CN111720467B - Lattice structure with stable zero Poisson ratio in large deformation state - Google Patents
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- 239000007787 solid Substances 0.000 claims description 5
- 230000001105 regulatory effect Effects 0.000 abstract description 2
- 239000000463 material Substances 0.000 description 27
- 230000006835 compression Effects 0.000 description 4
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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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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F2224/00—Materials; Material properties
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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
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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
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Abstract
The invention provides a lattice structure with stable zero Poisson's ratio in a large deformation state, which is formed by periodically arranging a lattice unit cell in a three-dimensional rectangular coordinate system along X, Y, Z directions; the unit cells are kept unchanged during the arrangement process, and the step pitch of the periodic arrangement is controlled by the unit cellsDetermining the size; when copying along the X direction and the Z direction, the step length is 2N +2L2(ii) a When copying along the Y direction, the step length is H; the number of the unit cells arranged periodically is determined according to the requirements of practical application. The lattice structure unit cell has good designability, the Poisson ratio performance can be regulated and controlled by designing the geometric parameters of the curved rod, and the lattice structure design capable of keeping stable Poisson ratio under the large deformation working condition is obtained.
Description
Technical Field
The invention relates to a lattice structure with stable zero Poisson's ratio under a large deformation state.
Background
With the development of engineering technology, various industries have put higher and higher requirements on the light weight and the multifunctionality of the structure. The variant aircraft has the advantages of strong flexibility, large flight envelope range and the like. The appearance of lattice structure materials provides a good foundation for the development of variant aircrafts. The lattice structure material has high porosity, high specific rigidity and specific strength, is easy to bury functional components, and is a novel structure material integrating the functions of light weight, high strength, heat insulation, energy absorption and the like. Dawn Bo, Huangjian, et al, at Harbin university, have studied the application of lattice structures in morphing aircraft. The dawn proposes a honeycomb lattice support structure with zero Poisson's ratio effect and an air pressure driving method of the structure in the research on variable-camber wing structures based on variable-stiffness skins and zero Poisson' ratio honeycombs. Zhang provides an arrow type negative Poisson ratio lattice structure for an automobile energy absorption box in axial compression performance research of a three-dimensional negative Poisson ratio multi-cell structure. Patent CN201710613345.8 discloses a three-dimensional controllable auxetic cellular structure based on 3D printing, which can adjust the elastic property of cellular material by changing the slenderness ratio and inclination angle of the rod. Patent CN201710231278.3 "a lattice material with functional gradient" discloses a lattice material with functional gradient, whose physical parameters can be changed in gradient with spatial position, and has strong designability. Patent CN201710609587.X discloses a lattice material with gradient negative Poisson ratio characteristics, wherein a unit cell is a negative Poisson ratio structure formed by reversely bent wire rods with constantly-changed sizes and shapes, and physical parameters such as elastic modulus, Poisson ratio, density and the like of the lattice material are in gradient change along with spatial positions.
Most materials in nature have a positive Poisson ratio value, and a zero Poisson ratio structural material means that the transverse dimension of the material is not changed when the material is unidirectionally pulled or pressed. The zero Poisson ratio lattice structure is applied to the fields of flexible skin of an aircraft, biological supports, deep-sea pressure-resistant structure design and the like. However, the poisson ratio and the mechanical property of many functional poisson ratio structures at present can change along with the deformation degree, and the unstable property makes the poisson ratio and the mechanical property difficult to popularize and apply in practical scenes. Therefore, a lattice structure capable of keeping a stable Poisson ratio in a large deformation state is provided, and the application range of the lattice structure can be expanded to a great extent.
Disclosure of Invention
The invention provides a structured lattice material with stable zero Poisson's ratio under a large deformation state. The whole lattice structure is formed by periodically arranging lattice unit cells along X, Y, Z three directions in a three-dimensional rectangular coordinate system; the shape of the unit cell remains unchanged during the alignment process, and the step pitch of the periodic alignment is determined by the unit cell size. The unit cell is circularly symmetrical, a plane axial symmetry figure on an XOY plane is stretched by a thickness b along a Z axis to form a three-dimensional solid structure, and then the structure is rotated by 90 degrees around the symmetry axis of the structure to be copied. The unit cell is composed of a straight rod and a curved rod, the curved rod is formed by connecting two arcs with opposite curvature directions, and the tangent slopes at the connecting points are the same. The lattice structure may be manufactured by means of 3D printing. The relative density, equivalent elastic modulus, equivalent Poisson's ratio and other performance parameters of the lattice structure can be designed by regulating and controlling the size of the single cell parameter, and the stable zero Poisson's ratio performance can be still maintained under the large deformation state.
