reaction force presents linear. In order to study the mechanism of the buckle structure, one side of the buckle structure is taken and appropriately simplified for theoretical analysis. The buckle structure theoretical model is shown as follows:

[0010]

[0011] where, E is the Young's modulus. The mechanical behavior of the buckle structure is mainly affected by the bending of the vertical beam. In other words, only the bending part of the vertical beam needs to be considered when analyzing the bending behavior of the buckle structure. Since adjusting the height or thickness or inclination of the vertical beam will greatly affect the stiffness of the buckle structure, these parameters can be adjusted according to the needs.

[0012] S2: Custom design of curved beams in metamaterial unit cells: In the custom design process of curved beams, the curved beams are first projected horizontally, and then a material field for topological optimization of the curved beams is constructed through uniformly distributed observation points, i.e., describing the presence or absence of materials. In order to reduce the number of design variables to speed up the solution, the material field is reduced in dimension using a series expansion strategy to construct the optimization design domain. The Latin hypercube sampling method is used to select sample points in the design domain, and then finite element analysis is performed on the obtained sample points to determine the distribution of the sample points in the target space, and a Kriging surrogate model is established to find the current optimal topology configuration. After completing one sub-optimization cycle, the design domain is gradually reduced according to the position of the current optimal sample points, and a new sub-optimization problem is solved. With the updating and solving of the sub-optimization problem, the optimal solution that meets the target is finally obtained. Unlike the traditional gradient-based optimization problem solving process, the entire optimization process of the non-gradient algorithm is divided into multiple sub-optimization steps. Although the target values of the sample points vary greatly within a single sub-optimization step, with the continuous updating of the sub-optimization steps, the design domain gradually decreases and the target value converges to a stable value.

[0013] Further, the geometric shape of the curved beam is represented by the equation where the parameter represents the length of the curved beam, y represents the height direction of the curved beam, represents the length direction of the curved beam, and the height is represented by the parameter .

[0014] S3: Design of metamaterial unit cell: Although both curved beam / straight beam structure and buckle structure achieve bistable design, they have different mechanical behaviors. The most prominent feature is that the former exhibits negative stiffness within a considerable deformation range, while the latter mainly exhibits positive stiffness. The opposite behaviors of the two mean complementarity in energy absorption process, which can be extended to multi-stable metamaterial with ideal energy absorption characteristics by combining design. By building buckle structure and customized curved beam together from functional components, rectangular force-displacement curve behavior can be achieved. This mechanism can be explained by the parallel of Hooke's springs. In the parallel case, the deformation of buckle structure and curved beam is equal to the external deformation, and their stiffnesses are added up to the total stiffness. Specifically, the buckle structure exhibits positive stiffness during loading, and when it exceeds a certain critical value, the reaction force of the buckle structure will jump to zero to achieve the transition of stable state. While the customized curved beam will exhibit negative stiffness after a short positive stiffness stage, and will again change to positive stiffness when the buckle structure jumps, completing the stable state transition. Coupling the buckle structure and the customized curved beam through functional components, the force-displacement curve of the combined structure not only has ideal rectangular to buffer and absorb energy, but also has the ability of stable state transition to lock energy, which can play a good application in the field of shock resistance.

[0015] Further, by assembling the buckle structure and the optimized curved beam through functional components, i.e. connecting components, a rectangular force-displacement curve behavior can be achieved, which endows the designed unit cell with ideal energy absorption characteristics and multi-stable characteristics to exhibit good shock resistance behavior.

[0016] Further, since the structure and deformation of the curved beam are symmetrical, it is equivalent to be divided into two parts after customization. The buckle structure is located in the middle of the unit cell, and the curved beam with symmetrical properties is located on both sides of the sliding groove.

[0017] Further, by programming the design of the unit cell, the energy absorption requirements under complex loads, such as longer displacement range force platform, larger effective load or multiple force platform segments, can be met.

[0018] S4: Finite element analysis of metamaterial unit cell: Based on the metamaterial unit cell constructed in S3, finite element numerical simulation is carried out. It is assumed that the upper surface and the lower surface of the unit cell have rigid plates to represent the pressure plates of the testing machine, and the finite element nodes of the rigid plates are coupled on the reference point located in the center through multi-point constraints for loading and observing the reaction force. The vertical downward displacement load is applied to the upper boundary, the lower boundary is fixed, and the two sides are subjected to sliding constraint, so that the unit cell deforms. The finite element model of the unit cell is divided into more than three layers in the in-plane thickness direction to improve the simulation accuracy of the bending behavior.

