Arc-connected three-dimensional negative Poisson mechanical metamaterial structure and design method

Abstract

The invention discloses an arc-connected three-dimensional negative Poisson mechanical metamaterial structure and a design method, and relates to the field of metamaterials, the arc-connected three-dimensional negative Poisson mechanical metamaterial structure comprises a plurality of unit cells which are periodically arrayed in the three-dimensional direction, and each unit cell is of a regular hexahedron structure and comprises an upper square plate and a lower square plate with four corners connected; two corners of each square plate are connected; the opposite square plates are parallel to each other, and the adjacent square plates are perpendicular to each other; 8 pairs of double-arc connecting ribs, wherein each pair of connecting ribs is composed of two sections of arcs; the square plates on the side faces are connected with the upper square plate and the lower square plate through double-arc connecting ribs, and each arc is tangent to the boundary at the connecting boundary of the arc and the square plate. When the unit cells are pressed in one direction, contraction perpendicular to the pressed direction is achieved through bending of the arc connecting ribs, rotation of the square plates around the shaft and smooth transition at the boundary, so that the negative Poisson's ratio characteristic is achieved, the service life of the structure can be prolonged, and the reliability of the structure can be improved.

Description

Technical Field

[0001] This invention relates to the field of metamaterials technology, and in particular to a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections and its design method. Background Technology

[0002] Metamaterials are a class of emerging materials that have garnered widespread attention since the 21st century. With their ability to overcome the limitations of traditional materials, powerful mechanical, optical, and acoustic control functions, advancements in advanced manufacturing technologies, tunability, and intelligent trends, they are driving transformations in multiple cutting-edge scientific fields. As a type of material not produced naturally, the properties of metamaterials stem from their structure, not their chemical composition. Researchers can design and modify the internal microstructure and repeating units of materials to obtain unconventional mechanical properties such as negative Poisson's ratio, negative compressibility, and negative stiffness. Among these, mechanical metamaterials with negative Poisson's ratios have found wide application in engineering due to their excellent fracture resistance, indentation resistance, sound absorption, and impact resistance.

[0003] Based on the different spatial levels of the structure used to construct mechanical metamaterials, they can be divided into two-dimensional (2D) and three-dimensional (3D) mechanical metamaterials. 3D mechanical metamaterials have a wider range of applications than 2D ones, but their structures are also more complex. Existing methods for constructing 3D mechanical metamaterials mainly extend from 2D to 3D, often based on linear units. This results in sharp corners at connections, stress concentration during deformation, and unstable deformation modes. Research on mechanical metamaterials constructed directly from 3D structures is relatively limited. Currently, most methods employ mechanism-based mechanical metamaterials with rigid components, which suffer from structural complexity, manufacturing difficulties, and friction-induced asynchronous motion in kinematic pairs. Summary of the Invention

[0004] To address the aforementioned challenges, this invention provides a three-dimensional negative Poisson ratio mechanical metamaterial structure and design method with circular arc connections. Based on the motion principle of a developable hexahedron, it retains the square panel of the developable hexahedron and its geometric relationships. The design method of a three-dimensional negative Poisson ratio mechanical metamaterial structure using two circular arc connections tangent to the cell boundary can achieve a smooth transition at the boundary.

[0005] To achieve the above objectives, this invention provides a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections, composed of a periodic array of multiple unit cells in a three-dimensional direction, wherein the unit cells are of a regular hexahedral configuration and include: Two square panels connected at the four corners; The side consists of four square panels connected at two corners; opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Eight pairs of double-arc connecting ribs, each pair of connecting ribs consisting of two arc segments; The square panels on the side are connected to the square panels on the top and bottom by double arc connecting ribs, and each arc is tangent to the boundary at its connection with the square panel. When a unit cell is compressed in one direction, it achieves contraction perpendicular to the direction of compression through the bending of the circular connecting ribs and the rotation of each square plate around the axis, thus exhibiting a negative Poisson's ratio characteristic.

[0006] Preferably, the cross-section of the arc connecting rib is square, and its side length is the same as the thickness of the square plate.

