Design method of multistable metamaterial with ideal energy absorption characteristic

Abstract

The invention belongs to the field of computer aided design, and discloses a design method of a multistable metamaterial with an ideal energy absorption characteristic, which comprises the following steps of: firstly, carrying out theoretical analysis on a buckle to establish a mathematical model; then, according to the theoretical solution of the rigidity value of the buckle structure, reverse topological optimization design is carried out on the curved beam, so that a force displacement curve of the curved beam has negative rigidity and peak force corresponding to the buckle. The buckle structure and the optimized and customized curved beam are assembled through the functional part, and the multistable metamaterial unit cell with the ideal energy absorption characteristic can be obtained. And programming design is carried out on the unit cells, so that the required metamaterial can be constructed to meet the energy absorption requirement under the complex load. The technical scheme is widely applicable to the fields of aerospace, automobile industry, building protection and the like, and excessive rebound of impact energy is avoided while the impact resistance of equipment is improved.

Description

Technical Field

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

[0002] Impact loads are extremely common in industrial production and daily life, and often cause irreversible damage to the accuracy, operating life and safety of instruments. Considering the urgent need for safety, research and development of structures that can resist impact have become a focus, especially in the protection of precision instruments and key equipment. Traditional energy-absorbing structures, such as tubular structures, composite structures, honeycomb structures, foam structures and flat structures, have been deeply explored in previous studies, but their performance still needs to be optimized. In order to make up for the shortcomings of traditional designs, researchers and engineers have begun to develop a variety of advanced structures including metamaterials. Energy-absorbing metamaterials / metastructures usually exhibit significant nonlinear behavior based on their cleverly designed microstructure composition, which gives them unique advantages in energy absorption and buffering. A common type of energy-absorbing metamaterial is a multistable metamaterial with negative stiffness characteristics, which is usually achieved by a preset structural deformation mode, such as the buckling of a flexible rod or shell, and the sliding of a buckle. These designs make the multistable metamaterial intentionally "collapse" or "deform" when it is impacted or compressed, rather than tightening or resisting, thereby achieving effective absorption and buffering of impact energy during steady-state transition. However, the ideal force-displacement curve of the energy-absorbing metamaterial should be rectangular and have a wide and gentle force platform. This allows it to maintain a relatively constant stress level during deformation, which not only helps to improve energy absorption efficiency, but also provides effective buffering under impact loads and reduces the impact force transmitted to the protected object.

[0003] By setting a specific stress-strain curve as a target and optimizing the material distribution for inverse design, the custom design of an ideal energy-absorbing metamaterial can be achieved (Inverse Design of Energy-absorbing Metamaterials by Topology Optimization, Advanced Science, 10 (2023) 1–10). However, the permanent plastic deformation caused by nonlinear behavior makes the metamaterial damaged after impact and difficult to reuse. Moreover, compared with multi-stable metamaterials, although the force platform characteristics of energy-absorbing metamaterials improve the energy absorption efficiency, they do not have the steady-state conversion capability to control energy rebound, resulting in the impact energy being released. The release may cause a secondary impact. Therefore, the ideal energy-absorbing material should not only have a force platform, but also have a bistable characteristic to lock the absorbed energy and prevent the occurrence of secondary collisions.

[0004] The Chinese invention patent application with publication number CN118070625A discloses a crash resistance design method for a high-speed train imitation bamboo anti-climbing energy absorption device. Inspired by the characteristics of bamboo, such as light weight and firmness, high specific energy absorption, and strong bending and torsion resistance, the invention provides a high-speed train imitation bamboo anti-climbing energy absorption device and its crash resistance design method, in order to enhance the crash resistance and axial crushing stability of the anti-climbing energy absorption device and give full play to its energy dissipation capacity in a limited space. However, the structure often generates a large reaction force during the impact process, causing stress concentration or local damage to the protected object. Summary of the invention

[0005] The technical problem solved by the present invention is: in order to overcome the problem that traditional impact-resistant structures have limited energy absorption capacity and cannot control energy rebound, the present invention proposes a multi-stable metamaterial design method with ideal energy absorption capacity, which utilizes its nonlinear mechanical properties to achieve multi-level energy absorption and dissipation, can effectively mitigate the initial impact force, and maintain overall stability and integrity while significantly reducing the rebound energy.