[0019] S5: Experimental verification of metamaterial unit cell: In order to test the mechanical properties of the designed energy-absorbing metamaterial unit cell, the mainstream jet fusion 3D printing technology is used to prepare the unit cell designed in step S3. Then, a general testing machine is used to test the compression of the unit cell. In the experiment, a specially designed rigid clamp is added to obtain the same constraint effect as the finite element analysis. The experiment is carried out by displacement loading. In order to reduce the influence of dynamic effects generated in the loading process on the experimental results, a constant loading rate of 2mm / min is set during the loading process, and the generated support force is measured by a high-precision sensor.

[0020] Further, the preparation material of the energy-absorbing unit cell can be common plastics such as nylon or resin, or various types of metals. Preferably, the material is nylon, and the reason for choosing this material is that it has low manufacturing cost and can enhance the flexibility of design.

[0021] S6: Design of a multi-stable metamaterial with ideal energy-absorbing properties: Based on the metamaterial unit cell constructed in step S3, the corresponding modular metamaterial can be formed by array strategy, and then the fastener is used to build the large-scale metamaterial required to meet different application scenarios. The specific way is: using unit cells with different force platforms to assemble in multiple layers, and each layer of sample is assembled in a central symmetric manner to maintain the stability of the overall structure. The arrangement direction of the unit cells is set to be consistent in each layer, and the layers are aligned vertically, and then bonded and fixed by the support plates located between the layers. The ideal energy-absorbing multi-stable metamaterial designed in this way realizes flexible impact resistance. When the impact is light, a weaker energy-absorbing mechanism is triggered, and the impact acceleration is also smaller. When the impact is heavy, a stronger energy-absorbing mechanism is triggered, and the impact acceleration is also larger.

[0022] A multi-stable metamaterial with ideal energy-absorbing properties is obtained by using the above design method, which is a promising multi-stage and impact-resistant solution. This kind of metamaterial not only can exhibit high energy-absorbing properties during the collision process, but also can flexibly cope with different degrees of impact, for example, used in the energy-absorbing system of a car, triggering a weaker energy-absorbing mechanism when colliding with a pedestrian, and triggering a stronger energy-absorbing mechanism when colliding with a wall, improving the passive safety of the vehicle.

[0023] The design principle of the present application is:

[0024] The present application can achieve rectangular force-displacement curve behavior with multi-stable characteristics by constructing the buckle structure and the customized curved beam from functional components. This not only provides multiple energy barriers, but also has good energy absorption efficiency, so as to achieve the ideal impact resistance effect. The mechanism can be explained by the parallel connection of Hookean springs. In the parallel connection case, the deformation of the buckle structure and the curved beam is equal to the external deformation, and the stiffness is equal to the total stiffness. Specifically, the buckle structure presents positive stiffness during loading, and when a certain critical value is exceeded, the reaction force of the buckle structure will jump to zero to realize the stable state conversion. While the customized curved beam presents negative stiffness after a short positive stiffness stage, and converts to positive stiffness again when the buckle structure jumps, completing the stable state conversion. Coupling the buckle structure and the customized curved beam into a unit cell through functional components, the force-displacement curve of the unit cell not only has an ideal rectangle to buffer and absorb energy, but also has a stable state conversion capability to lock energy, which can play a good application in the impact resistance field. Further, by programming, the unit cell is designed as a metamaterial, which can have a longer displacement range of force platform, a larger effective load, or multiple force platform segments, which can meet the energy absorption requirements under complex loads.

