CN213545921U - Novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient - Google Patents

Abstract

The utility model discloses a novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient, the three-dimensional structure comprises three-dimensional cell elements, each three-dimensional cell element comprises four same parallelograms, each parallelogram is divided into two same triangle units, the longest rod and two oblique rods of each triangle unit respectively have corresponding rod length and respectively comprise three materials, the three-dimensional structures of different triangle unit geometric parameters and material combinations have different elastic parameters and thermal expansion coefficients; in the three-dimensional structure, three-dimensional cells are periodically arranged along the direction of one side of a parallelogram on the bottom surface of the three-dimensional cells as the left-right direction, and are repeatedly distributed in a mirror image manner along the front-back direction and the up-down direction which are perpendicular to the left-right direction. The utility model discloses a select reasonable geometric parameters and material combination, can regulate and control the poisson's ratio and the coefficient of thermal expansion of three-dimensional mechanics metamaterial on a large scale.

Description

Novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient

Technical Field

The utility model relates to a novel three-dimensional structure technical field, in particular to novel three-dimensional structure of poisson's ratio and thermal expansion coefficient adjustable.

Background

Negative poisson's ratio material expands laterally when stretched and contracts laterally when compressed, which, due to its unique properties, has many advantages over other materials. And the physical and mechanical properties of the negative Poisson ratio material, such as shear modulus, indentation resistance, fracture resistance and the like, have a large promotion space.

Negative thermal expansion materials are materials that expand abnormally over a certain temperature range with changes in temperature, and have the characteristics opposite to those of common materials with thermal expansion and contraction. The material with controllable thermal expansion coefficient or expansion coefficient close to 0 is prepared by doping and compounding the material with different expansion coefficients.

Like the negative poisson's ratio, the coefficient of thermal expansion of a negative thermal expansion material is negative over a range of temperatures. Since natural negative thermal expansion materials are very rare and mechanical properties are often difficult to meet engineering requirements, researchers have attempted to prepare negative thermal expansion materials from two or more positive expansion materials, which are mainly lightweight materials. The light negative thermal expansion material can be divided into a bending dominant type and a stretching dominant type according to the characteristics of the microscopic structure thermal expansion deformation. The bending leading type structure depends on the bending deformation of the rod piece, so that the thermal expansion regulation is realized. Each rod piece of the stretching leading type structure is axially stretched and pressed to deform, and compared with the bending leading type structure, the stretching leading type structure has more excellent mechanical property.

Although researchers have made many studies on negative poisson's ratio materials and negative thermal expansion materials, so far, most of the existing materials can only achieve one between negative poisson's ratio and negative thermal expansion, and only a few of the researchers have designed materials capable of achieving both negative poisson's ratio and negative thermal expansion, for example, Joseph et al have designed triangular structures with negative poisson's ratio and negative thermal expansion. Ai and Gao et al design structures with negative Poisson's ratio and non-positive thermal expansion. Ha et al designed a structure with controllable thermal expansion and a Poisson ratio close to-1. Fang et al designed a cell structure that couples negative thermal expansion and negative poisson's ratio. But the structure with adjustable poisson ratio and thermal expansion coefficient has not been researched yet.

SUMMERY OF THE UTILITY MODEL

An object of the utility model is to overcome prior art's shortcoming and not enough, provide a novel three-dimensional structure of poisson's ratio and thermal expansion coefficient adjustable, the reasonable geometric parameters of this structure accessible and material combination realize the poisson's ratio of three-dimensional mechanics metamaterial and thermal expansion coefficient's regulation and control on a large scale.

The purpose of the utility model is realized through the following technical scheme: a novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient is composed of three-dimensional cells, each three-dimensional cell is composed of four same parallelograms, each parallelogram is divided into two same triangular units, the longest rod and two oblique rods of each triangular unit respectively have corresponding rod lengths and are respectively composed of three materials, and the three-dimensional structures with different geometric parameters of the triangular units and material combinations have different elastic parameters and thermal expansion coefficients;

in the three-dimensional structure, three-dimensional cells are periodically arranged along the direction of one side of a parallelogram on the bottom surface of the three-dimensional cells as the left-right direction, and are repeatedly distributed in a mirror image manner along the front-back direction and the up-down direction which are perpendicular to the left-right direction.