[0007] Preferably, the boundary dimensions of the hexahedron are: L The side length of the square board is The opposite square plate has a corner of 1. θ It satisfies the following relationship: .

[0008] Preferably, the arc-shaped connecting rib includes a radius of... R 1 and R 2 An arc of radius ∈ R satisfies the following relationship: ; .

[0009] Preferably, the central angles of the four arc segments of the eight pairs of double-arc connecting ribs on the upper and lower square plates are equal, and they are arranged in a swastika shape when viewed from the normal direction of the upper and lower square plates.

[0010] Preferably, the plurality of unit cells include a first unit cell and a second unit cell, wherein the second unit cell is a mirror image of the first unit cell, the top surface of the first unit cell is arranged in a swastika pattern, and the top surface of the second unit cell is arranged in a swastika pattern.

[0011] Preferably, the first unit cell and the second unit cell are in x and y Along the direction x direction and y The orientations are alternately spaced, and adjacent first and second unit cells share a square side plate for connection; in z Along the axial direction, multi-layer unit cell structures are stacked sequentially, with the bottom plate of the upper unit cell coinciding with the top plate of the lower unit cell.

[0012] Preferably, the initial design parameters are: boundary dimensions L =30mm, side length of square board =12.0203mm, radius of the circular arc. R 1 = 3.7151mm, radius of the circular arc.R 2 = 5.3816mm, relative to the corner of the square plate θ =45 ° .

[0013] A design method for a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections includes the following steps: S1: Determine the geometric design parameters of the unit cell, including: outer boundary dimensions. L The side length of the square plate Initial rotation angle relative to the square plate θ Radius of the double-arc connecting rib R 1 and R 2 and plate thickness t ; S2: Establish a finite element model and optimize and adjust the design parameters based on the target Poisson's ratio requirement; S3: Based on the optimized design parameters, construct the geometric model of the unit cell in three-dimensional space, specifically including: establishing two parallel blocks with side lengths of... The square plates serve as the top and bottom plates, and their positions are based on... L and θ Confirm; establish four blocks with side lengths of Square panels serve as side panels, connecting the top and bottom panels. Opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Double arc connecting ribs are constructed between adjacent square panels. The double arc is composed of two tangent arcs, and each arc is tangent to the boundary at its connection with the square panel. S4: The geometric model of the unit cell is arranged in a three-dimensional periodic array to construct a multi-cell structure. Specifically, this includes: mirroring the unit cell to obtain a unit cell with the opposite rotation direction; arranging the two types of unit cells alternately in the horizontal plane, and making adjacent unit cells share a square side plate to form a single-layer array structure; stacking the single-layer array structure in the vertical direction so that the bottom plate of the upper layer unit cell coincides with the top plate of the lower layer unit cell to obtain a three-dimensional multi-cell structure model.

[0014] Preferably, the single-layer array structure in S4 is a 4×4 array, and the number of layers in the stacked array is 4, thus forming a 4×4×4 multi-cell structure.

[0015] Therefore, the present invention employs the above-mentioned three-dimensional negative Poisson mechanical metamaterial structure and design method with circular arc connection, which has the following beneficial effects: (1) The present invention is composed of multiple unit cells arranged in a periodic array in three dimensions. The unit cell is a regular hexahedral configuration. The unit cell includes: two square plates connected at the top and bottom corners, four square plates connected at the sides corners, and eight pairs of double circular arc connecting ribs. It aims to solve the problems of sharp corners at the connection of the negative Poisson's ratio structure that extends from two dimensions to three dimensions, stress concentration and unstable deformation mode during deformation, as well as the problems of complex structure, difficult processing and manufacturing, and asynchronous motion caused by friction of kinematic pairs in the mechanical metamaterials directly constructed from three dimensions.