[0025] The beneficial effects of the present application are:

[0026] The present application designs a multi-stable metamaterial with a rectangular force-displacement curve based on a buckle structure and a customized curved beam. The rectangular force-displacement curve can achieve ideal energy absorption capability, and the multi-stable characteristic can realize energy locking mechanism. This is beneficial to prevent excessive rebound of impact energy, so as to make the protected structure stable and controllable after collision. The unit cells of these metamaterials are designed by combining buckle structures and customized topological curved beams, thereby giving the metamaterials rich programmability and flexibility. When the designed metamaterial is compressed, the customized topological curved beam first provides an initial energy barrier and absorbs part of the energy. Then the buckle structure gradually activates to ensure that the force-displacement curve presents an ideal rectangle and locks the system state when the energy absorption is completed. In addition, using 3D printing technology for integrated casting, the present application not only improves the energy absorption capability of the metamaterial, but also maintains a relatively low mass, which is of great significance for reducing the load of the overall system and improving energy efficiency. The present application not only provides an innovative design in theory, but also includes a set of experimental verification mechanism to ensure the feasibility and effect of the design. This combination of experiment and theory improves the scientificity and practicality of the invention. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 The flowchart of the design method according to the embodiment of the present application.

[0028] Figure 2a The design form and design parameters of the buckle structure in the metamaterial unit cell are shown.

[0029] Figure 2b Theoretical analysis results of taking half of the buckle structure based on symmetry.

[0030] Figure 2c The deformation state of the buckle structure in the compressed state and its force analysis diagram are shown.

[0031] Figure 3a The customization process of the curved beam in the metamaterial unit cell is shown, and the material field of the curved beam is described by observing points to customize the peak force and negative stiffness of the force displacement curve.

[0032] Figure 3b The schematic diagram of using a non-gradient topology optimization strategy to customize the material layout of the curved beam is shown.

[0033] Figure 3c The customized curved beam that meets the target and constraint obtained by multiple iterations is shown.

[0034] Figure 4a The schematic diagram of the customized curved beam and the buckle structure in the metamaterial unit cell composed of the buckle structure and the corresponding customized curved beam is shown.

[0035] Figure 4b The mechanical properties of the metamaterial unit cell come from: the force displacement curve of the unit cell is formed in parallel according to Hooke's law by the force displacement curve of the buckle structure and the customized curved beam.

[0036] Figure 4c The combination strategy (series, parallel and series-parallel) of the metamaterial unit cell and the force displacement curve under different combinations are shown.

[0037] Figure 5 The finite element model of the metamaterial unit cell designed according to the embodiments of the present application.

[0038] Figure 6a The three-dimensional CAD structure schematic diagram of sample 1 unit cell for verifying the example and mechanical properties of the metamaterial unit cell designed by the present application is shown.

[0039] Figure 6b The three-dimensional CAD structure schematic diagram of sample 2 unit cell for verifying the example and mechanical properties of the metamaterial unit cell designed by the present application is shown.

[0040] Figure 6c The force-displacement curve of the finite element analysis and test of sample 1 unit cell for verifying the example and mechanical properties of the metamaterial unit cell designed by the present application is shown, and the strain cloud diagram when the unit cell strain is maximum is given.

[0041] Figure 6dThe force-displacement curve of sample 2 cell finite element analysis and test of the sample for verifying the example and mechanical properties of the designed metamaterial cell of the application is shown, and the strain cloud diagram at the maximum strain of the cell is given.

[0042] Figure 7a The force-displacement curve of the metamaterial under compression test of the metamaterial in the configuration of the multistable metamaterial verification with ideal energy absorption characteristics of the combination of sample 1 and sample 2 in parallel and then in series is shown.

[0043] Figure 7b The deformation state of the metamaterial under compression test of the metamaterial in the configuration of the multistable metamaterial verification with ideal energy absorption characteristics of the combination of sample 1 and sample 2 in parallel and then in series is shown. DETAILED DESCRIPTION

[0044] The specific embodiments of the application are described in detail below in combination with the technical solutions and the drawings:

[0045] The application utilizes the buckle structure and the customized curved beam, and designs a multistable metamaterial with ideal energy absorption characteristics by combination, and performs theoretical analysis, finite element simulation and experimental verification.

