A dual-material double-layer curved beam negative stiffness multi-stable energy-absorbing structure

Abstract

The application discloses a double-material double-layer curved-beam negative-stiffness multi-stable energy-absorbing structure and relates to the field of mechanical metamaterial printing technology. The multi-stable energy-absorbing structure can solve the problems of high peak force and low energy-absorbing efficiency of the existing negative-stiffness multi-stable metamaterial. The multi-stable energy-absorbing structure comprises a plurality of cells. Each cell comprises a first curved beam, a second curved beam, an upper horizontal support beam and a lower horizontal support beam. An intermediate connecting beam is arranged on the lower surface of the upper horizontal support beam. Two side connecting beams are arranged on the upper surface of the lower horizontal support beam. The middle part of the first curved beam is connected to the intermediate connecting beam, and the two ends of the first curved beam are connected to the side connecting beams. The second curved beam is located below the first curved beam and has the same bending direction as the first curved beam. The middle part of the second curved beam is connected to the intermediate connecting beam through a first fitting structure, and the two ends of the second curved beam are connected to the side connecting beams through a second fitting structure. The first curved beam is made of a hard material, and the second curved beam is made of a soft material. The application is used for improving the performance of the negative-stiffness multi-stable metamaterial.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of mechanical metamaterials, and particularly relates to a double-material double-layer curved beam negative stiffness multi-stable energy absorption structure. BACKGROUND

[0002] Mechanical metamaterials can exhibit unique physical properties beyond natural materials by designing their internal structures, and have important application values in the fields of biomedicine, aerospace, marine engineering and multifunctional intelligent structures. Negative stiffness multi-stable metamaterials are an important branch of mechanical metamaterials. Negative stiffness multi-stable superstructures have significant advantages in energy absorption and impact shock absorption. After being subjected to impact, the negative stiffness multi-stable material can maintain the deformed shape even without external load, and store energy in the structure through elastic deformation, thereby effectively avoiding or reducing secondary damage and providing excellent cushioning performance.

[0003] With the progress of science and technology, the safety of ships under extreme loads and complex environments faces higher requirements. Under the action of impact, negative stiffness multi-stable metamaterials undergo layer-by-layer buckling within the elastic range, efficiently absorb energy through elastic deformation of the structure, and are particularly suitable for the impact resistance requirements of ships in extreme environments such as deep sea and polar ice regions. In addition, negative stiffness multi-stable metamaterials are also widely used in protective packaging of precision components, aerospace engineering, vehicle engineering and other fields. However, the existing negative stiffness multi-stable energy absorption materials have the problems of high peak force and low energy absorption efficiency. SUMMARY

[0004] Embodiments of the application provide a double-material double-layer curved beam negative stiffness multi-stable energy absorption structure, which solves the problems of high peak force and low energy absorption efficiency of the existing negative stiffness multi-stable metamaterials.

[0005] To achieve the above-mentioned purpose, the embodiments of the application provide a double-material double-layer curved beam negative stiffness multi-stable energy absorption structure, which comprises a plurality of unit cells; the unit cell comprises a first curved beam, a second curved beam, an upper horizontal support beam and a lower horizontal support beam; the upper horizontal support beam is provided with an intermediate connecting beam on the lower surface thereof; the lower horizontal support beam is provided with two side connecting beams on the upper surface thereof; the first curved beam is connected to the intermediate connecting beam at the middle portion thereof and connected to the side connecting beams at the two ends thereof; the second curved beam is located below the first curved beam and has the same bending direction as the first curved beam, the middle portion of the second curved beam is connected to the intermediate connecting beam through a first fitting structure, and the two ends of the second curved beam are connected to the side connecting beams through a second fitting structure; the first curved beam is made of hard material, and the second curved beam is made of soft material.

[0006] Furthermore, the number of the cells is eight; the eight cells are arranged in four layers; the setting directions of the cells in two adjacent layers are opposite, and the first curved beam and the second curved beam in the cells in the top layer are both bent downward; the first curved beam and the second curved beam in the cells in the bottom layer are both bent upward.