Preferably, the three-dimensional cell element has the same elasticity parameters and thermal expansion coefficients in the x-axis direction and the y-axis direction, the elasticity parameters comprise Young's modulus and Poisson's ratio, wherein the x-axis and the y-axis are two coordinate axes of a Cartesian coordinate system which is constructed by taking the centroid of the three-dimensional cell element as an origin and taking the direction of one of the diagonal rods of one triangular unit at the bottom surface of the three-dimensional cell element as the z-axis, the y-axis is perpendicular to the z-axis on the horizontal plane, and the x-axis is perpendicular to the z-axis on the vertical plane.

Furthermore, for a cell element in which the upper and lower surfaces in the x-axis direction, the front and rear surfaces in the y-axis direction, and the left and right end points of the diagonal rod in the z-axis direction respectively bear a certain displacement, the equivalent young modulus is:

wherein E is_zIs the equivalent Young's modulus of the cell element in the z direction; e_xIs the equivalent Young's modulus of the cell element in the x direction; e_yIs the equivalent Young's modulus of the cell element in the y direction; taking an oblique rod as a z-axis as a first oblique rod, taking another oblique rod of the triangular unit as a second oblique rod, and N₂Is the axial force of the second diagonal; n is a radical of₃Is the axial force of the longest rod;

is the included angle of two diagonal rods; theta is an included angle between the longest rod and the first diagonal rod; u is the distance the parallelogram at the bottom of the cell moves forward along the x-axis; l is₁Is the length of the first diagonal rod; e₁Is the young's modulus of the first diagonal; a. the₁Four times the cross-sectional area of the first diagonal.

Furthermore, for a cell whose upper and lower surfaces in the x direction simultaneously bear a certain displacement, the equivalent poisson's ratio in the x and y directions and in the x and z directions is:

wherein, v_xyIs the equivalent Poisson's ratio of the cell in the x and y directions; v is_xzIs the equivalent Poisson's ratio of the cell in the x and z directions; u is the distance the parallelogram at the bottom of the cell moves forward along the x-axis;

is the included angle of two diagonal rods; theta is an included angle between the longest rod and the first diagonal rod; v is the distance that the parallelogram connecting the upper and lower surfaces simultaneously moves in the forward direction along the y-axis; w is a_BThe distance is that the end points of two diagonal rods which are simultaneously connected in a parallelogram connecting an upper surface and a lower surface move along the negative direction of a z axis; w is a_AIs the distance of forward movement along the z-axis of the end point of the parallelogram connecting the longest rod and the second diagonal rod simultaneously in the parallelogram connecting the upper and lower surfaces.

Furthermore, for a cell carrying a certain displacement at both the left and right endpoints in the z-direction, the equivalent poisson ratio in the z-axis direction and the x-axis direction is:

ν_zxis the equivalent Poisson's ratio of the cell in the z and x axis directions;

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

Furthermore, for a three-dimensional cell which changes in temperature and carries a unit load, the equivalent thermal expansion coefficients α in the x, y and z directions_x、α_y、α_zComprises the following steps:

wherein t is the variation of temperature; l is₃Is the length of the longest rod; delta_AVDisplacement of the load bearing end point due to temperature change; alpha is alpha₁Is the coefficient of thermal expansion of the first diagonal; alpha is alpha₂Is the coefficient of thermal expansion of the second diagonal; alpha is alpha₃Is the coefficient of thermal expansion of the longest rod;

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

Further, by

Or

The novel three-dimensional structure constructed by the three-dimensional cell is a three-dimensional structure with zero thermal expansion coefficient in the directions of an x axis and a y axis, wherein,

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

Preferably, the angle θ is 90 °,

or

The novel three-dimensional structure constructed by the three-dimensional cell elements with the angle of more than 0 and less than 17 degrees is a three-dimensional zero Poisson ratio structure, wherein,

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

The utility model discloses for prior art have following advantage and effect:

(1) the utility model discloses triangle-shaped unit design adjustable negative poisson ratio and thermal expansion coefficient's three-dimensional structure based on three materials, to this structure, through reasonable geometric parameter and material combination, can realize three-dimensional negative poisson ratio and two-way negative thermal expansion, and three-dimensional structure's poisson ratio and thermal expansion coefficient control range are big, and the regulative mode is also simple and convenient, can provide the reference for the structural design who has temperature sensitivity and mechanical sensitivity simultaneously.

