CN115614414B - Metamaterial with three-dimensional negative poisson ratio and compression torsion coupling function and preparation method thereof - Google Patents
Metamaterial with three-dimensional negative poisson ratio and compression torsion coupling function and preparation method thereofInfo
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- CN115614414B CN115614414B CN202211226688.6A CN202211226688A CN115614414B CN 115614414 B CN115614414 B CN 115614414B CN 202211226688 A CN202211226688 A CN 202211226688A CN 115614414 B CN115614414 B CN 115614414B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/12—Vibration-dampers; Shock-absorbers using plastic deformation of members
- F16F7/128—Vibration-dampers; Shock-absorbers using plastic deformation of members characterised by the members, e.g. a flat strap, yielding through stretching, pulling apart
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/12—Vibration-dampers; Shock-absorbers using plastic deformation of members
- F16F7/123—Deformation involving a bending action, e.g. strap moving through multiple rollers, folding of members
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
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Abstract
本发明公开了一种三维负泊松比与压扭耦合的超材料及其制备方法，所述超材料由若干相同的结构单元周期性延拓构成；所述每个结构单元包括正交杆组及偏心杆组；所述正交杆组由两个菱形或椭圆形相互垂直在两点连接构成；所述两个菱形或椭圆形连接形成的两个连接点，用于与竖向方向的相邻的所述结构单元连接；所述偏心杆组由四个嵌套的偏心杆件组成，每个所述偏心杆件的一个端点分别与所述菱形或椭圆形相连接，另一端点用以连接相邻的所述结构单元。该超材料在z轴方向压缩(或拉伸)时出现整体收缩(或膨胀)；在x轴或y轴方向压缩或拉伸时绕z轴旋转。
The present invention discloses a three-dimensional metamaterial with a negative Poisson's ratio and compression-torsion coupling, and a preparation method thereof. The metamaterial is composed of a periodic extension of several identical structural units; each structural unit includes an orthogonal rod group and an eccentric rod group; the orthogonal rod group is composed of two rhombuses or ellipses connected perpendicularly at two points; the two connection points formed by the connection of the two rhombuses or ellipses are used to connect to adjacent structural units in the vertical direction; the eccentric rod group is composed of four nested eccentric rods, one end of each eccentric rod is connected to the rhombus or ellipse, and the other end is used to connect to adjacent structural units. The metamaterial undergoes overall contraction (or expansion) when compressed (or stretched) in the z-axis direction; and rotates about the z-axis when compressed or stretched in the x-axis or y-axis direction.
Description
Technical Field
The invention relates to the technical field of metamaterial preparation, in particular to a metamaterial coupling three-dimensional negative poisson ratio and compression torsion and a preparation method thereof.
Background
Negative poisson's ratio metamaterials refer to materials that contract (expand) under uniaxial compression (tension) perpendicular to the loading direction, achieving properties opposite to natural materials. Due to the complexity of the three-dimensional space, the design of the negative poisson ratio structure is mainly limited to two dimensions at present, and the application requirements cannot be completely met. Is extremely important for the design and manufacture of structural units (basic cells) of the three-dimensional mechanical metamaterial.
Accordingly, there is still a need in the art for further improvements and enhancements.
Disclosure of Invention
In view of the shortcomings of the prior art, the invention aims to provide a metamaterial with three-dimensional negative poisson ratio and compression-torsion coupling and a preparation method thereof, and aims to solve the problem that the existing metamaterial can only be used in a plane.
A metamaterial coupled with a three-dimensional negative poisson ratio and a compression torque, wherein the metamaterial is formed by periodically extending a plurality of same structural units;
each structural unit comprises an orthogonal rod group and an eccentric rod group, wherein the orthogonal rod group is formed by connecting two central symmetry patterns with the same shape at two points in a mutually perpendicular way;
The eccentric rod group consists of four nested eccentric rod pieces, one end point of each eccentric rod piece is connected with one side or one vertex of the central symmetrical graph respectively, and the other end point is used for being connected with the eccentric rod piece of the adjacent structural unit.
Optionally, the three-dimensional negative poisson ratio and the compression torsion are coupled metamaterial, wherein the eccentric rod piece is a straight rod or a curved rod.
Optionally, the three-dimensional metamaterial with negative poisson ratio and torque coupling is formed by four eccentric rods, wherein the four eccentric rods are arranged anticlockwise or clockwise.
Optionally, the three-dimensional negative poisson ratio and the compression torsion are coupled with metamaterial, wherein one end point of each eccentric rod piece is fixedly connected with a part, different from a connecting point, on the central symmetrical graph respectively.
Optionally, the three-dimensional negative poisson's ratio and compression torsion coupled metamaterial stretches along a longitudinal z-axis and expands along lateral x-and y-axes.