The technical scheme of the invention is as follows:
a lattice structure with stable zero Poisson's ratio under large deformation state is formed by periodically arranging a lattice unit cell along X, Y, Z three directions in a three-dimensional rectangular coordinate system; the unit cells are kept unchanged in the arrangement process, and the step pitch of periodic arrangement is determined by the size of the unit cells; when copying along the X direction and the Z direction, the step length is 2N +2L2(ii) a When copying along the Y direction, the step length is H; the number of the periodically arranged unit cells is determined according to the actual application requirement;
the lattice unit cells are circularly symmetrical and are composed of straight rods and curved rods; stretching a plane axisymmetric graph on an XOY plane by a width b along a Z axis to form a three-dimensional solid structure, and then rotating the three-dimensional solid structure by 90 degrees around the symmetric axis to copy to form a three-dimensional lattice unit cell;
lattice unit cells contain the following parameters: the length of the cell wall is L1The included angle of the unit cell is theta, the length of the transverse cell wall is N, the height of the unit cell is H, the distance between the head and the tail of the curved rod part in the Y direction is M, and the distance between the head and the tail of the curved rod part in the X direction is L2The length of the outer horizontal short rod is N/2, and the thickness of the cell element is T; the shape of the curved bar part is formed by connecting two arcs with opposite curvature directions, and the slopes of the arcs at the connecting points are the same; the radius of the circular arc is R,
the point D is the intersection point of the two arcs, and the slope of the tangent lines of the two arcs at the point D is the same according to the geometric relation; structural parameter L1、L2θ, H, M are not independent of each other, but satisfy the relationship: l is2 2+M2＝L1 2+H2-2HL1cos θ and L2 2+(H+M)2＝L1 2The other two parameters are known to be solved for three parameters.
The invention has the following beneficial results:
(1) the invention designs a structured lattice material with stable zero Poisson's ratio under large deformation.
(2) The invention realizes the geometric parameter regulation design of the mechanical property of the structured lattice material.
(3) The zero-Poisson ratio structured lattice material provided by the invention can ensure the stability of the Poisson ratio under the condition of limited deformation in the working condition.
(4) The structured material of the invention has simple structure, convenient manufacture and easy realization of the result.
Drawings
FIG. 1 is a schematic overall view of a structured lattice material with a stable zero Poisson's ratio under large deformation.
FIG. 2 is a schematic diagram of a structured lattice material unit cell with stable zero Poisson's ratio under large deformation.
FIG. 3 is a schematic diagram of the two-dimensional planar characteristic parameters of a structured lattice material unit cell with stable zero Poisson's ratio under large deformation.
FIG. 4 is a graph of the theoretical results of the relationship between the relative density and the structural parameters of a structured lattice material with a stable zero Poisson's ratio under large deformation. Wherein (a) is and L1The relationship (b) is related to T, (c) is related to N, (d) is related to R, (e) is related to H, and (f) is related to theta.
FIG. 5 is a graph of the simulation result of the relationship between the equivalent Poisson's ratio and the structural parameters of a structured lattice material with a stable zero Poisson's ratio under large deformation. Wherein (a) is and L1The relationship (b) is related to T, (c) is related to N, (d) is related to R, (e) is related to H, and (f) is related to theta.
FIG. 6 is a graph of simulation results of the relationship between the equivalent Poisson's ratio and the compression distance of a structured lattice material with a stable zero Poisson's ratio under large deformation.