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

[0007] A method for designing a multi-stable metamaterial with ideal energy absorption characteristics is disclosed. The method adopts a combination of customized curved beams and buckle structures to design, thereby giving the metamaterial rich programmability and enabling it to have flexible adjustment capabilities. When these metamaterials are compressed, the curved beam customized by topological optimization first provides an initial energy barrier and absorbs part of the energy. Then the buckle structure is gradually activated to ensure that the force displacement curve presents an ideal rectangle and locks the system state when the energy absorption is completed. The present 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 a steady-state conversion occurs. In addition, the impact resistance and protection capabilities of the designed metamaterial are confirmed by impact tests. This staged energy absorption mechanism not only effectively improves the energy absorption efficiency, but also avoids excessive rebound of impact energy by precisely controlling the deformation process of the metamaterial, ensuring the stability and controllability of the protected structure after the impact.

[0008] The proposed design method solves the integration problem of traditional energy-absorbing metamaterials in complex nonlinear mechanical behaviors, and provides new possibilities for developing efficient, stable and controllable energy-absorbing systems. Specifically, it includes the following steps:

[0009] S1: Design and theoretical analysis of the snap-fit ​​structure in the metamaterial unit cell: The snap-fit ​​structure consists of a vertical beam with a cantilever hook and a slide groove with an inclination, which are arranged symmetrically. Considering the assembly of the snap-fit ​​structure and the curved beam, a boss is set at the bottom of the snap-fit ​​structure with a length of Other known parameters include: the inclination angle of the chute ,high and the width of the bottom The thickness and height of the vertical beam are and In order to obtain the vertical force and vertical displacement The relationship between the vertical beam and the vertical beam is assumed to be a slender elastic beam with a fixed constraint at the bottom. When the chute can only move vertically, the vertical beam will bend due to the horizontal extrusion, and the friction will increase, making the overall reaction force linear. In order to facilitate the study of the mechanism of the buckle structure, one side of the buckle structure is taken and appropriately simplified for theoretical analysis. The theoretical model of the buckle structure is shown below:

[0010]

[0011] in, is Young's modulus. The mechanical behavior of the snap-fit ​​structure is mainly affected by the bending of the vertical beam. In other words, when analyzing the bending behavior of the snap-fit ​​structure, only the bending part of the vertical beam needs to be considered. Since adjusting the height, thickness or inclination of the vertical beam will have a great impact on the stiffness of the snap-fit ​​structure, these parameters can be adjusted according to needs.

[0012] S2: Customized design of curved beams in metamaterial unit cells: In the customized design process of curved beams, the curved beams are first projected horizontally, and then the material field of the curved beams for topological optimization is constructed through uniformly distributed observation points, that is, the presence or absence of materials is described. In order to reduce the number of design variables and speed up the solution, the material field is reduced in dimension using the series expansion strategy to construct the optimization design domain. Sample points are selected in the design domain using the Latin hypercube sampling method, and then the obtained sample points are subjected to finite element analysis to determine the distribution of the samples in the target space, and the Kriging proxy model is established to find the current optimal topological configuration. After completing a sub-optimization cycle, the design domain is gradually reduced according to the position of the current optimal sample point, and the new sub-optimization problem is solved. With the update and solution 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 value of the sampling point varies greatly in a single sub-optimization step, with the continuous update of the sub-optimization step, the design domain will gradually decrease, and the target value will tend to converge stably.

[0013] Furthermore, the geometry of the curved beam is given by the equation Indicates that the parameters 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.