Optionally, the three-dimensional negative poisson's ratio is coupled with a compression twist of the metamaterial, wherein the metamaterial is compressed along a longitudinal z-axis and is contracted along a transverse x-axis and y-axis.
Optionally, the three-dimensional negative poisson ratio and compression torsion coupled metamaterial, wherein the metamaterial is stretched along a transverse x-axis or y-axis and twisted around a z-axis.
The preparation method of the metamaterial with the three-dimensional negative poisson ratio and the compression-torsion coupling comprises the following steps:
Building a structural unit model and carrying out array prolongation on the structural unit model;
and selecting corresponding materials, and manufacturing according to the structural unit model and the array prolongation result to obtain the metamaterial with the three-dimensional negative poisson ratio and the compression-torsion coupling.
Optionally, in the preparation method of the metamaterial coupled with the compression torsion, when the orthogonal rod group is formed by connecting two rhombus mutually perpendicular points, the three-dimensional negative poisson ratio value is predicted by adopting the following formula:
E is the elastic modulus of the material, A is the sectional area of the orthogonal rod group, F p is the applied load, l is the side length of the diamond, and θ is the vertical included angle of the orthogonal rod group;
The rotation angle is predicted using the following formula:
Wherein e is the eccentricity of the eccentric rod piece, R is the radius thereof, delta 1 is the moving distance of the tail end of the curved rod, and w is the deflection of the straight rod group on the horizontal plane.
Optionally, the method for preparing the metamaterial with the three-dimensional negative poisson ratio coupled with the compression torsion includes the steps of constructing a structural unit model and carrying out array extension on the structural unit model, wherein the method specifically includes:
Determining the relation between the parameters according to the requirements on the negative poisson v ratio and the torsion angle omega by utilizing the formulas (1) and (2);
Load F p, displacement constraint V p and material parameter elastic modulus E under a preset application working condition, so that partial parameters in a formula are determined;
And determining any two parameters of the eccentric moment, the radius, the characteristic length and the characteristic angle, solving the remaining parameters according to the formula (1) and the formula (2), and then carrying out cell modeling and array continuation according to the geometric shapes of the orthogonal rod group and the eccentric rod group.
Compared with the prior art, the invention has the beneficial effects that the three-dimensional negative poisson ratio and compression torsion coupled metamaterial is obtained by constructing the structural unit with the orthogonal rod group and the eccentric rod group and carrying out array extension on the structural unit, and the metamaterial is integrally contracted (or expanded) when compressed (or stretched) in the z-axis direction and rotates around the z-axis when compressed or stretched in the x-axis or y-axis direction. Compared with the defect that the two-dimensional metamaterial can only be used in a plane, the metamaterial with the three-dimensional negative poisson ratio coupled with the compression torsion can be applied to a transmission mechanism, a multidirectional vibration absorbing device and the like in the three-dimensional orthogonal direction.
Drawings
Fig. 1 is a three-dimensional negative poisson ratio and compression-torsion coupled metamaterial provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of the left-handed and right-handed structure of a three-dimensional negative Poisson's ratio and torsionally coupled metamaterial;
FIG. 3 is a perspective view of a structural element of a metamaterial with a negative Poisson's ratio coupled with torsion in a rhombic set of orthogonal rods;
FIG. 4 is a top view of a structural element of a metamaterial with a negative Poisson's ratio coupled with torsion in a rhombus as a set of orthogonal rods;
FIG. 5 is a front view of a structural element of a metamaterial with a negative Poisson's ratio coupled with torsion in a diamond-shaped set of orthogonal rods;
FIG. 6 is a perspective view of a structural element of a metamaterial with an oval quadrature pole set with negative Poisson's ratio coupled with torsion;
FIG. 7 is a top view of a structural element of a metamaterial with an oval quadrature pole set with negative Poisson's ratio coupled with torsion;
fig. 8 is a front view of a structural unit of a metamaterial with an oval quadrature pole set with negative poisson's ratio coupled with torsion.
Detailed Description
The invention provides a metamaterial with three-dimensional negative poisson ratio and compression torsion coupling and a preparation method thereof, and the metamaterial is further described in detail below for making the purposes, the technical scheme and the effects of the metamaterial clearer and more definite. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In order to solve the problem that the existing metamaterial can only be used in a two-dimensional plane. The embodiment provides a metamaterial with three-dimensional negative poisson ratio and compression torsion coupling, which is formed by periodically extending a plurality of identical structural units, wherein the structural units can be formed by connecting a group of orthogonal central symmetrical patterns, such as a diamond-shaped rod group and a group of eccentric curved rods according to a certain rule, as shown in figures 1 to 8. The structure is a central symmetrical structure, and the two rod groups respectively comprise four rod pieces, and the rod piece of each orthogonal rod group is connected with one eccentric bent rod. It will be readily appreciated that the structural units may also be formed by a set of orthogonal elliptical bars and an eccentric curved bar connected according to a certain rule. The structure is a central symmetry structure, and the rod piece of each orthogonal rod group is linked with an eccentric curved rod.