(2) The utility model discloses the poisson ratio and the three-dimensional structure of thermal expansion coefficient adjustable that construct, the utility model provides a young modulus, poisson ratio and thermal expansion coefficient equivalent formula, and calculated the geometric parameter condition and the material combination condition that realize zero poisson ratio and zero thermal expansion, be favorable to the research of the three-dimensional mechanics metamaterial of high performance.

Drawings

Fig. 1 is a schematic view of a three-dimensional truss structure designed based on triangular units, wherein (a) is a schematic view of a parallelogram formed by two triangular units; (b) the figure is a schematic diagram of a three-dimensional cell; (c) the figure is a schematic diagram of a three-dimensional truss structure formed by four cells.

Fig. 2 is a diagram illustrating basic calculation parameters of a three-dimensional cell.

Fig. 3 is a schematic diagram of the deformation of a three-dimensional cell under the application of displacement.

Fig. 4 is a schematic view of a cell cut in a direction perpendicular to the x-axis.

Fig. 5 is a schematic view of a cell cut along a direction perpendicular to the y-axis.

Fig. 6 is a schematic diagram of a cell cut along the vertical z-axis.

Fig. 7 is a schematic view of a quarter cell cut along the z-axis.

Fig. 8 is a diagram showing the basic calculation parameters of the delta unit when the cell is made to achieve negative thermal expansion.

Fig. 9 to 10 are schematic diagrams of a unit load method performed on a triangular unit when negative thermal expansion is achieved in the cell.

FIG. 11 to FIG. 13 show the Poisson's ratio v under the first set of parameters in embodiment 1 of the present invention_xy,v_xz,v_zxYoung's modulus E_x,E_zAnd coefficient of thermal expansion a_x,a_zThe comparison graph of the result NR of the numerical simulation verification and the result AR of the formula calculation is shown.

FIG. 14 to FIG. 16 show the Poisson's ratio v under the first set of parameters in embodiment 1 of the present invention_xy,v_xz,v_zxYoung's modulus E_x,E_zAnd coefficient of thermal expansion a_x,a_zThe comparison graph of the result NR of the numerical simulation verification and the result AR of the formula calculation is shown.

Fig 17 and 18 show that when θ is 90,

to structural poisson's ratio v_xyAnd modulus of elasticity E_x,E_ySchematic diagram of the effect of (c).

FIG. 19 and FIG. 20 are each a cross-sectional view of a cross

The poisson ratio v of the structure of theta_xyAnd modulus of elasticity E_x,E_ySchematic diagram of the effect of (c).

FIG. 21 is a schematic view of the x-axis and y-axis directions to achieve zero thermal expansion.

Detailed Description

The present invention will be described in further detail with reference to the following examples and drawings, but the present invention is not limited thereto.

Examples

The embodiment discloses a novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient, and various novel three-dimensional structures, such as a three-dimensional zero-Poisson's ratio structure and a three-dimensional structure with zero thermal expansion coefficient in the directions of an x axis and a y axis, can be finally constructed through the novel three-dimensional structure.

The three-dimensional structure is composed of three-dimensional cells, each three-dimensional cell is composed of four identical parallelograms, and each parallelogram is divided into two identical triangular units. The longest rod and the two diagonal rods of each triangular unit respectively have corresponding rod lengths and are respectively made of three materials, and the three-dimensional structures of different triangular unit geometric parameters and material combinations have different elastic parameters and thermal expansion coefficients.

In the three-dimensional structure, three-dimensional cells are periodically arranged along the direction of one side of a parallelogram on the bottom surface of the three-dimensional cells as the left-right direction, and are repeatedly distributed in a mirror image manner along the front-back direction and the up-down direction which are perpendicular to the left-right direction.

For a three-dimensional cell, it has the same elastic parameters and thermal expansion coefficients in the x-axis direction and the y-axis direction, and the elastic parameters include young's modulus and poisson's ratio. The X axis and the Y axis are two coordinate axes of a Cartesian coordinate system which is constructed by taking the centroid of the three-dimensional cell element as an origin point and taking the direction of one of the diagonal rods of one triangular unit on the bottom surface of the three-dimensional cell element as the Z axis, the Y axis is vertical to the Z axis on the horizontal plane, and the X axis is vertical to the Z axis on the vertical plane.