[0014] S3: Design of metamaterial unit cell: Although both the curved / straight beam structure and the snap-in structure achieve a bistable design, they differ in their mechanical performance. 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 imply complementarity in the energy absorption process, which can be expanded into a multistable metamaterial with ideal energy absorption characteristics through combined design. By building the snap-in structure and the customized curved beam together with functional components, a rectangular force-displacement curve behavior can be achieved. This mechanism can be explained by the parallel connection of Hookean springs. In the parallel case, the deformation of the snap-in structure and the curved beam is equal to the external deformation, and the sum of their stiffness is equal to the total stiffness. Specifically, the snap-in structure exhibits positive stiffness during loading, and when a certain critical value is exceeded, the reaction force of the snap-in structure will suddenly jump to zero to achieve a steady-state transition. The customized curved beam will exhibit a negative stiffness that is exactly opposite to the stiffness of the snap-in structure after a short positive stiffness stage, and will be converted to positive stiffness again when the snap-in structure jumps, completing the steady-state transition. By coupling the snap-on structure and the customized curved beam through functional components, the force-displacement curve of the combined structure not only has an ideal rectangle for buffering and energy absorption, but also has a steady-state conversion capability for locking energy, which can be well applied in the field of impact resistance.

[0015] Furthermore, by assembling the snap-fit ​​structure with the optimized curved beam through functional components, namely connecting components, a rectangular force-displacement curve behavior can be achieved, which gives the designed unit cell ideal energy absorption characteristics and multi-stable characteristics to exhibit good impact resistance behavior.

[0016] Furthermore, since the structure and deformation of the curved beam are symmetrical, it is equivalently divided into two parts after customization. The snap-fit ​​structure is located in the middle of the unit cell, while the curved beam with symmetrical properties is located on both sides of the slide.

[0017] Furthermore, by programming the unit cell, it is possible to meet the energy absorption requirements under complex loads, such as a force platform with a longer displacement range, a larger payload, or multiple force platform segments.

[0018] S4: Finite element analysis of metamaterial unit cell: Based on the metamaterial unit cell constructed in S3, a finite element numerical simulation was performed. It is assumed that there are rigid plates on the upper and lower surfaces of the unit cell to represent the platen of the test machine, and the finite element nodes of the rigid plates are coupled to the reference point at its center through multi-point constraints for loading and observing the reaction force. A vertical downward displacement load is applied to the upper boundary, the lower boundary is fixed, and both sides are subject to sliding constraints, so that the unit cell is deformed. The finite element model of the unit cell is divided into more than three layers of mesh in the in-plane thickness direction to improve the simulation accuracy of the bending behavior.

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

[0020] Furthermore, the energy absorbing unit cell can be made of common plastics such as nylon or resin, or various types of metals, preferably nylon, because it has low manufacturing cost and can enhance design flexibility.

[0021] S6: Design of multi-stable metamaterials with ideal energy absorption characteristics: Based on the metamaterial unit cell constructed in step S3, the corresponding modular metamaterials can be formed through array strategies, and then the large metamaterials required for fastener construction can be improved to meet different application scenarios. The specific method is: use unit cells with different force platforms to assemble in multiple layers, and the samples of each layer are assembled in a centrally symmetrical 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 up and down, and then bonded and fixed through the support plate located between the layers. The ideal energy-absorbing multi-stable metamaterial designed in this way achieves flexible impact resistance. When the impact is lighter, a weaker energy absorption mechanism is triggered, and the impact acceleration generated is also smaller. When the impact is heavier, a stronger energy absorption mechanism is triggered, and the impact acceleration generated is also larger.

[0022] A multi-stable metamaterial with ideal energy absorption characteristics, obtained by the above design method, is a promising multi-level, impact-resistant solution. This type of metamaterial can not only show efficient energy absorption characteristics during collision, but also flexibly respond to different degrees of impact. For example, the energy absorption system used in automobiles can trigger a weaker energy absorption mechanism when colliding with pedestrians and a stronger energy absorption mechanism when colliding with walls, thereby improving the passive safety of vehicles.