[0007] Furthermore, the horizontal projection lengths of the first curved beam and the second curved beam are equal, and the cross-sectional thickness and vertical height of the second curved beam are both greater than those of the first curved beam.

[0008] Furthermore, the geometric shape of the first curved beam in its natural state satisfies the functional relationship Wherein, w1 is the coordinate variable of the first curved beam along the height direction; h1 is the height of the first curved beam; l is the horizontal projection length of the first curved beam or the second curved beam; x1 is the coordinate variable of the first curved beam along the length direction;

[0009] The geometric shape of the second curved beam in its natural state satisfies the functional relationship Among them, w2 is the coordinate variable of the second curved beam along the height direction; h2 is the height of the second curved beam; x2 is the coordinate variable of the second curved beam along the length direction.

[0010] Furthermore, the first curved beam, the middle connecting beam, the side connecting beam, the upper horizontal support beam and the lower horizontal support beam are all made of nylon or polylactic acid.

[0011] Furthermore, the second curved beam is made of thermoplastic polyurethane.

[0012] Furthermore, the first engaging structure includes a first groove and a first engaging portion adapted to the first groove; the first groove is provided on the lower surface of the middle connecting beam; and the first engaging portion is provided on the upper surface of the second curved beam.

[0013] Furthermore, the second engaging structure includes a second groove and a second engaging portion adapted to the second groove; the second groove is provided on the side surface of the side connecting beam; and the second engaging portion is provided on the end surface of the second curved beam.

[0014] Furthermore, the upper horizontal support beam and the lower horizontal support beam have the same structure; the middle connecting beam and the side connecting beam have the same structure; the first curved beam, the upper horizontal support beam, the lower horizontal support beam, the middle connecting beam and the side connecting beam are integrally formed.

[0015] Furthermore, when the ratio of the height to the thickness of the first curved beam Q1 ≥ 5 and the ratio of the height to the thickness of the second curved beam Q2 ≤ 2.31, the force-displacement curve of the cell during the buckling process includes three segments, where the force F1 in the first segment satisfies the formula:

[0016]

[0017] Wherein, h1 is the height of the first curved beam; t1 is the thickness of the first curved beam; E1 is the elastic modulus of the first curved beam; I1 is the moment of inertia of the cross section of the first curved beam; l is the horizontal projection length of the first curved beam or the second curved beam; d is the displacement during the buckling process; h2 is the height of the second curved beam; t2 is the thickness of the second curved beam; E2 is the elastic modulus of the second curved beam; I2 is the moment of inertia of the cross section of the second curved beam;

[0018] The force F2 in the second paragraph satisfies the formula:

[0019]

[0020] The force F3 in the third paragraph satisfies the formula:

[0021]

[0022] Compared with the prior art, this application has the following beneficial effects:

[0023] 1. The dual-material double-layer curved beam negative stiffness multi-stable energy absorption structure of the embodiment of the present application utilizes the difference in the buckling position of curved beams of different thicknesses and heights to make the peak forces of the first curved beam and the second curved beam appear at different displacement stages, and uses hard materials and soft materials to construct the two curved beams of the cell respectively, thereby effectively reducing the peak force of the structure and improving the energy absorption efficiency per unit volume, while realizing bistable characteristics.

[0024] 2. The double-material double-layer curved beam negative stiffness multi-stable energy-absorbing structure of the embodiment of the present application obtains the force-displacement relationship expression during the cell buckling process through theoretical derivation, verifies its mechanical properties, and significantly improves the structural design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0026] Figure 1 This is a schematic diagram of the three-dimensional structure of the double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to an embodiment of the present application;

[0027] Figure 2 This is a front view of a double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to an embodiment of the present application;

[0028] Figure 3 This is a cell model and its decomposition diagram in the double-material double-layer curved beam negative stiffness multi-stable energy absorption structure of the embodiment of the present application;

[0029] Figure 4 This is a deformation diagram of a cell in the double-material double-layer curved beam negative stiffness multistable energy-absorbing structure according to an embodiment of the present application when it is compressed;

[0030] Figure 5 This is a theoretical graph showing the superposition of force-displacement curves of the first curved beam and the second curved beam in the dual-material, double-layer curved beam negative stiffness multi-stable energy-absorbing structure according to an embodiment of the present application;