[0016] (2) The present invention provides a design method for a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection, which can achieve an adjustable negative Poisson ratio within a certain range by adjusting the design parameters.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a three-dimensional schematic diagram of a single cell in an embodiment of the present invention; Figure 2 This is a schematic diagram of a single-cell plane in an embodiment of the present invention; Figure 3 This is a schematic diagram of the relative corners of the square plate in an embodiment of the present invention; Figure 4 This is a schematic diagram of a single-cell structure in an embodiment of the present invention; Figure 5 This is a schematic diagram of unit cell deformation in an embodiment of the present invention; wherein, (a) is a top view of unit cell deformation, and (b) is a front view of unit cell deformation; Figure 6 This is a schematic diagram of a single-layer 4×4 structure in an embodiment of the present invention; Figure 7 This is a single-layer 4×4 top view in an embodiment of the present invention; Figure 8 This is a schematic diagram of a multicellular structure in an embodiment of the present invention. Detailed Implementation

[0019] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0021] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0022] Example A three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections, such as Figures 1-4 As shown, it is composed of a periodic array of multiple unit cells in three dimensions, wherein the unit cells are of a regular hexahedral configuration and include: Two square panels connected at the four corners; The side consists of four square panels connected at two corners; opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Eight pairs of double-arc connecting ribs, each pair of connecting ribs consisting of two arc segments; The square panels on the side are connected to the square panels on the top and bottom by double arc connecting ribs, and each arc is tangent to the boundary at its connection with the square panel. When a unit cell is compressed in one direction, it achieves contraction perpendicular to the direction of compression through the bending of the circular connecting ribs and the rotation of each square plate around the axis, thus exhibiting a negative Poisson's ratio characteristic.

[0023] The cross-section of the arc connecting rib is square, and its side length is the same as the thickness of the square plate.

[0024] Based on the principles of motion of the developable hexahedron, retaining the square panel and its geometric relationships, we divide it into three pairs that revolve around... x axis, y shaft and z The plates that rotate relative to each other are connected by two circular arcs. z The sum of the four corner points of two square plates perpendicular to the axis z Two square plates with parallel axes along zTwo corner points along the axial direction ensure that the two arc segments are tangent to the cell boundary, achieving a smooth transition at the boundary. This structure has boundary dimensions. L , side length of square board The radius of the circular arc R 1 , R 2 Corner of relative square board θ ,thickness t These design parameters, with boundary dimensions of... L The side length of the square board is The opposite square plate has a corner of 1. θ It satisfies the following relationship: .

[0025] The four arcs of the eight pairs of double-arc connecting ribs on the upper and lower square plates have equal central angles and are arranged in a swastika shape when viewed from the normal direction of the upper and lower square plates.

[0026] The circular arc connecting rib includes a radius of R 1 and R 2 An arc of radius ∈ R satisfies the following relationship: ; .

[0027] Multiple units include a first unit and a second unit. The second unit is a mirror image of the first unit. The top surface of the first unit is arranged in a swastika pattern, and the top surface of the second unit is also arranged in a swastika pattern.

[0028] The first and second cells are in x and y Along the direction x direction and y The orientations are alternately spaced, and adjacent first and second unit cells share a square side plate for connection; in z Along the axial direction, multi-layer unit cell structures are stacked sequentially, with the bottom plate of the upper unit cell coinciding with the top plate of the lower unit cell.

[0029] Initial design parameters are: boundary dimensions L =30mm, side length of square board l =12.0203mm, radius of the circular arc. R 1 = 3.7151mm, radius of the circular arc. R 2 = 5.3816mm, relative to the corner of the square plate θ =45 ° .

[0030] The specific working principle is as follows: Mechanism of force and motion transmission: when the structure is in z When subjected to an external compressive load in the axial direction, the load first acts on the upper and lower square plates. Since the square plates are relatively rigid, the force is transmitted through the plate body to the double-arc connecting ribs that connect the upper and lower plates with the side plates.

[0031] Flexible deformation drives rigid body rotation: The double-arc connecting rib acts as the main elastic deformation element, undergoing bending deformation (change in curvature) under compression. Since the arc rib is fixedly connected to the square plate, the bending of the arc connecting rib forces the rigid body to rotate. z The upper and lower plates perpendicular to the axis and with z The side panels, parallel to the axis, overcome the internal forces of the structure and rotate around their respective geometric central axes. x axis, y shaft or z The shaft undergoes relative rotation.