[0046] The principle realized by the application is:

[0047] By means of the locking mechanism of the buckle structure and the energy absorption characteristics of the bistable structure, the application adopts a multi-step design method to develop a multistable metamaterial with ideal energy absorption characteristics. The metamaterial has a rectangular force-displacement curve to effectively improve the energy absorption efficiency, and the multistable locking mechanism avoids excessive rebound of impact energy to maintain the stability and controllability of the protected structure after collision. The unique mechanical behavior is derived from the combination of the buckle structure and the curved beam in the cell of the metamaterial. In the design process of the metamaterial, first, the buckle structure is theoretically analyzed to establish a mathematical model. Then, according to the theoretical solution of the buckle structure stiffness value, the curved beam is inversely topologically optimized to make its force-displacement curve have negative stiffness and peak force corresponding to the buckle structure. By assembling the buckle structure and the optimized and customized curved beam through functional components, a multistable metamaterial cell with ideal energy absorption characteristics can be obtained. Then, the cell is programmed and designed to construct the required metamaterial to meet the energy absorption requirements under complex loads. In addition, the application also includes a complete verification mechanism, which uses finite element simulation and quasi-static compression experiments to deeply analyze the energy absorption capacity, bistable characteristics and programmable characteristics of the metamaterial. The technical solution is widely applicable to the fields of aerospace, automobile industry and building protection, etc., which improves the impact resistance of equipment while avoiding excessive rebound of impact energy.

[0048] Figure 1The embodiment flowchart of the present application is depicted, i.e. design of the buckle structure in the unit cell, customization of the curved beam in the unit cell through topological optimization, construction of the unit cell from the buckle structure and the customized curved beam, finite element analysis of the metamaterial unit cell, experimental verification of the metamaterial unit cell, and design of a multi-stable metamaterial with ideal energy absorption characteristics.

[0049] According to Figure 1 , the design method in the embodiments of the present application comprises the following steps:

[0050] S1: design and theoretical analysis of the buckle structure in the metamaterial unit cell.

[0051] The buckle structure is composed of a vertical beam with a cantilever hook and a chute with an inclination angle, which are symmetrically arranged, as shown in Figure 2a . Considering the assembly of the buckle structure and the curved beam, a boss is arranged at the bottom end of the buckle structure, with a length of . Other known parameters include the inclination angle of the chute, the height and the width of the lower end . The thickness and height of the vertical beam are and respectively. In order to obtain the relationship between the vertical force and the vertical displacement , the vertical beam is assumed to be an elongated elastic beam with a fixed constraint at the bottom end. When the chute can only move vertically, the vertical beam will deflect due to horizontal extrusion, which will increase the friction force, so that the overall reaction force presents linear. In order to predict the stiffness of the buckle structure during compression, the buckle structure is simplified and theoretically derived, and the geometric parameters of the buckle structure are given in Figure 2a . Based on the symmetry of the buckle structure, one side of the buckle structure is taken for theoretical analysis, as shown in Figure 2b .

[0052] The deformation mode of the simplified buckle structure under vertical load is shown in Figure 2c , and the deflection differential equation of the vertical beam can be written as:

[0053]

[0054] where is the bending moment of the vertical beam, is the inherent Young's modulus of the material, is the second moment of inertia of the vertical beam, represents the width of the vertical beam, i.e. the width of the curved beam, is the deflection of the vertical beam. At the intersection of the chute and the vertical beam, the chute is subjected to the vertical force and the horizontal force due to the bending deformation of the vertical beam.The relationship between the horizontal displacement of the intersection point of the inclined block and the vertical beam and the horizontal force is:

[0055]

[0056] wherein it is assumed that the intersection point of the inclined block and the vertical beam is located at the midpoint of the cantilever hook. Herein, for the convenience of calculation, the length of the vertical beam is simplified as .

[0057] The normal force of the vertical beam subjected to the force of the sliding groove projected to the normal of the inclined surface is and the friction force can be written as:

[0058]

[0059]

[0060] wherein, is the friction factor between the sliding groove and the vertical beam. By projecting the force of the sliding groove to the inclined surface, the friction force of the vertical beam can be expressed as:

[0061]

[0062] By solving equations (4) and (5) simultaneously, the vertical force of the sliding groove can be obtained as:

[0063]

[0064] Since the vertical displacement of the sliding groove is related to the horizontal displacement of the vertical beam , the relationship can be expressed as:

[0065]

[0066] By solving equations (2), (6) and (7) simultaneously, the vertical force of the vertical beam can be expressed as:

[0067]

[0068] Therefore, the stiffness of the buckle structure during the loading process can be expressed as:

[0069]

[0070] Thus, the theoretical model of the buckle structure can be constructed by the above equations (1) to (9) to predict its stiffness during the compression process.

[0071] ​S2: Customizing the curved beam in the metamaterial unit cell by topology optimization.