[0031] Figure 6 This is a comparison diagram of the force-displacement curves of the double-material double-layer curved beam negative stiffness multi-stable energy absorption structure and the double-layer 1mm nylon curved beam in the embodiment of the present application;

[0032] Figure 7 This is a comparison chart of the unit volume energy absorption curves of the double-material double-layer curved beam negative stiffness multi-stable energy absorption structure and the double-layer 1mm nylon curved beam in the embodiment of the present application. DETAILED DESCRIPTION

[0033] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0034] In the description of this application, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0035] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "install", "connect", and "connect" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection. For ordinary technicians in this field, they can understand the specific meanings of the above terms in this application according to specific circumstances.

[0036] The terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, features qualified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of this application, unless otherwise specified, "plurality" means two or more.

[0037] Reference Figures 1 to 4 The embodiment of the present application provides a dual-material, dual-layer curved beam negative stiffness multi-stable energy absorption structure, comprising eight cells 9 arranged in four layers. Each cell 9 includes a first curved beam 1, a second curved beam 2, an upper horizontal support beam 3, a lower horizontal support beam 4, a middle connecting beam 5, and two side connecting beams 6.

[0038] The middle connecting beam 5 is connected to the middle portion of the lower surface of the upper horizontal support beam 3 , and the two side connecting beams 6 are connected to the left and right ends of the upper surface of the lower horizontal support beam 4 .

[0039] The middle of the first curved beam 1 is connected to the middle connecting beam 5, and its ends are connected to the side connecting beams 6. The second curved beam 2 is located below the first curved beam 1 and has the same curvature direction as the first curved beam 1. The middle of the second curved beam 2 is connected to the middle connecting beam 5 via a first interlocking structure 7, and its ends are connected to the side connecting beams 6 via a second interlocking structure 8.

[0040] The cells 9 of two adjacent layers are arranged facing each other or facing away from each other, that is, the first curved beams 1 and second curved beams 2 in the cells 9 of the two adjacent layers are bent in opposite directions. Specifically, the first curved beams 1 and second curved beams 2 in the cells 9 of the top layer and the third layer from the top are bent downward, while the first curved beams 1 and second curved beams 2 in the cells 9 of the second layer and the bottom layer are bent upward. This improves energy absorption per unit volume and provides good buffering protection.

[0041] The height of the first curved beam 1 is h1=6mm, and the thickness is t1=1mm; the height of the second curved beam 2 is h2=5mm, and the thickness is t2=2.6mm; the horizontal projection length of the first curved beam 1 and the second curved beam 2 is l=85mm, and the out-of-plane thickness is b=20mm.

[0042] Substitute h1=6mm, l=85mm into the functional relationship The geometric shape function relationship of the first curved beam 1 in the embodiment of the present application can be obtained as follows: Wherein, w1 is the coordinate variable of the first curved beam along the height direction, and x1 is the coordinate variable of the first curved beam 1 along the length direction.

[0043] Then substitute h2=5mm and l=85mm into the functional relationship The geometric shape function relationship of the second curved beam 2 in the embodiment of the present application can be obtained as follows: Wherein, w2 is the coordinate variable of the second curved beam along the height direction, and x2 is the coordinate variable of the second curved beam 1 along the length direction.

[0044] The first curved beam 1, the middle connecting beam 5, the two side connecting beams 6, the upper horizontal support beam 3, and the lower horizontal support beam 4 are all made of nylon (PA) or polylactic acid (PLA) with an elastic modulus of 1000 MPa and a Poisson's ratio of 0.3. The first curved beam 1, the middle connecting beam 5, the two side connecting beams 6, the upper horizontal support beam 3, and the lower horizontal support beam 4 are integrally machined.

[0045] The second curved beam 2 is interlocked with the middle connecting beam 5 via a first interlocking structure 7. The second curved beam 2 is interlocked with the side connecting beam 6 via a second interlocking structure 8. The second curved beam 2 is made of thermoplastic polyurethane (TPU) with an elastic modulus of 80 MPa and a Poisson's ratio of 0.3.