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

[0024] The present invention can realize a rectangular force-displacement curve behavior with multi-stable characteristics by constructing the buckle structure and the customized curved beam together by functional components. This can not only provide multiple energy barriers, but also have good energy absorption efficiency, thereby achieving an ideal impact resistance effect. The mechanism can be explained by the parallel connection of Hooke springs. In the parallel case, the deformation of the buckle structure and the curved beam is equal to the external deformation, and the addition of their 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 achieve a steady-state conversion. The customized curved beam will present a negative stiffness that is exactly opposite to the stiffness of the buckle structure after a short positive stiffness stage, and will be converted to positive stiffness again when the buckle structure jumps, completing the steady-state conversion. The buckle structure and the customized curved beam are coupled into a unit cell through functional components, and the force-displacement curve of the unit cell not only has an ideal rectangle to buffer energy absorption, but also has a steady-state conversion capability to lock energy, which can be well applied in the field of impact resistance. Furthermore, the unit cell is designed into a metamaterial through programming, and the metamaterial can have a force platform with a longer displacement range, a larger payload, or multiple force platform segments, which can meet the energy absorption requirements under complex loads.

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

[0026] The present invention designs a multi-stable metamaterial with a rectangular force-displacement curve based on a snap-on structure and a customized curved beam. The rectangular force-displacement curve can achieve an ideal energy absorption capacity, and the multi-stable characteristics can achieve an energy locking mechanism. This is conducive to preventing excessive rebound of impact energy, so as to ensure the stability and controllability of the protected structure after the collision. The unit cells of these metamaterials are designed by combining the snap-on structure and the customized topological curved beam, thereby giving the metamaterial rich programmability and enabling it to have the ability to be flexibly adjusted. 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 snap-on structure is gradually activated to ensure that the force-displacement curve presents an ideal rectangle and locks the system state when the energy absorption is completed. In addition, by using 3D printing technology for integral casting, the present invention not only improves the energy absorption capacity of the metamaterial, but also maintains a low quality, which is of great significance for reducing the load of the overall system and improving energy efficiency. The present invention not only provides a theoretical innovative design, but also includes a set of experimental verification mechanisms to ensure the feasibility and effect of the design. This method of combining experiments with theories improves the scientificity and practicality of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flowchart of the implementation of the design method according to an embodiment of the present invention.

[0028] Figure 2a Shown are the design form and design parameters of the snap-in structure in the metamaterial unit cell.

[0029] Figure 2b Shown are the results of a theoretical analysis based on symmetry of half of the buckle structure.

[0030] Figure 2c Shown is the deformation state of the buckle structure under compression and its force analysis diagram.

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

[0032] Figure 3b Schematic diagram showing the use of a non-gradient topology optimization strategy to customize the material layout of a curved beam.

[0033] Figure 3c Shown is a schematic diagram of a customized curved beam that meets the objectives and constraints after multiple iterations.

[0034] Figure 4a Shown is a schematic diagram of a customized curved beam and snap-fit ​​structure in a metamaterial unit cell composed of a snap-fit ​​structure and a corresponding customized curved beam.

[0035] Figure 4b The figure shows the origin of the mechanical properties of the metamaterial unit cell: the rectangular force-displacement curve of the unit cell is formed by connecting the force-displacement curves of the snap-fit ​​structure and the customized curved beam in parallel according to Hooke's law.

[0036] Figure 4c Shown are the combination strategies of metamaterial unit cells (series, parallel, and series-parallel) and the force-displacement curves under different combinations.

[0037] Figure 5 The finite element model of the metamaterial unit cell designed according to an embodiment of the present invention.

[0038] Figure 6a The figure shows a three-dimensional CAD structure schematic diagram of a sample 1 unit cell used for an example of a metamaterial unit cell designed by the present invention and verification of mechanical properties.

[0039] Figure 6b Shown is a schematic diagram of the three-dimensional CAD structure of a sample 2 unit cell used for an example of a metamaterial unit cell designed by the present invention and verification of mechanical properties.