The novel three-dimensional structure is constructed as follows:

s1-1, designing a triangular unit based on three materials, namely, the longest rod and two oblique rods of the triangular unit are respectively composed of three materials.

S1-2, a parallelogram is formed by two identical triangle units, which can be seen in fig. 1 (a), and then a three-dimensional cell is constructed based on four identical parallelograms (AA ' D, ABCD, BB ' C ' C, A ' B ' C ' D '), which can be seen in fig. 1 (B) and fig. 2.

As shown in FIG. 2, the cell has three types of rods of different lengths, the first type being one of the diagonal rods AD, A 'D', BC and B 'C' of a triangular unit, which is defined as the first diagonal rod, having a length L₁Cross sectional area of

E is the modulus of elasticity and the coefficient of thermal expansion₁、α₁. Define the included angle of the two diagonal rods as

For example

An included angle between the longest rod and the first oblique rod is defined as theta, and for example, angle ACB is equal to theta. The second type is another diagonal rod BB ', B' A ', A' A, AB, CD, CC ', C' D of the triangular unit, which is defined as a second diagonal rod with the length of

Cross-sectional area of

E is the modulus of elasticity and the coefficient of thermal expansion₂、α₂. The third type of bar is the longest bar of the triangular unit AC, AD ', B' C, B 'D' having a length of

Cross-sectional area of

E is the modulus of elasticity and the coefficient of thermal expansion₃、α₃。

S1-3, taking the direction of one side of the parallelogram of the bottom surface of the three-dimensional cell as the left-right direction, arranging the three-dimensional cells periodically along the direction, and repeatedly mirroring along the front-back direction and the up-down direction perpendicular to the direction to finally obtain a novel three-dimensional truss structure, for example, a three-dimensional truss structure composed of four cells as shown in fig. 1 (c).

The elastic parameters and the thermal expansion coefficient of the novel three-dimensional structure can be obtained by performing mechanical analysis on a three-dimensional cell of the three-dimensional truss structure and solving by a displacement method and a unit load method, and the process is as follows:

(1) firstly, a three-dimensional cell element is cut out from a three-dimensional truss structure, the centroid of the three-dimensional cell element is used as an origin O, the direction of one of the diagonal rods of one triangular unit on the bottom surface of the three-dimensional cell element is used as a z-axis, a Cartesian coordinate system is established, the y-axis of the Cartesian coordinate system is perpendicular to the z-axis on a horizontal plane, and the x-axis of the Cartesian coordinate system is perpendicular to the z-axis on a vertical plane. As shown in fig. 2 and 3, the x-axis direction is vertically upward, the y-axis direction is outward, and the z-axis direction is horizontally rightward.

(2-1) applying displacements to the upper and lower surfaces of the three-dimensional cell element in the x-axis direction, as shown in fig. 3, calculating the displacements of the three-dimensional cell element in the x, y and z-axis directions, and obtaining the equivalent poisson's ratio and the equivalent young's modulus of the three-dimensional cell element based on the displacements.

(2-2) applying displacement to the front surface and the rear surface of the three-dimensional cell element in the y-axis direction, referring to fig. 3, calculating the displacement of the three-dimensional cell element in the x-axis direction, the y-axis direction and the z-axis direction, and calculating the equivalent poisson ratio and the equivalent young modulus of the three-dimensional cell element based on the displacement; here, the equivalent parameters in the x-axis direction and the y-axis direction are the same according to the deformation symmetry relationship of the cell.

Step (2-2) is illustrated with the three-dimensional cell of fig. 2. The displacements of the points (A, B, C, D, A ', B', C ', D') along the x, y, z axes are denoted by u, v, w, respectively, as shown in FIG. 3 for parallelogram BB 'C' C moving in the positive direction u along the x axis and parallelogram AA 'D' D moving in the negative direction u along the x axis. According to the deformation characteristics of the cell element, the parallelogram ABCD moves v along the y axis in the positive direction, and the parallelogram A 'B' C 'D' moves v along the y axis in the negative direction. The displacement w of each point along the z-axis direction has the following relationship:

in the formula, w_A、w_B、w_C、w_D、w_A'、w_B'、w_C'、w_D' displacement of points A, B, C, D, A ', B ', C ', D ', respectively, along the Z-axis. In each point displacement, assume u is a known quantity, w_A、w_B、w_C、w_D、w_A'、w_B'、w_C'、w_D' and v are unknowns.