[0046] The spacing between the first curved beam 1 and the second curved beam 2 is 4 mm at both ends and 3 mm in the middle. The middle connecting beam 5 and the side connecting beams 6 are both 11.5 mm long and 6 mm wide. The upper horizontal support beam 3 and the lower horizontal support beam 4 are both 85 mm long and 6 mm wide.

[0047] The first interlocking structure 7 includes a first groove 71 and a first interlocking portion 72 that fits with the first groove 71. The first groove 71 is provided on the lower surface of the middle connecting beam 5, and the first interlocking portion 72 is provided on the upper surface of the second curved beam 2. The second interlocking structure 8 includes a second groove 81 and a second interlocking portion 82 that fits with the second groove 81. The second groove 81 is provided on the inner surface of the side connecting beam 6, and the second interlocking portion 82 is provided on the end surface of the second curved beam 2. Both the first groove 71 and the second groove 81 are T-shaped grooves.

[0048] Reference Figure 3 When preparing the energy-absorbing structure, first prepare the integrated part consisting of the first curved beam 1, the middle connecting beam 5, the two side connecting beams 6, the upper horizontal support beam 3 and the lower horizontal support beam 4, and the second curved beam 2 respectively, and then embed the second curved beam 2.

[0049] Figure 4 A diagram showing the deformation of cell 9 in the energy-absorbing structure of an embodiment of the present application under compression shows that, when cell 9 is subjected to external compressive force, the peak forces of the first and second curved beams 1 and 2 occur at different stages of displacement due to the different thicknesses and heights, and therefore the difference in their buckling positions. Furthermore, the different materials of the two curved beams effectively reduce the peak force of the energy-absorbing structure, improve the energy absorption efficiency per unit volume, and achieve bistable properties.

[0050] When the ratio of the height to the thickness of the first curved beam 1 is The ratio of the height to the thickness of the second curved beam 2 When , the force-displacement curve of cell 9 during the buckling process includes three segments. The force F1 in the first segment satisfies the formula:

[0051]

[0052] Wherein, h1 is the height of the first curved beam 1; t1 is the thickness of the first curved beam 1; E1 is the elastic modulus of the first curved beam 1; I1 is the moment of inertia of the cross section of the first curved beam 1; l is the horizontal projection length of the first curved beam 1 or the second curved beam 2; d is the displacement during the buckling process; h2 is the height of the second curved beam 2; t2 is the thickness of the second curved beam 2; E2 is the elastic modulus of the second curved beam 2; I2 is the moment of inertia of the cross section of the second curved beam 2;

[0053] The force F2 in the second paragraph satisfies the formula:

[0054]

[0055] The force F3 in the third paragraph satisfies the formula:

[0056]

[0057] Set h1 = 6 mm, t1 = 1 mm, E1 = 1000 MPa, l=85mm, h2=5mm, t2=2.6mm; E2=80MPa, Substituting the above three formulas, we can obtain the three-segment force-displacement curves of the cell 9 during the buckling process in the embodiment of the present application:

[0058] F1=0.082d 3 -1.484d 2 +14.740dd∈(0,1.17)

[0059] F2=0.082d 3 -1.484d 2 +4.970d+11.416d∈(1.17,9.20)

[0060] F3=0.082d 3 -1.484d 2 +17.016d+99.393d∈(9.20,10.13)

[0061] like Figure 5 As shown in the figure, the force-displacement curve of the compression deformation of cell 9 shows that the structural load presents a gentle change area near the peak value, and then the load gradually decreases. There is a negative stiffness area, and the minimum value of the curve is below zero, which has obvious bistability characteristics.

[0062] Comparison of mechanical properties between a double-material double-layer curved beam negative stiffness multi-stable energy-absorbing structure and a single-material negative stiffness multi-stable structure Figure 6 、 Figure 7 shown.

[0063] Depend on Figure 6 and Figure 7 The results show that the two-layer cellular structure composed of 1mm nylon (PA) and 2.6mm thermoplastic polyurethane (TPU) reduces peak force by 14.78% and increases energy absorption per unit volume by 25.4% compared to the two-layer 1mm nylon (PA) cellular structure. The optimized structure reduces peak force while increasing energy absorption per unit volume. After impact, it can maintain a stable deformed state without external forces. Energy stored in the structure through elastic deformation effectively avoids or reduces secondary damage, providing excellent cushioning and protection.