[0040] Figure 6c Shown are force-displacement curves of the finite element analysis and test of the sample 1 unit cell used for the example of the metamaterial unit cell designed by the present invention and verification of the mechanical properties, and a strain cloud diagram when the unit cell strain is maximum is given.

[0041] Figure 6dShown are force-displacement curves of the finite element analysis and test of the sample 2 unit cell used for the example of the metamaterial unit cell designed by the present invention and verification of the mechanical properties, and a strain cloud diagram when the unit cell strain is maximum is given.

[0042] Figure 7a Shown is the force-displacement curve of the metamaterial under the configuration of multi-stable metamaterial verification with ideal energy absorption characteristics, in which sample 1 and sample 2 are combined in parallel and then in series.

[0043] Figure 7b The figure shows the deformation state of the metamaterial verified by the multi-stable metamaterial with ideal energy absorption characteristics, which is combined by connecting sample 1 and sample 2 in parallel and then in series, under the compression test. DETAILED DESCRIPTION

[0044] The specific embodiments of the present invention are described in detail below in combination with the technical scheme and the accompanying drawings:

[0045] The present invention utilizes a snap-fit ​​structure and a customized curved beam to design a multi-stable metamaterial with ideal energy absorption characteristics through combination, and performs theoretical analysis, finite element simulation and experimental verification on it.

[0046] The principle implemented by the present invention is:

[0047] By means of the locking mechanism of the buckle structure and the energy absorption characteristics of the bistable structure, the present invention 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 the collision. This unique mechanical behavior comes from the combination of the buckle structure and the curved beam in the unit cell of the metamaterial. In the design process of the metamaterial, the buckle structure is first theoretically analyzed to establish a mathematical model. Then, the curved beam is reversely topologically optimized and designed according to the theoretical solution of the buckle structure stiffness value, so that its force-displacement curve has a negative stiffness and peak force corresponding to the buckle structure. The buckle structure is assembled with the optimized and customized curved beam through functional components, and a multistable metamaterial unit cell with ideal energy absorption characteristics can be obtained. The unit cell is then programmed and designed, and the required metamaterial can be constructed to meet the energy absorption requirements under complex loads. In addition, the present invention also includes a complete set of verification mechanisms, using finite element simulation and quasi-static compression experiments to conduct in-depth analysis of the energy absorption capacity, bistable characteristics and programmable characteristics of metamaterials. This technical solution is widely applicable to aerospace, automotive industry and building protection, and it can improve the impact resistance of equipment while avoiding excessive rebound of impact energy.

[0048] Figure 1Depicted is a flow chart for the implementation of the present invention, namely: designing a snap-fit ​​structure in a unit cell, customizing a curved beam in a unit cell through topological optimization, constructing a unit cell from the snap-fit ​​structure and the customized curved beam, finite element analysis of a metamaterial unit cell, experimental verification of a metamaterial unit cell, and designing a multistable metamaterial with ideal energy absorption characteristics.

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

[0050] S1: Design and theoretical analysis of snap-in structures in metamaterial unit cells.

[0051] The snap-on structure consists of a vertical beam with a cantilever hook and a chute with an angle, which are arranged symmetrically, such as Figure 2a Considering the assembly of the buckle structure and the curved beam, a boss is provided at the bottom of the buckle structure with a length of Other known parameters include: the inclination angle of the chute ,high and the width of the bottom The thickness and height of the vertical beam are and In order to obtain the vertical force and vertical displacement The relationship between the vertical beam and the vertical beam is assumed to be a slender elastic beam with a fixed constraint at the bottom. When the slide can only move vertically, the vertical beam will bend due to the horizontal compression, and the friction will increase, making the overall reaction force linear. In order to predict the stiffness of the buckle structure during the compression process, it is simplified and theoretically derived. Figure 2a The geometric parameters of the buckle structure are given in . Based on the symmetry of the buckle structure, one side of the buckle structure is taken for theoretical analysis, such as Figure 2b shown.