For a three-dimensional cell, there are 16 rods for a cell, 5 rods with different axial forces: n is a radical of₁Representing the axial force, N, of the rods AD, A ' D ', BC, B ' C₂Axial force, N ' of levers AB, B ' A ', CD, C ' D '₂Representing the axial force, N, of the rods A 'A, BB', CC ', D' D₃Axial force, N ' representing rod AC, B ' D '₃Representing the axial force of the rods AD ', B' C. The axial force expression for these 5 rods is as follows:

the cell was cut in a direction perpendicular to the x-axis as shown in fig. 4. The cell is cut in a direction perpendicular to the y-axis, as shown in FIG. 5, where the stress σ in the y-direction _y0. The cell is cut in a direction perpendicular to the z-axis, as shown in FIG. 6, where the stress σ in the z-direction _z0. The quarter-cell is cut along the z-direction as shown in fig. 7, in which shear stressτ_xz＝0。σ_y＝0、σ_z＝0、τ_xzThe value of 0 can be directly obtained according to the stress characteristics and the balance condition of the whole cell in fig. 3.

In summary, the following set of equations can be obtained:

by combining the above equation set (3) and each shaft force expression (2), w can be decoupled_A、w_B、v。

So strain ∈_x、ε_y、ε_zCan be expressed as:

thus, it is possible to obtain:

when the displacement is applied to the upper surface and the lower surface of the cell in the x direction, the poisson ratio equivalent formula is as follows:

wherein, v_xyIs the equivalent Poisson's ratio of the cell in the x and y directions; v is_xzIs the equivalent Poisson's ratio of the cell in the x and z directions.

Stress σ in the x-direction when the cell is cut along a direction perpendicular to the x-axis as shown in fig. 4_xExpressed as:

after displacement is respectively applied to the upper surface and the lower surface of the cell in the x direction and the front surface and the rear surface in the y direction, the equivalent Young modulus of the cell is as follows:

wherein E is_yIs the equivalent Young's modulus of the cell element in the y direction; e_xIs the equivalent young's modulus of the cell in the x-direction.

(2-3) applying displacements to the left and right end points of the diagonal rods of the three-dimensional cell element in the z-axis direction, as shown in fig. 3, calculating the displacements of the three-dimensional cell element in the x, y, and z-axis directions, and obtaining the equivalent poisson's ratio and the equivalent young's modulus of the three-dimensional cell element based on the displacements.

Specifically, w is the cell of fig. 2 pulled simultaneously based on both the left and right endpoints_A、w_B'、w_C、w_D' is a known amount, w_B、w_D、w_A'、w_C' and u, v are unknowns. According to the deformation symmetry of the cell, u is v, N₂＝N'₂,N₃＝N'₃Wherein, τ _xz0. In summary, the following system of equations can be obtained:

by combining the above equation set (8) and the shaft force expressions (2), the following can be solved:

strain epsilon_x、ε_zComprises the following steps:

equivalent Poisson ratio v of cell element in z-axis and x-axis directions_zx(i.e., the Poisson's ratio equivalent equation) is:

as shown in fig. 6, the cell is cut along a direction perpendicular to the z-axis, stress σ in the z-direction_zComprises the following steps:

equivalent Young's modulus E of cell element in z direction_zComprises the following steps:

for orthotropic materials, the following conclusions can also be drawn:

E_zν_xz＝E_xν_zx (14)

(3) when the temperature changes, a unit load is applied to the three-dimensional cell, the displacement of the three-dimensional cell in the three directions of the x axis, the y axis and the z axis is calculated, and the equivalent thermal expansion coefficient of the three-dimensional cell is obtained based on the displacement and the temperature.

In particular, when the material combinations of the cells are different, it is possible to achieve bidirectional negative thermal expansion. The mechanism by which the cell achieves negative thermal expansion is a delta unit, as shown in figure 8. When the temperature changes t, firstly, the displacement delta of the point A in the vertical direction is obtained by a unit load method_AV. A vertical upward unit force K of 1 is applied to point a, resulting in the virtual state shown in fig. 9, and the internal forces of the rods (AB, AC, BC) are:

wherein the displacement delta is caused by temperature change_AVComprises the following steps:

in the formula (I), the compound is shown in the specification,

the axial force of each rod caused by unit load is shown as i, the number of the ith rod is shown as i, and n is the total number of the rods in the cell structure.