[0064] The above are only specific embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or replacements within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A double-material double-layer curved beam negative stiffness multi-stable energy absorption structure, characterized in that: The invention comprises a plurality of cells, wherein the cells comprise a first curved beam, a second curved beam, an upper horizontal support beam, and a lower horizontal support beam; an intermediate connecting beam is provided on the lower surface of the upper horizontal support beam; two side connecting beams are provided on the upper surface of the lower horizontal support beam; the middle portion of the first curved beam is connected to the intermediate connecting beam, and the two ends are connected to the side connecting beams; the second curved beam is located below the first curved beam and has the same bending direction as the first curved beam; the middle portion of the second curved beam is connected to the intermediate connecting beam via a first interlocking structure, and the two ends are connected to the side connecting beams via a second interlocking structure; the first curved beam is made of a hard material, and the second curved beam is made of a soft material; The number of cells is eight; the eight cells are arranged in four layers; the cells in two adjacent layers are arranged in opposite directions, and the first curved beam and the second curved beam in the cells in the top layer are both curved downward; the first curved beam and the second curved beam in the cells in the bottom layer are both curved upward; The horizontal projection lengths of the first curved beam and the second curved beam are equal, and the cross-sectional thickness and vertical height of the second curved beam are both greater than those of the first curved beam; The geometric shape of the first curved beam in its natural state satisfies the functional relationship ,in, w 1 is the coordinate variable of the first curved beam along the height direction; h 1 is the height of the first curved beam; l is the horizontal projection length of the first curved beam or the second curved beam; x 1 is the coordinate variable of the first curved beam along the length direction; The geometric shape of the second curved beam in its natural state satisfies the functional relationship ,in, w 2 is the coordinate variable of the second curved beam along the height direction; h 2 is the height of the second curved beam; x 2 is the coordinate variable of the second curved beam along the length direction.

2. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 1 is characterized in that: The first curved beam, the middle connecting beam, the side connecting beam, the upper horizontal support beam and the lower horizontal support beam are all made of nylon or polylactic acid, and the first curved beam, the upper horizontal support beam, the lower horizontal support beam, the middle connecting beam and the side connecting beam are integrally formed.

3. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 1, characterized in that: The second curved beam is made of thermoplastic polyurethane.

4. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 1, characterized in that: The first engaging structure includes a first groove and a first engaging portion adapted to the first groove; the first groove is opened on the lower surface of the middle connecting beam; and the first engaging portion is arranged on the upper surface of the second curved beam.

5. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 4, characterized in that: The second engaging structure includes a second groove and a second engaging portion adapted to the second groove; the second groove is opened on the side surface of the side connecting beam; and the second engaging portion is arranged on the end surface of the second curved beam.

6. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 5, characterized in that: The upper horizontal support beam and the lower horizontal support beam have the same structure; the middle connecting beam and the side connecting beam have the same structure.

7. The double-material double-layer curved beam negative stiffness multi-stable energy absorption structure according to claim 1, characterized in that: When the ratio of the height to the thickness of the first curved beam Q1 ≥ 5 and the ratio of the height to the thickness of the second curved beam Q2 ≤ 2.31, the force-displacement curve of the cell during the buckling process includes three segments, of which the force in the first segment is F 1 satisfies the formula: in, h 1 is the height of the first curved beam; t 1 is the thickness of the first curved beam; E 1 is the elastic modulus of the first curved beam; I 1 is the moment of inertia of the cross section of the first curved beam; l is the horizontal projection length of the first curved beam or the second curved beam; d is the displacement of the upper horizontal support beam of the cell during the buckling process; h 2 is the height of the second curved beam; t 2 is the thickness of the second curved beam; E 2 is the elastic modulus of the second curved beam; I 2 is the moment of inertia of the cross section of the second curved beam; The force in the second paragraph F 2 satisfies the formula: The force in the third paragraph F 3 satisfies the formula: 。

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