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

[0053]

[0054] in, is the bending moment of the vertical beam, is the Young's modulus inherent to the material, is the second moment of inertia of the vertical beam, Indicates the width of the vertical beam, that is, the width of the curved beam. is the deflection of the vertical beam. At the intersection of the chute and the vertical beam At the point where the chute is subjected to vertical force and the horizontal force due to the bending deformation of the vertical beam By solving the differential equation, the intersection point The relationship between the horizontal displacement and the horizontal force at is:

[0055]

[0056] It is assumed that the intersection of the inclined block and the vertical beam is located at the midpoint of the cantilever hook. For the convenience of calculation, the length of the vertical beam is simplified to .

[0057] Project the force on the chute to the normal of the inclined plane, and the normal force on the vertical beam is With friction It can be written as:

[0058]

[0059]

[0060] In the formula, is the friction factor between the chute and the vertical beam. By projecting the force on the chute onto the inclined plane, the friction force on the vertical beam can be expressed as:

[0061]

[0062] By combining equations (4) and (5), we can get the vertical force of the chute: for:

[0063]

[0064] Due to the vertical displacement of the chute With vertical beam The relationship between the horizontal displacement of

[0065]

[0066] Combining equations (2), (6) and (7), the vertical force of the vertical beam is It can be expressed as:

[0067]

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

[0069]

[0070] At this point, the stiffness of the buckle structure during compression can be predicted using the theoretical model of the buckle structure constructed using the above formulas (1) to (9).

[0071] S2: Customizing curved beams in metamaterial unit cells via topology optimization.

[0072] The goal of topology optimization of curved beams is to achieve the desired negative stiffness in the force-displacement curve. and peak force Therefore, the negative stiffness region in the curved beam force displacement curve is selected To define the required stiffness value, which is also target 1. Since the negative stiffness region has large fluctuations at both ends, the range of the region is reduced to By accurately calculating the slope changes between adjacent data in these areas, representative negative stiffness can be obtained. ,like Figure 3a As shown in the lower right corner. In this way, the goal of the present invention can be changed 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 of is also as small as possible, which is also goal 2. In addition, the minimum peak force of the constrained curved beam during loading , so that it is limited to a range less than 0 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 generated by the curved beam during loading is Constraints are also imposed. Based on this, the topology optimization listing of the curved beam for customization can be expressed as:

[0073]

[0074] In the formula, It is the sum of the negative stiffness error and the peak force error. In order to make them at the same order of magnitude, they are equivalent. is the penalty factor, which is an even number when selected to be close to the expected value. middle, The introduction of is to make the curved beam retain more obvious bistable characteristics. is the maximum strain allowed for the preparation material, Represents the topological layout of a material.

[0075] S3: Construction of metamaterial unit cells by snap-fit ​​structures and customized curved beams.

[0076] Although both the curved / straight beam structure and the snap-on structure achieve a bistable design, they differ in their mechanical performance. 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 imply complementarity in the energy absorption process, which can be expanded into a multi-stable metamaterial with ideal energy absorption characteristics through combined design. By building the snap-on structure and the customized curved beam together from functional components, a rectangular force-displacement curve behavior can be achieved. This mechanism can be explained by the parallel connection of Hooke springs, such as Figure 4b As shown. In the parallel case, the deformation of the buckle structure and the curved beam is equal to the external deformation, and the sum of their stiffness is equal 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 suddenly jump to zero to achieve a steady-state transition. The customized curved beam will exhibit a negative stiffness that is exactly opposite to the stiffness of the buckle structure after a short positive stiffness stage, and will be converted to positive stiffness again when the buckle structure jumps, completing the steady-state transition. The buckle structure and the customized curved beam are coupled through functional components, so that the force-displacement curve of the combined structure not only has an ideal rectangle to buffer energy absorption, but also has a steady-state conversion capability to lock energy, which can be well applied in the field of impact resistance.