Detailed Description
A structured lattice material with stable zero Poisson's ratio under large deformation is shown in figure 1, the whole lattice structure is formed by periodically arranging a lattice unit cell along X, Y, Z directions in a three-dimensional rectangular coordinate system, and the shape of the unit cell is kept unchanged during the arrangement process. With reference to fig. 3, the projection of the unit cell of the lattice structure on the XOY plane is circularly symmetric, and the two-dimensional configuration characteristics thereof include the following parameters: the length of the cell wall is L1The included angle between the cell wall and the vertical direction is theta, twoThe length of the horizontal long rods is N, the unit cell height, namely the distance between the two horizontal long rods, is H, the distance between the head and the tail of the curved rod part in the Y direction is M, and the distance between the head and the tail of the curved rod part in the X direction is L2The length of the outer horizontal short rod is N/2, and the thickness of the whole unit cell is T. The shape of the curved bar part is composed of two arcs with the same shape, the radius of the arc is R,
on the left side of the symmetry axis, two sections of connected arcs along the positive direction of the X are concave first and then convex. Structural parameter L1、L2θ, H, M satisfy the relationship: l is2 2+M2＝L1 2+H2-2HL1cos θ and L2 2+(H+M)2＝L1 2Knowing the three parameters, the other two parameters can be found. With reference to fig. 2 and fig. 3, the two-dimensional design configuration of the unit cell on the XOY plane is stretched by the thickness b along the Z axis, and then the formed structure is copied by rotating 90 degrees around the symmetrical axis, so that the two-dimensional lattice unit cell becomes a three-dimensional lattice unit cell. When the unit cell is copied along the X direction and the Z direction, the step length is 2N +2L2(ii) a When copying in the Y direction, the step size is H. The number of copied unit cells is determined according to the requirements of practical application.
A stable zero poisson ratio lattice structure can be through 3D printing mode integrated into one piece, material saving.
In order to make the technical solution and advantages of the present invention clearer, the present invention will be described in detail and fully with reference to the accompanying drawings and embodiment examples, which are a part of the examples of the present invention and not all of the examples.
The relative density of a stable zero-poisson's ratio lattice structure can be parametrically expressed as:
in combination with fig. 4, it can be predicted from the theoretical formula of relative density that the relative density of two-dimensional and three-dimensional lattice structures changes with one of the parameters under the condition that five of the six structural parameters are kept unchanged. The parameters are respectively set to L150mm, 0.5mm, 10mm, 6.3mm, 29mm, 20 ° θ. FIG. 4(a)
In FIG. 4(b)
In FIG. 4(c)
In FIG. 4(d)
In FIG. 4(e)
In FIG. 4(f)
The relative density of the zero Poisson ratio lattice structure can be designed by changing the size of the unit cell parameter according to the actual requirement.
The estimation of the equivalent Poisson's ratio and the Poisson's ratio performance prediction under large deformation are both carried out by adopting a finite element method, and the technical scheme of the invention is exemplarily explained by specific implementation examples.
Materials for the examples:
carbon short fiber reinforced polylactic acid with density of 1450kg/m3Young's modulus 80GPa and Poisson's ratio 0.35.
Implementation example structure dimensions:
finite element analysis is carried out on the novel zero Poisson ratio two-dimensional structure, the model structure is shown in figure 3, line body modeling is adopted, the beam unit is divided into grids, and the length L of the cell wall1＝50mm，The cell thickness T is 0.5mm, the transverse cell wall length N is 10mm, the circular arc radius R is 6.3mm, the cell height H is 29mm, and the cell angle θ is 20 °. And when the influence rule of one parameter on the structure equivalent Poisson ratio performance is researched, keeping the other five parameters to be the values. The simulation analysis used a 6X 6 lattice structure, i.e. 6 cells were arrayed in both the X and Y directions, as shown in fig. 1.
Model constraints and stress conditions: regardless of geometric non-linearity, the beam cell grid size is 1 mm. And all the degrees of freedom of the bottom surface of the structure are limited, and the top surfaces of 6 unit cells apply compression displacement with the size of 1mm in the Y direction.
Numerical simulations were performed using the above materials and structure dimensions, and the equivalent poisson's ratio of the structure is represented by the deformation of the middle two sets of unit cells, with the results shown in fig. 5. FIG. 5(a)
In FIG. 5(b)
In FIG. 5(c)
In FIG. 5(d)
FIG. 5(e)
In FIG. 5(f)
As can be seen from the figure, the equivalent Poisson's ratio of the structure of the invention can be changed along with the change of the structural parameters, namely, the design of the equivalent Poisson's ratio of the structure can be realized by changing the structural parameters.