In this embodiment, as shown in fig. 3, the orthogonal diamond-shaped rod group refers to a structure formed by two diamond-shaped rods perpendicular to each other, and one diagonal of the two diamond-shaped rods is coincident, where 101 is an orthogonal rod group, and 102 is an eccentric rod group. The points at which the two diamonds are connected are used for connecting with adjacent structural units in the vertical direction. It will be readily appreciated that the orthorhombic set of bars is placed in a three dimensional coordinate system with the joints of the two diamonds being arranged along the z-axis, with the upper and lower joints of each orthorhombic assembly being joined to the joints of adjacent structural assemblies. The eccentric rod group refers to four rods arranged on the orthogonal rod group, and the four rods are nested, wherein the four rods can be curved rods or straight rods. One ends of the four rods of the eccentric rod group are respectively connected with the orthogonal rod group, namely, the four rods of the eccentric rod group are respectively fixed at the vertexes of the diamond on the x axis and the y axis. The other end is used for being connected with the eccentric rod group on the adjacent structural unit, so that the extension is carried out, and the metamaterial shown in the figure 1 can be obtained.
In this embodiment, as shown in fig. 2, the structural unit may be a left-handed structure or a right-handed structure, and it is easy to understand that the left-handed structure refers to a clockwise direction when the eccentric rod group is forced to rotate the orthorhombic assembly, and the right-handed structure refers to a counterclockwise direction when the eccentric rod group is forced to rotate the orthorhombic assembly.
In this embodiment, as shown in fig. 4 and 5, the vertical included angle between the orthogonal rod group of the structural unit with negative poisson ratio and torsional coupling is θ, the rod length is l, the eccentric moment of the eccentric curved rod group is e, the radius of the curved rod is R, and the sections of the two rod groups can be a×b rectangle or a circle with radius R.
The negative poisson's ratio of the structure should be:
Wherein E is the elastic modulus of the material used, A is the cross-sectional area of the orthogonal rod group, and F p is the magnitude of the applied load.
The rotation angle of the structure is measured and predicted by the following formula:
Wherein e is the eccentricity of the eccentric rod piece, R is the radius thereof, delta 1 is the moving distance of the tail end of the curved rod, and w is the deflection of the straight rod group on the horizontal plane.
The negative poisson ratio value of the designed metamaterial can be theoretically predicted through the formula, and the design efficiency of the metamaterial is improved. By changing the geometric parameters in the formula, the metamaterial with different negative poisson ratios and torsion angles can be designed and prepared according to the requirements.
Illustratively, the elastic modulus 1GMp of the structural material is used to prepare a Poisson's ratio of-0.4 and a corner ratio of 2.3 under conditions of a force load of 10N and a displacement load of 5 mm. According to the mentioned design flow, the radius R is firstly determined to be 15mm, the sectional area is 1mm 2, the characteristic length l is 20mm, the characteristic angle is obtained by solving the two formulas, and the eccentricity is 3mm. After the design stage, a cell model is built and periodically extended by adopting three-dimensional modeling software (such as solidworks), materials are selected according to the determined structural material parameters, the built model is exported and sliced, and finally the 3D printing technology is utilized for preparation.
In this embodiment, unlike the previous combination designs such as concave polygon or paper folding base structure, the present invention adopts a unique spatial structure to perform displacement transformation, and the proposed three-dimensional metamaterial structural unit (base unit) and its array are extended, and the obtained three-dimensional negative poisson ratio and compression torsion coupled metamaterial is subjected to load in the longitudinal direction, and the deformation of the orthogonal rod group drives the nested curved rods to transfer the deformation to the adjacent units, so as to realize the special mechanical properties of tension-compression. Under transverse loading, the nested bent rods deform, torque is applied to four points of the diamond-shaped rod group on the middle plane, the rotation of the diamond-shaped rod group is promoted, and the special mechanical property of tension, compression and torsion is realized. The structural material type of the metamaterial can be selected according to actual application scenes (such as various metals, high polymer materials and the like), and can also be a combination of various materials. Can be completed by adopting different manufacturing technologies according to actual requirements (such as basic unit scale, performance requirement, manufacturing cost and the like). For example, if a metamaterial is required to have a micrometer-scale base unit, the metamaterial of the present invention may be implemented using additive manufacturing techniques.