As shown in FIG. 2, the equivalent thermal expansion coefficient α of the cell in the x-direction and the y-direction is determined according to the deformation symmetry of the cell_x、α_ySimilarly, based on the definition of the thermal expansion coefficient (the thermal expansion coefficient is the displacement caused by temperature divided by the original length of the cell in a certain direction), equation (17) is obtained:

wherein t is the variation of temperature; l is₃Is the length of the longest rod; delta_AVDisplacement of the load bearing end point due to temperature change; alpha is alpha₁Is the coefficient of thermal expansion of the first diagonal; alpha is alpha₂Is the coefficient of thermal expansion of the second diagonal; alpha is alpha₃Is the coefficient of thermal expansion of the longest rod;

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod, L₃sin θ is the cell vertical equivalent height, i.e., the original length in the vertical direction.

Then when the temperature change t is solved, the horizontal displacement delta of the point B_BHThe horizontal right unit force Q applied at point B becomes 1, and the virtual state shown in fig. 10 is formed, and the internal force of each rod is:

wherein the displacement delta is caused by temperature change_BHComprises the following steps:

for a three-dimensional cell as shown in fig. 2, the z-direction equivalent thermal expansion coefficient is:

l here₁The horizontal equivalent length of the cell, i.e. the original length in the horizontal direction.

Therefore, it can be obtained from the above process that for a cell element in which the upper and lower surfaces in the x-axis direction, the front and rear surfaces in the y-axis direction, and the left and right end points of the diagonal rod in the z-axis direction respectively bear a certain displacement, the equivalent young's modulus is:

for a cell carrying a certain displacement on the upper surface and the lower surface in the x direction, the equivalent poisson ratio in the x and y directions and in the x and z directions is as follows:

for a cell carrying a certain displacement at the same time at the left end point and the right end point in the z direction, the equivalent poisson ratio in the z-axis direction and the x-axis direction is as follows:

for a three-dimensional cell which generates temperature change and bears unit load, the equivalent thermal expansion coefficient alpha in the directions of x, y and z axes_x、α_y、α_zComprises the following steps:

when three-dimensional structures with different Poisson ratios and thermal expansion coefficients are needed, the three-dimensional structures can be obtained by selecting different geometric parameters and material combinations of the triangular units and constructing according to the steps (1) to (3), and the corresponding Poisson ratios and the corresponding thermal expansion coefficients can be calculated by utilizing the equivalent formulas of the elastic parameters and the thermal expansion coefficients.

The above process can be implemented on a terminal device having a processor function, such as a desktop computer, a notebook computer, and the like.

In addition, the present embodiment also verifies the above equivalent formula through finite element data simulation. The numerical simulation used a cell type of BEAM189, setting a three-dimensional structure with 8 layers of cells in the x-axis and y-axis directions and 30 layers of cells in the z-axis direction. In the three materials of the triangular unit, the material parameters of iron are used for the first material and the second material, and the Young modulus, the Poisson ratio and the thermal expansion coefficient are respectively as follows: e₁＝E₂＝80.65GPa，ν₁＝ν₂＝0.29，α₁＝α₂＝1.22×10^-5V. C. The material III uses the material parameters of aluminum, and the Young modulus, the Poisson ratio and the thermal expansion coefficient are respectively as follows: e₃＝71.7GPa，ν₃＝0.33，α₃＝2.32×10^-5V. C. The cross-sectional area of three rods constituting the cell is taken as A₁＝A₂＝A₃＝1.5×1.5mm²。

Here, the numerical simulation is performed in two groups, the first group: let L₁＝30mm，L₂＝20mm，

Taking values of 60 degrees, 70 degrees, 80 degrees, 90 degrees, 100 degrees, 110 degrees and 120 degrees; second group: let L₂＝28mm，

Wherein k takes the values of 0.5, 0.5714, 0.9286, 1.1429, 1.3571, 1.5714, 1.7857 and 2. Poisson's ratio v of structure obtained through numerical simulation_xy、ν_xz、ν_zxModulus of elasticity E_x、E_zCoefficient of thermal expansion α_x、α_z。