[0072] The goal of the curved beam topology optimization is to achieve the desired negative stiffness and peak force in the force-displacement curve. Therefore, the negative stiffness region in the force-displacement curve of the curved beam is selected to define the required stiffness value, which is also the goal 1. Since the two ends of the negative stiffness region have large fluctuations, the range of the region is reduced to . By precisely calculating the slope change between adjacent data in these regions, the representative negative stiffness Figure 3a is obtained, as shown in the lower right corner. In this way, the goal of the present application can be changed to minimize the error between the actual negative stiffness of the curved beam and the desired negative stiffness . At the same time, in order to obtain the expected maximum peak force of the curved beam, the error between the maximum peak force of the curved beam and is also as small as possible, which is also the goal 2. In addition, the minimum peak force of the curved beam during loading is constrained to be less than 0, so as to maintain the bistable characteristics of the curved beam. In order to avoid optimizing some results that cannot be applied in actual engineering, the maximum strain of the curved beam during loading is also constrained.

[0073] Based on this, the topology optimization for customizing the curved beam can be represented as:

[0074] In the formula, is the sum of the negative stiffness error and the peak force error, and in order to make them in the same order of magnitude, they are equivalent respectively. is the penalty factor, which is selected to be an even number to approach the desired value. In the constraint condition , is introduced to make the curved beam retain obvious bistable characteristics. is the maximum strain allowed by the preparation material, represents the topology layout of the material.

[0075] S3: Constructing the metamaterial unit cell from the buckle structure and the customized curved beam.

[0076] While both the curved beam / straight beam structure and the buckle structure achieve bistable design, they differ in mechanical behavior. The most prominent feature is that the former exhibits negative stiffness within a considerable deformation range, while the latter mainly exhibits positive stiffness. The opposite behaviors of the two mean complementarity in energy absorption process, thus can be extended to a multi-stable metamaterial with ideal energy absorption characteristics by combined design. By building the buckle structure and the customized curved beam together from functional components, the rectangular force-displacement curve behavior can be achieved. This mechanism can be explained by the parallel of Hookean springs, as shown in Figure 4b In the parallel case, the deformation of the buckle structure and the curved beam is equal to the external deformation, and their stiffnesses add up to the total stiffness. Specifically, the buckle structure exhibits positive stiffness during loading, and when a certain critical value is exceeded, the reaction force of the buckle structure will jump to zero to achieve the transition of stable state. While the customized curved beam will exhibit negative stiffness after a short positive stiffness stage, and will again transition to positive stiffness when the buckle structure jumps, completing the stable state transition. By coupling the buckle structure and the customized curved beam through functional components, the force-displacement curve of the combined structure not only has an ideal rectangular shape to buffer and absorb energy, but also has the ability to lock energy through stable state transition, which can play a good application in the field of shock resistance.

[0077] In the construction of metamaterial unit cells, the structure and deformation of the curved beam are symmetrical, and it is equivalent to be divided into two parts after customization. The buckle structure is located in the middle of the unit cell, and the curved beam with symmetrical properties is located on both sides of the sliding groove, and the two are connected through functional components, as shown in Figure 4a To prevent the buckle structure from generating undesirable friction with the functional components, the width of the sliding groove is greater than the width of the vertical beam, which increases the spatial redundancy of the side surface of the buckle structure. It should be noted that the buckle structure, curved beam and functional components are manufactured by integrated 3D printing technology using the same material, ensuring the integrity of the designed unit cell. Further, by programming the unit cell, the energy absorption requirements under complex loads can be met, such as longer displacement range force platform, larger effective load or multiple force platform segments, as shown in Figure 4c .

[0078] The geometry of the curved beam can be represented by the equation , where the parameters and represent the length and in-plane cross-sectional thickness of the curved beam, respectively, y represents the height direction of the curved beam, represents the length direction of the curved beam, and the height is represented by the parameter .

[0079] S4: Optionally, finite element analysis of the metamaterial unit cell.

[0080] A unit cell of metamaterial based on S3 is constructed and its finite element numerical simulation is performed. It is assumed that the upper and lower surfaces of the unit cell are rigid plates to represent the pressure plates of the testing machine, and the finite element nodes of the rigid plates are coupled on the reference point at the center of the plates by multi-point constraints for loading and observing the reaction force, as shown in Figure 5 The vertical downward displacement load is applied to the upper boundary, the lower boundary is fixed, and the two sides are subjected to sliding constraints, so that the unit cell is deformed. The finite element model of the unit cell is divided into a grid with a thickness of more than three layers in the in-plane direction to improve the simulation accuracy of the bending behavior.