[0077] When constructing a metamaterial unit cell, the present invention divides the curved beam into two parts after customization because its structure and deformation are symmetrical. 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 slide. The two are connected by functional components, such as Figure 4a As shown. In order to prevent the buckle structure from generating undesirable friction with the functional components, the width of the slide groove is made larger than the width of the vertical beam, which increases the space redundancy on the side of the buckle structure. It should be noted that the buckle structure, curved beam and functional components are manufactured using the same material using integrated 3D printing technology to ensure the integrity of the designed unit cell. Furthermore, by programming the unit cell, it is possible to meet the energy absorption requirements under complex loads, such as a force platform with a longer displacement range, a larger payload or multiple force platform segments, such as Figure 4c shown.

[0078] The geometry of the curved beam can be described by the equation Indicates that the parameters and They represent the length of the curved beam and the thickness of the cross section in the plane, 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.

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

[0080] Finite element numerical simulation was performed on the metamaterial unit cell constructed based on S3. It is assumed that there are rigid plates on the upper and lower surfaces of the unit cell to represent the pressure plate of the test machine, and the finite element nodes of the rigid plate are coupled to the reference point at its center through multi-point constraints for loading and observing the reaction force, such as Figure 5 As shown in Figure 1. A vertical downward displacement load is applied to the upper boundary, the lower boundary is fixed, and both sides are subject to sliding constraints, so that the unit cell is deformed. The finite element model of the unit cell is divided into more than three layers of mesh in the in-plane thickness direction to improve the simulation accuracy of the bending behavior.

[0081] In order to numerically simulate the metamaterial unit cell, the present invention uses commercial finite element software to perform finite element analysis on the unit cell. Specifically, the nylon material adopts a linear elastic model, and Young's modulus and Poisson's ratio are measured by tensile tests. The mechanical response of the unit cell is calculated using a general static analysis step to obtain a smooth force-displacement curve. Geometric nonlinearity is enabled to handle large deformations and very complex sliding friction that occur during the calculation process. The surfaces that come into contact during the loading process are all considered to have normal and tangential behaviors of face-to-face contact, wherein "hard" contact is used to define the normal behavior of the contact, and a "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 eight-node linear hexahedral units are used for meshing, and in order to accurately simulate the bending of the curved beam, at least four solid grids are generated along the thickness direction of the curved beam.

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

[0083] In order to verify the mechanical properties of the designed energy-absorbing unit cell, two designed unit cell samples were prepared, and their force platforms were (Sample 1) and (Sample 2). Their specific geometric parameters and expected peak forces are given in Table 1 and Figure 6a and 6b They were displayed separately. Figure 6c and Figure 6dThe force-displacement curves of samples 1 and 2 are compared with the experimental and finite element results. They are both ideal rectangles with bistable characteristics. When the sample is in compression, the curved beam is deformed first, and the reaction force shows an increasing trend. Then, when the curved beam enters the negative stiffness region (at point A), the buckle structure begins to deform and provide positive stiffness. At this time, the reaction force of the sample remains almost unchanged. As the loading progresses until the buckle structure is locked (at point B), the positive stiffness it provides disappears, the force-displacement curve jumps, and the stable state is converted. At this time, the reaction force is provided by the curved beam again. The maximum errors between the expected force platform and the experimentally measured force platform of samples 1 and 2 are 14.67% and 13.03%, respectively, and those measured by finite element analysis are 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 are slight differences between the experimental results and the finite element results. In general, the experimental results are in good agreement with the finite element analysis results, both showing 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 present invention.

[0084] Table 1 Geometric parameters of metamaterial unit cell

[0085] sample h(mm) l(mm) b(mm) t(mm) <![CDATA[h b (mm)]]> <![CDATA[h s (mm)]]> <![CDATA[l b (mm)]]> <![CDATA[t s (mm)]]> <![CDATA[t b (mm)]]> θ(°°) <![CDATA[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 of multistable metamaterials with desirable energy absorption properties.