And finally, comparing the numerical simulation result with a formula calculation result. Fig. 11 to 16 are graphs comparing the numerical simulation results with the analytical formula results, fig. 11 to 13 are the results of the first set of data, and fig. 14 to 16 are the results of the second set of data. Where NR represents the numerical simulation result and AR represents the analytical formula result. As can be seen from fig. 11 to 16, the numerical simulation result is substantially consistent with the calculation result of the formula, and thus, the equivalent formula of this embodiment can well predict the elastic parameter and the thermal expansion coefficient of the three-dimensional structure constructed by this embodiment, and the adjustment ranges of the poisson's ratio and the thermal expansion coefficient are relatively large, the adjustment mode is relatively simple, and the three-dimensional negative poisson's ratio and the bidirectional negative thermal expansion of the structure can be simultaneously realized only by combining reasonable geometric parameters and materials.

The present embodiment also performs parameter analysis based on the special three-dimensional structure, so that the special three-dimensional structure can be constructed based on the parameter combination obtained by the analysis.

For example, (I) when zero poisson's ratio design is required, it is possible to determine if zero poisson's ratio, if any, is equal to 90 ° or

Then (c) is performed. Therefore, when θ is 90 °, the following can be obtained:

data visualization when θ is 90 ° is shown in fig. 17-18, where the geometric parameters and material combinations are the same as the first set of numerical simulations, i.e., E₁＝E₂＝80.65GPa，E₃＝71.7GPa，L₁＝30mm，A₁＝A₂＝A₃＝1.5×1.5mm²。

Order to

The following can be obtained:

when in use

The data visualization is shown in fig. 19-20, where the geometric parameters and material combinations are the same as the numerical simulation first set, i.e., E₁＝E₂＝80.65GPa，E₃＝71.7GPa，

L₁＝30mm，A₁＝A₂＝A₃＝1.5×1.5mm²。

As can be seen from fig. 17 to 20, when θ is 90 °,

or

Theta is more than 0 and less than 17 DEG, v is more than-0.01_xy< 0, i.e. v_xy≈ν_xz＝ν_zxAnd (5) constructing a three-dimensional zero-Poisson ratio structure when the number is 0.

(II) when the zero thermal expansion design in the x-axis and y-axis directions needs to be carried out, let alpha_xThe conditions for achieving zero thermal expansion in the x-axis and y-axis directions are found to be 0:

finally, according to the formula (23), two special cases for realizing the zero thermal expansion of the three-dimensional structure in the x-axis direction and the y-axis direction are obtained:

handle

(in this case, the triangle unit is an isosceles triangle structure) is substituted into equation (23), and the following can be obtained:

handle

(in this case, the triangle is singleElement is a right triangle structure) into equation (23), it can be obtained:

therefore, when

Or

And meanwhile, a three-dimensional structure with zero thermal expansion coefficient in the directions of the x axis and the y axis can be constructed through corresponding material selection.

For example, numerical simulations are used here to simulate the material parameters α of the first group₁＝α₂＝1.22×10^-5/℃，α₃＝2.32×10^-5/. degree.C., alpha.can be obtained_x＜0、α_x＝0、α_xData visualization for > 0, as shown in FIG. 21, the abscissa of FIG. 21 is θ and the ordinate is

From FIG. 21, it is clear that_x＝0、α_x> 0 and alpha_xIn the case of < 0,

Size.

The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be equivalent replacement modes, and all are included in the scope of the present invention.

Claims (8)

1. A novel three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient is characterized in that the three-dimensional structure is composed of three-dimensional cell elements, each three-dimensional cell element is composed of four same parallelograms, each parallelogram is divided into two same triangular units, the longest rod and two oblique rods of each triangular unit respectively have corresponding rod lengths and are respectively composed of three materials, and the three-dimensional structures with different geometric parameters of the triangular units and material combinations have different elastic parameters and thermal expansion coefficients;

in the three-dimensional structure, three-dimensional cells are periodically arranged along the direction of one side of a parallelogram on the bottom surface of the three-dimensional cells as the left-right direction, and are repeatedly distributed in a mirror image manner along the front-back direction and the up-down direction which are perpendicular to the left-right direction.