[0081] In order to numerically simulate the unit cell of metamaterial, the finite element analysis of the unit cell is performed by using a commercial finite element software. Specifically, the nylon material adopts a linear elastic model, and the Young's modulus and Poisson's ratio are measured by tensile test. The mechanical response of the unit cell is calculated by using a general static analysis step to obtain a smooth force-displacement curve. The geometric nonlinearity is turned on to handle large deformation and very complex sliding friction that occurs during calculation. The surfaces that occur contact during loading are considered as the normal behavior and tangential behavior of the surface-to-surface contact, wherein the "hard" contact is used to define the normal behavior of the contact, and the "penalty" model with a friction coefficient of 0.3 is used to define the tangential behavior of the contact. The obtained finite element model is shown in the figure, wherein an eight-node linear hexahedral element is used for meshing, and at least four solid grids are generated along the thickness direction of the curved beam to accurately simulate the bending of the curved beam.

[0082] S5: Optionally, experimental verification of the unit cell of metamaterial.

[0083] In order to verify the mechanical properties of the designed energy-absorbing unit cell, two samples of the designed unit cell are prepared, and the force platforms thereof are (sample 1) and (sample 2). Their specific geometric parameters and expected peak forces are given in Table 1, and are shown in Figure 6a and 6b Figure 6c and Figure 6d ​The force-displacement curve comparison between the experiment and finite element results of sample 1 and sample 2 respectively shows an ideal rectangle and a bistable characteristic. When the sample is in a compression state, the curved beam in the sample deforms first, and the reaction force shows a trend of increase, then when the curved beam enters the negative stiffness region (at point A), the buckle structure starts to deform and provides positive stiffness, at this time, the reaction force of the sample remains almost unchanged. With the loading proceeding to the locking of the buckle structure (at point B), the positive stiffness provided by the buckle structure disappears, the force-displacement curve jumps, and the stable state changes, at this time, the reaction force is provided by the curved beam again. The maximum error between the expected force platform of sample 1 and sample 2 and the force platform measured in the experiment is 14.67% and 13.03% respectively, and the error measured by the finite element analysis is 3.40% and 5.35% respectively. This is because it is difficult to achieve ideal conditions in the experiment (there are manufacturing and experimental errors), so there is a small difference between the experimental results and the finite element results. Overall, the experimental results and the finite element analysis results can better match, both show an ideal force platform, and the measured peak force is close to the expected value, which proves the effectiveness of the design method of the application.

[0084] Table 1 Geometric parameters of metamaterial unit cells

[0085] Sample h (mm) l (mm) b (mm) t (mm) h b (mm) h s (mm) l b (mm)]]> <![CDATA[t s (mm)]]> <![CDATA[t b (mm)]]> θ (°°) F e (N)]]> 1 10 100 20 1 15 13.3 15.3 2 2 80 7.5 2 10 100 20 1 15 13.3 15.3 2 2.2 80 10

[0086] S6: Design a multi-stable metamaterial with ideal energy absorption characteristics.

[0087] The application can design a multi-stable metamaterial with ideal energy absorption characteristics by stacking energy absorption unit cells with force platforms. In order to demonstrate the effectiveness of this design strategy, sample 1 and sample 2 are combined in a parallel-serial manner to explore their response under complex combination, as shown in Figure 7a The results show that this mixed configuration not only can realize the regulation of force platform on the force-displacement curve, but also can provide enhanced load bearing capacity and maintain a large force platform. In addition, Figure 7b shows four typical deformation states of the assembly shown in Figure 7a The positions of the four states are marked in Figure 7a . Among them, the first two marks correspond to the starting point and the ending point of the first force platform (also the point of the first jump), and the last two marks correspond to the starting point and the ending point of the second force platform (also the point of the first jump). By observation, it can be found that when one of the parallel sample layers corresponding to the force platform deforms, the other parallel sample layer corresponding to the force platform hardly deforms. This is because the difference in force platform provides a force barrier for sample deformation, thereby realizing the controllable energy absorption and locking of the metamaterial, which ensures the flexible response capability of the metamaterial under complex impact load.