Considering the geometric non-linearity, the grid size is 1mm, limiting all degrees of freedom of the structure bottom surface, 6 cell top surfaces impose the-Y direction, giving a compressive displacement of increasing size from 1mm to 7 mm. The results of the change of the novel zero-poisson-ratio lattice structure and the common arrow-type negative-poisson-ratio lattice structure along with the compression amount under large deformation are compared as shown in fig. 6. As can be seen from FIG. 6, the lattice structure of the present invention has stable zero Poisson's ratio performance, and is more suitable for practical engineering.
Claims (1)
1. A lattice structure with stable zero Poisson's ratio under large deformation state is characterized in that the lattice structure is formed by periodically arranging a lattice unit cell along X, Y, Z three directions in a three-dimensional rectangular coordinate system; the unit cells are kept unchanged in the arrangement process, and the step pitch of periodic arrangement is determined by the size of the unit cells; when copying along the X direction and the Z direction, the step length is 2N +2L2(ii) a When copying along the Y direction, the step length is H; the number of the periodically arranged unit cells is determined according to the actual application requirement;
the lattice unit cells are circularly symmetrical and are composed of straight rods and curved rods; stretching a plane axisymmetric graph on an XOY plane by a width b along a Z axis to form a three-dimensional solid structure, and then rotating the three-dimensional solid structure by 90 degrees around the symmetric axis to copy to form a three-dimensional lattice unit cell;
lattice unit cells contain the following parameters: the length of the cell wall is L1The included angle of the unit cell is theta, the length of the transverse cell wall is N, the height of the unit cell is H, the distance between the head and the tail of the curved rod part in the Y direction is M, and the distance between the head and the tail of the curved rod part in the X direction is L2The length of the outer horizontal short rod is N/2, and the thickness of the cell element is T; the shape of the curved bar part is formed by connecting two arcs with opposite curvature directions, and the slopes of the arcs at the connecting points are the same; the radius of the circular arc is R,
the point D is the intersection point of the two arcs, and the slope of the tangent lines of the two arcs at the point D is the same according to the geometric relation; structural parameter L1、L2θ, H, M are not independent of each other, but satisfy the relationship: l is2 2+M2＝L1 2+H2-2HL1cos θ and L2 2+(H+M)2＝L1 2The other two parameters are known to be solved for three parameters.
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| CN112800553B (en) * | 2021-01-04 | 2024-01-30 | 中国科学院力学研究所 | Multi-stage controllable progressive energy-absorbing lattice structure |
| KR102357704B1 (en) * | 2021-03-30 | 2022-02-08 | 성균관대학교산학협력단 | A zero Poisson's ratio structure and a planar structure of zero Poisson's ratio in which the structure is matrixed in a plane |
| CN113103638B (en) * | 2021-04-22 | 2022-01-18 | 大连理工大学 | Zero Poisson ratio honeycomb structure and interlocking assembly manufacturing method thereof |
| CN114005426B (en) * | 2021-10-12 | 2024-06-18 | 武汉理工大学 | Five-mode material structure with arbitrary curved edges |
| CN114263697B (en) * | 2021-11-30 | 2022-11-01 | 大连理工大学 | Recoverable multi-step deformation buffering energy-absorbing metamaterial structure |
| CN114880791B (en) * | 2022-04-13 | 2023-11-03 | 汕头大学 | Chiral multicellular structure unit, assembly and intelligent construction method |
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| GB2514074A (en) * | 2011-09-06 | 2014-11-19 | Univ Malta | Stents with zero poisson's ratio cells |
| CN107023074B (en) * | 2017-04-10 | 2019-03-05 | 东南大学 | A kind of lattice material with functionally gradient |
| CN107401218B (en) * | 2017-07-25 | 2019-02-05 | 东南大学 | A kind of lattice material with gradient negative poisson's ratio characteristic |
| CN108170977A (en) * | 2018-01-11 | 2018-06-15 | 南京大学 | A kind of adjustable three-dimensional backhand negative poisson's ratio structure and preparation method |
| CN110541906B (en) * | 2019-08-06 | 2021-02-09 | 哈尔滨工业大学（威海） | Double-arrow type negative Poisson ratio structure body |
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