2. The new three-dimensional structure with adjustable poisson's ratio and thermal expansion coefficient as claimed in claim 1, wherein the three-dimensional cell element has the same elasticity parameter and thermal expansion coefficient in the x-axis direction and the y-axis direction, the elasticity parameter includes young's modulus and poisson's ratio, wherein the x-axis and the y-axis are two coordinate axes of a cartesian coordinate system constructed by using the centroid of the three-dimensional cell element as the origin and one of the diagonal rods of one triangular unit on the bottom surface of the three-dimensional cell element as the z-axis, the y-axis is perpendicular to the z-axis on the horizontal plane, and the x-axis is perpendicular to the z-axis on the vertical plane.

3. The new three-dimensional structure with adjustable poisson's ratio and thermal expansion coefficient as claimed in claim 2, wherein for the two surfaces above and below the x-axis direction, the two surfaces above and below the y-axis direction and the two ends above and below the diagonal rod in the z-axis direction respectively carrying a certain displacement, the equivalent young's modulus is:

wherein E is_zIs the equivalent Young's modulus of the cell element in the z direction; e_xIs the equivalent Young's modulus of the cell element in the x direction; e_yIs the equivalent Young's modulus of the cell element in the y direction; taking an oblique rod as a z-axis as a first oblique rod, taking another oblique rod of the triangular unit as a second oblique rod, and N₂Is the axial force of the second diagonal;N₃is the axial force of the longest rod;

is the included angle of two diagonal rods; theta is an included angle between the longest rod and the first diagonal rod; u is the distance the parallelogram at the bottom of the cell moves forward along the x-axis; l is₁Is the length of the first diagonal rod; e₁Is the young's modulus of the first diagonal; a. the₁Four times the cross-sectional area of the first diagonal.

4. The novel three-dimensional structure with adjustable poisson's ratio and thermal expansion coefficient as claimed in claim 2, wherein for a cell with upper and lower surfaces in x-direction simultaneously bearing a certain displacement, the equivalent poisson's ratio in x-and y-axis directions and in x-and z-axis directions is:

wherein, v_xyIs the equivalent Poisson's ratio of the cell in the x and y directions; v is_xzIs the equivalent Poisson's ratio of the cell in the x and z directions; u is the distance the parallelogram at the bottom of the cell moves forward along the x-axis;

is the included angle of two diagonal rods; theta is an included angle between the longest rod and the first diagonal rod; v is the distance that the parallelogram connecting the upper and lower surfaces simultaneously moves in the forward direction along the y-axis; w is a_BThe distance is that the end points of two diagonal rods which are simultaneously connected in a parallelogram connecting an upper surface and a lower surface move along the negative direction of a z axis; w is a_AIs the distance of forward movement along the z-axis of the end point of the parallelogram connecting the longest rod and the second diagonal rod simultaneously in the parallelogram connecting the upper and lower surfaces.

5. The new three-dimensional structure with adjustable poisson's ratio and thermal expansion coefficient as claimed in claim 2, wherein for a cell with a certain displacement carried by two endpoints in the z-direction, the equivalent poisson's ratio in the z-and x-axis directions is:

ν_zxis the equivalent Poisson's ratio of the cell in the z and x axis directions;

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

6. The new three-dimensional structure with adjustable poisson's ratio and thermal expansion coefficient as claimed in claim 2, wherein the equivalent thermal expansion coefficient α in x, y and z directions for the three-dimensional cell with temperature variation and unit load bearing capability_x、α_y、α_zComprises the following steps:

wherein t is the variation of temperature; l is₃Is the length of the longest rod; delta_AVDisplacement of the load bearing end point due to temperature change; alpha is alpha₁Is the coefficient of thermal expansion of the first diagonal; alpha is alpha₂Is the coefficient of thermal expansion of the second diagonal; alpha is alpha₃Is the coefficient of thermal expansion of the longest rod;

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

7. The new three-dimensional structure with adjustable poisson's ratio and coefficient of thermal expansion as claimed in claim 2, wherein the new three-dimensional structure is made of

Or

The novel three-dimensional structure constructed by the three-dimensional cell is a three-dimensional structure with zero thermal expansion coefficient in the directions of an x axis and a y axis, wherein,

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

8. The new three-dimensional structure with adjustable poisson's ratio and coefficient of thermal expansion as claimed in claim 1, wherein the structure is formed by a number θ -90 °,

or

The novel three-dimensional structure constructed by the three-dimensional cell elements with the angle of more than 0 and less than 17 degrees is a three-dimensional zero Poisson ratio structure, wherein,

is the included angle of two diagonal rods; theta is the angle between the longest rod and the first diagonal rod.

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