Based on the same inventive concept, the invention also provides a preparation method of the metamaterial with the three-dimensional negative poisson ratio coupled with the compression torsion, which comprises the following steps:
Determining the relation between parameters according to the requirements at the negative poisson V ratio and the torsion angle omega by utilizing the formulas (1) and (2), presetting a load F p, a displacement constraint V p and a material parameter elastic modulus E under an application working condition to determine partial parameters in the formulas, determining any two parameters of an eccentric moment, a radius, a characteristic length and a characteristic angle, solving the rest parameters according to the formulas (1) and (2), and then carrying out cell modeling and array prolongation according to the geometric shapes of an orthogonal rod group and an eccentric rod group. And selecting a material for manufacturing to obtain the metamaterial with the three-dimensional negative poisson ratio and the compression-torsion coupling.
In summary, the invention provides a metamaterial coupled with a compression twist and a preparation method thereof, wherein the metamaterial is formed by periodically extending a plurality of identical structural units, each structural unit comprises an orthogonal rod group and an eccentric rod group, the orthogonal rod group is formed by connecting two rhombus or ellipse at two points in a mutually perpendicular manner, two connecting points formed by connecting the two rhombus or ellipse are used for connecting adjacent structural units in the vertical direction, the eccentric rod group is formed by four nested eccentric rod pieces, one end point of each eccentric rod piece is connected with the rhombus or ellipse respectively, and the other end point of each eccentric rod piece is used for connecting the adjacent structural units. The metamaterial is integrally contracted (or expanded) when compressed (or stretched) in the z-axis direction, and rotates around the z-axis when compressed or stretched in the x-axis or y-axis direction. Compared to the disadvantage that two-dimensional metamaterials can only be used in-plane.
It is to be understood that the invention is not limited in its application to the examples described above, but is capable of modification and variation in light of the above teachings by those skilled in the art, and that all such modifications and variations are intended to be included within the scope of the appended claims.
Claims (7)
1. The metamaterial is characterized by being formed by periodically extending a plurality of same structural units;
Each structural unit comprises an orthogonal rod group and an eccentric rod group, wherein the orthogonal rod group is formed by connecting two central symmetrical patterns with the same shape at two points in a mutually perpendicular way;
The eccentric rod group consists of four nested eccentric rod pieces, one end point of each eccentric rod piece is connected with one edge or one vertex of the central symmetrical graph, and the other end point is connected with the eccentric rod piece of the adjacent structural unit;
stretching the metamaterial along a longitudinal z-axis, expanding the metamaterial along transverse x-and y-axes, compressing the metamaterial along the longitudinal z-axis, contracting the metamaterial along the transverse x-and y-axes, stretching the metamaterial along the transverse x-or y-axis, and twisting the metamaterial around the z-axis.
2. The three-dimensional negative poisson's ratio and torque coupled metamaterial according to claim 1, wherein the eccentric rod is a straight rod or a curved rod.
3. The three-dimensional negative poisson's ratio and torque coupled metamaterial according to claim 1, wherein four of the eccentric rods are arranged counterclockwise or clockwise.
4. The metamaterial coupled with the compression torsion by the three-dimensional negative poisson ratio according to claim 1, wherein one end point of each eccentric rod piece is fixedly connected with a part, different from a connecting point, on the central symmetrical graph.
5. A method for preparing the metamaterial coupled with the compression torsion by the three-dimensional negative poisson ratio as claimed in claim 1, which is characterized by comprising the following steps:
Building a structural unit model and carrying out array prolongation on the structural unit model;
and selecting corresponding materials, and manufacturing according to the structural unit model and the array prolongation result to obtain the metamaterial with the three-dimensional negative poisson ratio and the compression-torsion coupling.
6. The method for preparing the metamaterial coupling the three-dimensional negative poisson ratio with the compression torque according to claim 5, wherein when the orthogonal rod group is formed by connecting two rhombus shapes at two points in a mutually perpendicular mode, the three-dimensional negative poisson ratio value is predicted by adopting the following formula:
(1)
As a function of the modulus of elasticity of the material used, Is the cross-sectional area of the orthogonal bar set,In order to apply the magnitude of the load,For the side length of the diamond shape,Is the vertical included angle of the orthogonal rod group;
The rotation angle is predicted using the following formula:
(2)
Wherein e is the eccentricity of the eccentric rod piece, R is the radius thereof, delta 1 is the moving distance of the tail end of the curved rod, and w is the deflection of the straight rod group on the horizontal plane.
7. The method for preparing the metamaterial coupled with the compression torsion by the three-dimensional negative poisson ratio according to claim 6, wherein the method for constructing the structural unit model and carrying out array extension on the structural unit model specifically comprises the following steps:
Determining the relation between the parameters by using the formulas (1) and (2) according to the required negative poisson ratio v and the torsion angle omega;
The load F p, the displacement constraint V p and the material parameter elastic modulus E under the preset application working condition are determined so as to determine geometric parameters in a formula, namely radius R, eccentric moment E, side length l, sectional area A and vertical included angle According to the formula (1) and the formula (2), solving the remaining parameters, and then carrying out cell modeling and array extension according to the geometric shapes of the orthogonal rod group and the eccentric rod group.
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