[0088] The essence of the present application is to design a multi-stable metamaterial with ideal energy absorption capacity through the parallel mechanism of buckle structure and customized curved beams, and to realize the energy absorption mechanism in stages, avoid excessive rebound of impact energy, and ensure the stability and controllability of the metamaterial after energy absorption. These metamaterials composed of unit cells also have rich programmability and flexible adjustment ability, making them show superior adaptability and effect in a wider range of application scenarios. It should be pointed out that the mechanical properties of the designed metamaterial depend on the geometric design, so it can be realized by different 3D printing materials. The proposed metamaterial design strategy solves the fusion problem of traditional energy absorption metamaterials in complex nonlinear mechanical behavior, and provides new possibilities for developing efficient, stable and controllable energy absorption systems.

[0089] The above-mentioned embodiments only express the implementation of the present application, but cannot be interpreted as a limitation on the scope of the present patent. It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of protection of the present application.

Claims

1. A design method for a multistable metamaterial with ideal energy absorption characteristics, characterized in that: The method comprises constructing a metamaterial unit cell of the multistable metamaterial by using a snap-fit ​​structure and a curved beam, and comprising: Conduct theoretical analysis on the buckle structure and explore the parameters affecting the positive stiffness of the buckle structure during loading; performing reverse topology optimization on the curved beam to customize the design based on the positive stiffness value of the snap-fit ​​structure so that its force-displacement curve has a negative stiffness and peak force corresponding to the snap-fit ​​structure; By assembling the snap-fit ​​structure with the optimized curved beam to construct the force platform of the metamaterial unit cell, a multistable metamaterial with ideal energy absorption characteristics is designed. The multistable metamaterial has a rectangular force-displacement curve to effectively improve energy absorption efficiency, and the multistable locking mechanism prevents excessive rebound of impact energy, thereby maintaining the stability and controllability of the protected structure after a collision. The buckle structure in the metamaterial unit cell is configured such that the buckle structure is composed of a vertical beam with a cantilever hook and a sliding groove with an inclination angle, wherein the vertical beam and the sliding groove are symmetrically arranged; a boss is provided at the bottom end of the buckle structure; The curved beam in the metamaterial unit cell is shaped as follows: the negative stiffness region in the curved beam force-displacement curve is selected. To define the required stiffness value, the range of the negative stiffness region is reduced to By accurately calculating the slope changes between adjacent data in these areas, the representative negative stiffness can be obtained. , to minimize the actual negative stiffness of the curved beam With expected negative stiffness At the same time, in order to obtain the expected maximum peak force of the curved beam , set the maximum peak force of the curved beam and The error is as small as possible; Among them, the curved beam is equivalently divided into two parts; the snap-on structure is located in the middle of the metamaterial unit cell, and the curved beam with symmetrical properties is located on both sides of the slide, and the two are connected by functional components; so that the width of the slide is greater than the width of the vertical beam.

2. The design method according to claim 1, characterized in that: The minimum peak force constraining the curved beam during loading , so that it is limited to a range less than 0 to maintain the bistable characteristics of the curved beam.

3. The design method according to claim 1, characterized in that: The method further includes the steps of programming and designing the metamaterial unit cell so that it has a force platform with a longer displacement range, a larger effective load and / or multiple force platform segments to meet the energy absorption requirements under complex loads.

4. The design method according to claim 1, characterized in that: The method further includes the following steps: designing a multistable metamaterial with ideal energy absorption characteristics, including assembling the metamaterial unit cells with different force platforms in multiple layers based on the constructed metamaterial, and assembling the samples of each layer in a centrally symmetrical manner; the arrangement direction of the metamaterial unit cells is set to be consistent in each layer, and the layers are aligned up and down, and then bonded and fixed through a support plate located between the layers.

5. The design method according to claim 1, characterized in that: The geometry of the curved beam is given by the equation Indicates that represents the length of the curved beam, y represents the height direction of the curved beam, Indicates the length direction of the curved beam, and the height is determined by the parameter express.

6. The design method according to claim 1, characterized in that: The buckle structure and the optimized curved beam are assembled through functional components.

7. The design method according to claim 1, characterized in that: The metamaterial unit cell is made of a plastic non-metallic material or various types of metal materials.

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