[0032] Specifically, such as Figure 5 As shown, from z Viewed from above, when under pressure, the arc-shaped connecting ribs, which are originally arranged in a swastika shape (or a mirrored swastika shape), will curl and shrink, driving the connected side plates to rotate inward and close together.

[0033] Example 1 A design method for a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections includes the following steps: S1: Determine the geometric design parameters of the unit cell, including: outer boundary dimensions. L The side length of the square plate Initial rotation angle relative to the square plate θ Radius of the double-arc connecting rib R 1 and R 2 and plate thickness t ; S2: Establish a finite element model and optimize and adjust the design parameters based on the target Poisson's ratio requirement; S3: Based on the optimized design parameters, construct the geometric model of the unit cell in three-dimensional space, specifically including: establishing two parallel blocks with side lengths of... The square plates serve as the top and bottom plates, and their positions are based on... L and θ Confirm; establish four blocks with side lengths of Square panels serve as side panels, connecting the top and bottom panels. Opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Double arc connecting ribs are constructed between adjacent square panels. The double arc is composed of two tangent arcs, and each arc is tangent to the boundary at its connection with the square panel. Specifically, based on the principle of motion of the developable hexahedron, in x axis, y axis, z axis Establish side length Coaxial relative rotation angle θ A square is formed, and each square is stretched in a direction away from the origin. t This forms six square panels that are paired off. Using the inner plane of the top and front square panels as reference planes, draw a radius of... R 1 and R 2 The circular arc connecting rib has two arc segments that are tangent to the boundary at the cell boundary and connect there. The cross-sectional dimensions of the circular arc connecting rib are... t × t For the two circular arcs z The axes are arranged in a circular array, with a total of 4 arrays; then the resulting circular arcs are wrapped around... x The axis is arranged in a circular array, with two arrays, to obtain the unit cell. Viewed from above, the four arc segments at the top are arranged in a swastika shape. This structure... z When compressed in the axial direction, the structure achieves its stability through the bending of the arc-connecting ribs and the rotation of each panel around the axis. x shaft and y By changing the design parameters, different Poisson's ratio curves can be obtained by shrinking in the axial direction.

[0034] S4: The geometric model of the unit cell is arranged in a three-dimensional periodic array to construct a multi-cell structure. Specifically, this includes: mirroring the unit cell to obtain a unit cell with the opposite rotation direction; arranging the two types of unit cells alternately in the horizontal plane, and making adjacent unit cells share a square side plate to form a single-layer array structure; stacking the single-layer array structure in the vertical direction so that the bottom plate of the upper layer unit cell coincides with the top plate of the lower layer unit cell to obtain a three-dimensional multi-cell structure model.

[0035] Specifically, cell A is constructed, and cell B is obtained by mirroring cell A. Cells A and B are then compared and contrasted. x and y The cells are arranged in a directional, spaced-out array, with adjacent cells A and B sharing a side plate for connection, resulting in a single-layer 4×4 structure, as shown below. Figures 6-7 As shown. After completing the single-layer array, all unit cells in the single-layer structure are...z By arranging the layers in an axial direction so that the bottom plate of the upper layer coincides with the top plate of the lower layer, and then arranging them sequentially, a 4×4×4 multicell structure can be obtained, such as... Figure 8 As shown.

[0036] Therefore, this invention employs the aforementioned three-dimensional negative Poisson mechanical metamaterial structure and design method with circular arc connections. Through the use of a compliant circular arc connection design, compared to traditional straight-line connection structures, stress concentration at the nodes is significantly reduced. This makes the structure less prone to fatigue fracture under repeated impact or vibration loads, greatly improving its service life and reliability. Simultaneously, utilizing the compressive compaction characteristics of negative Poisson ratio structures and the bending deformation mechanism of the circular arc connection ribs, energy can be absorbed more efficiently under impact, providing excellent buffering protection.