[0087] The present invention can design a multistable metamaterial with ideal energy absorption characteristics by stacking energy absorption units with force platforms. In order to demonstrate the effectiveness of this design strategy, sample 1 and sample 2 are combined in parallel and then in series to explore their responses under complex combinations, such as Figure 7a The results show that this hybrid configuration can not only achieve the regulation of the force platform in the force-displacement curve, but also provide enhanced load bearing capacity and maintain a large force platform. In addition, Figure 7b Shows Figure 7a Four typical deformation states of the assembly shown in Figure 7a The positions of these four states are marked in the figure. The first two marks correspond to the starting point and end point of the first force platform (also the point where the first sudden jump occurs), and the last two marks correspond to the starting point and end point of the second force platform (also the point where the first sudden jump occurs). It can be found through observation that when the parallel sample layer corresponding to one of the force platforms is deformed, the parallel sample layer corresponding to the other force platform will hardly deform. This is because the difference in force platforms provides a force barrier for sample deformation, thereby realizing the adjustable energy absorption and energy locking of the metamaterial, which ensures the metamaterial's flexible response capabilities under complex impact loads.

[0088] The essence of the present invention is to design a multi-stable metamaterial with ideal energy absorption capacity by means of a snap-on structure and a customized curved beam through a parallel mechanism, thereby realizing a phased energy absorption mechanism, avoiding excessive rebound of impact energy, and ensuring the stability and controllability of the metamaterial after energy absorption. These metamaterials composed of unit cells also have rich programmability and the ability to be flexibly adjusted, enabling them to demonstrate superior adaptability and effects 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, and therefore can be achieved through different 3D printing materials. The proposed metamaterial design strategy solves the problem of integrating traditional energy-absorbing metamaterials in complex nonlinear mechanical behaviors, and provides new possibilities for the development of efficient, stable and controllable energy absorption systems.

[0089] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for designing a multi-stable metamaterial with ideal energy absorption characteristics, characterized in that: The method comprises constructing a metamaterial unit cell of the multistable metamaterial by a snap-fit ​​structure and a curved beam, and comprising: The buckle structure is theoretically analyzed to explore the parameters affecting the positive stiffness of the buckle structure during loading; Performing reverse topological optimization on the curved beam to customize the design according to 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; The force platform of the metamaterial unit cell is constructed by assembling the snap-fit ​​structure with the optimized curved beam, and then the multistable metamaterial with ideal energy absorption characteristics is designed; wherein the multistable 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 the collision.

2. The design method according to claim 1, characterized in that: The method comprises the following steps: configuring the buckle structure in the metamaterial unit cell so that the buckle structure is composed of a vertical beam with a cantilever hook and a slide groove with an inclination, wherein the vertical beam and the slide groove are symmetrically arranged; and providing a boss at the bottom end of the buckle structure.

3. The design method according to claim 1, characterized in that: The method further comprises the steps of: shaping the curved beam in the metamaterial unit cell as follows: selecting a negative stiffness region in the curved beam force displacement curve To define the required stiffness value, the negative stiffness region is reduced to By accurately calculating the slope changes between adjacent data in these areas, 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 , setting the maximum peak force of the curved beam and The error should be as small as possible.

4. The design method according to claim 3, 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.

5. The design method according to claim 1, characterized in that: in, The curved beam is equivalently divided into two parts; the buckle 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; the width of the slide is greater than the width of the vertical beam.

6. The design method according to claim 1, characterized in that: The method further comprises 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.

7. The design method according to claim 1, characterized in that: The method further includes the steps of: designing a multi-stable 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.

8. 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, x represents the length direction of the curved beam, and the height is determined by the parameter express.

9. The design method according to claim 1, characterized in that: The buckle structure is assembled with the optimized curved beam through functional components.

10. The design method according to claim 2, characterized in that: The preparation material of the metamaterial unit cell is a plastic non-metallic material or various types of metal materials.

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