[0037] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections, characterized in that, It is composed of a periodic array of multiple unit cells in three dimensions, wherein each unit cell has a hexahedral configuration and includes: Two square panels connected at the four corners; The side consists of four square panels connected at two corners; opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Eight pairs of double-arc connecting ribs, each pair of connecting ribs consisting of two arc segments; The square panels on the sides are connected to the square panels on the top and bottom by double arc connecting ribs, and each arc is tangent to the boundary at its connection with the square panel. When a unit cell is compressed in one direction, it achieves contraction perpendicular to the direction of compression through the bending of the circular connecting ribs and the rotation of each square plate around the axis, thus exhibiting a negative Poisson's ratio characteristic.

2. The three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 1, characterized in that, The cross-section of the arc connecting rib is square, and its side length is the same as the thickness of the square plate.

3. The three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 2, characterized in that, The boundary dimensions of the hexahedron are L The side length of the square board is The opposite square plate has a corner of 1. θ It satisfies the following relationship: 。 4. The three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 3, characterized in that, The circular arc connecting rib includes a radius of R 1 and R 2 An arc of radius ∈ R satisfies the following relationship: ； 。 5. The three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 4, characterized in that, The eight pairs of double-arc connecting ribs have equal central angles on the four arc segments of the upper and lower square plates, and are arranged in a swastika shape when viewed from the normal direction of the upper and lower square plates.

6. The three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 5, characterized in that, Multiple units include a first unit and a second unit. The second unit is a mirror image of the first unit. The top surface of the first unit is arranged in a swastika pattern, and the top surface of the second unit is also arranged in a swastika pattern.

7. A three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 6, characterized in that, The first and second cells are in x and y Along the direction x direction and y The orientations are alternately spaced, and adjacent first and second unit cells share a square side plate for connection; in z Along the axial direction, multi-layer unit cell structures are stacked sequentially, with the bottom plate of the upper unit cell coinciding with the top plate of the lower unit cell.

8. A three-dimensional negative Poisson mechanical metamaterial structure with circular arc connection as described in claim 7, characterized in that, Initial design parameters are: boundary dimensions L =30mm, side length of square board =12.0203mm, radius of the circular arc. R 1 = 3.7151mm, radius of the circular arc. R 2 = 5.3816mm, relative to the corner of the square plate θ =45 ° .

9. A design method for a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections as described in any one of claims 1-8, characterized in that, Includes the following steps: S1: Determine the geometric design parameters of the unit cell, including: outer boundary dimensions. L The side length of the square plate Initial rotation angle relative to the square plate θ Radius of the double-arc connecting rib R 1 and R 2 and plate thickness t ; S2: Establish a finite element model and optimize and adjust the design parameters based on the target Poisson's ratio requirement; S3: Based on the optimized design parameters, construct the geometric model of the unit cell in three-dimensional space, specifically including: establishing two parallel blocks with side lengths of... The square plates serve as the top and bottom plates, and their positions are based on... L and θ Confirm; establish four blocks with side lengths of Square panels serve as side panels, connecting the top and bottom panels. Opposite square panels are parallel to each other, and adjacent square panels are perpendicular to each other. Double arc connecting ribs are constructed between adjacent square panels. The double arc is composed of two tangent arcs, and each arc is tangent to the boundary at its connection with the square panel. S4: The geometric model of the unit cell is arranged in a three-dimensional periodic array to construct a multi-cell structure. Specifically, this includes: mirroring the unit cell to obtain a unit cell with the opposite rotation direction; arranging the two types of unit cells alternately in the horizontal plane, and making adjacent unit cells share a square side plate to form a single-layer array structure; stacking the single-layer array structure in the vertical direction so that the bottom plate of the upper layer unit cell coincides with the top plate of the lower layer unit cell to obtain a three-dimensional multi-cell structure model.

10. The design method for a three-dimensional negative Poisson mechanical metamaterial structure with circular arc connections as described in claim 9, characterized in that, In S4, the single-layer array structure is a 4×4 array, and the number of layers in the stacked array is 4, thus forming a 4×4×4 multi-cell structure.

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