CN114909419A - Single cell structure and zero Poisson ratio honeycomb structure - Google Patents
Single cell structure and zero Poisson ratio honeycomb structure Download PDFInfo
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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
- F16F7/121—Vibration-dampers; Shock-absorbers using plastic deformation of members the members having a cellular, e.g. honeycomb, structure
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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
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Abstract
The invention discloses a unit cell structure and a zero Poisson ratio honeycomb structure, wherein the unit cell structure comprises a first horizontal wall, a first inclined wall, a first vertical wall, a second inclined wall, a second horizontal wall, a third inclined wall, a second vertical wall and a fourth inclined wall which are sequentially connected end to end, and a closed shape in an antisymmetric octagon shape is formed; the anti-symmetric octagonal closed shape comprising the first vertical wall and the second vertical wall ensures that the unit cell structure has lower rigidity and has better deformability on the premise of ensuring the zero Poisson's ratio characteristic. The unit cell structure further comprises a first horizontal extension wall connected with the intersection point of the first horizontal wall and the first inclined wall and a second horizontal extension wall connected with the intersection point of the second inclined wall and the second horizontal wall, and when the unit cell structure array forms a honeycomb structure, the first horizontal extension wall and the second horizontal extension wall serve as connecting media to improve the connection mode of points and points between the unit cell structures, so that the honeycomb structure is more convenient to assemble, and meanwhile, the in-plane bending deformation capability of the whole structure is improved.
Description
Technical Field
The invention relates to the technical field of metamaterials, in particular to a single cell structure and a zero Poisson ratio honeycomb structure.
Background
The metamaterial refers to an artificial composite structure or material with extraordinary physical properties which are not possessed by natural materials, and the metamaterial has excellent mechanical properties, so that the metamaterial is widely applied to the fields of automobiles, aerospace, packaging engineering and the like. The main extraordinary physical property of the auxetic metamaterial is that the auxetic metamaterial is provided with an extraordinary Poisson ratio effect. Poisson's ratio is a basic mechanical property of a material, and the property of a reaction material that deforms perpendicular to the direction of a load when subjected to a uniaxial load. The poisson's ratio of most materials is generally positive, so-called extraordinary poisson's ratio, which includes negative poisson's ratio and zero poisson's ratio. The negative Poisson ratio metamaterial transversely contracts (expands) under uniaxial compression (tension), and has special mechanical properties in the aspects of energy absorption, impact resistance and shear resistance. However, in the fields of medical devices, sensors, protective devices, soft robots and the like, unidirectional deformation of zero poisson's ratio cellular metamaterials is required, i.e. no transverse contraction occurs under uniaxial compression.
The zero Poisson ratio metamaterial in the related art generally has the following problems: 1. the existing single cell structure and zero Poisson ratio honeycomb structure have obvious stress concentration problem; 2. the unit structure is complex, and certain difficulty exists in preparation; 3. the traditional zero-Poisson ratio honeycomb structure is a two-dimensional topological structure, and the in-plane tensile rigidity, the out-of-plane flat compression rigidity and the transverse shear rigidity are reduced while the external deformation capacity of the structure is increased.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a single cell structure and a zero-Poisson ratio honeycomb structure, which have simple structure and convenient preparation, and the whole structure has better deformability while keeping stable zero-Poisson ratio characteristic.
In one aspect, an embodiment of the present invention provides a unit cell structure, including a first horizontal wall, a second horizontal wall, a first inclined wall, a second inclined wall, a third inclined wall, a fourth inclined wall, a first vertical wall, a second vertical wall, a first horizontally extending wall, and a second horizontally extending wall, where the first horizontal wall, the first inclined wall, the first vertical wall, the second inclined wall, the second horizontal wall, the third inclined wall, the second vertical wall, and the fourth inclined wall are sequentially connected end to form a closed shape, and the closed shape is an inverse symmetric octagon;
the first horizontally extending wall is connected with the intersection point of the first horizontal wall and the first inclined wall, the second horizontally extending wall is connected with the intersection point of the second inclined wall and the second horizontal wall, the first horizontally extending wall and the first horizontal wall are located on the same straight line, and the second horizontally extending wall and the second horizontal wall are located on the same straight line;
the first horizontal wall and the second horizontal wall are parallel to each other, the first vertical wall and the second vertical wall are parallel to each other, the first sloped wall and the fourth sloped wall are parallel to each other, the second sloped wall and the third sloped wall are parallel to each other, and the first horizontal wall and the first vertical wall are perpendicular to each other;
the first inclined wall, the second inclined wall, the third inclined wall and the fourth inclined wall are equal in length, the first horizontal wall and the second horizontal wall are equal in length, the first vertical wall and the second vertical wall are equal in length, and the first horizontally extending wall and the second horizontally extending wall are equal in length.
The unit cell structure provided by the embodiment of the invention at least has the following beneficial effects: the unit cell structure comprises a first horizontal wall, a first inclined wall, a first vertical wall, a second inclined wall, a second horizontal wall, a third inclined wall, a second vertical wall and a fourth inclined wall which are sequentially connected end to end, and a closed shape in the shape of an antisymmetric octagon is formed, wherein the first horizontal wall and the second horizontal wall are parallel to each other and have the same length, the first vertical wall and the second vertical wall are parallel to each other and have the same length, and the first horizontal wall and the first vertical wall are perpendicular to each other; the unit cell structure has smaller rigidity due to the antisymmetric octagonal closed shape comprising the first vertical wall and the second vertical wall, and the structure has better deformability on the premise of ensuring the zero Poisson ratio characteristic. In addition, the unit cell structure further comprises a first horizontally extending wall connected with the intersection point of the first horizontal wall and the first inclined wall and a second horizontally extending wall connected with the intersection point of the second inclined wall and the second horizontal wall; when the first horizontal extension wall and the second horizontal extension wall form the honeycomb structure in the unit cell structure array, the first horizontal extension wall and the second horizontal extension wall serve as connecting media to improve the connection mode of points between the unit cell structures, so that the honeycomb structure is more convenient to assemble, and the in-plane bending deformation capability of the whole structure is improved.
According to some embodiments of the present invention, a junction of the first horizontal wall and the first inclined wall, a junction of the first inclined wall and the first vertical wall, a junction of the first vertical wall and the second inclined wall, a junction of the second inclined wall and the second horizontal wall, a junction of the second horizontal wall and the third inclined wall, and a junction of the third inclined wall and the second vertical wall, where a junction of the second vertical wall and the fourth inclined wall, a junction of the fourth inclined wall and the first horizontal wall, a junction of the first horizontally extending wall and the first inclined wall, and a junction of the second horizontally extending wall and the second inclined wall are all provided with a chamfer structure.
According to some embodiments of the invention, the wall thickness of the first horizontal wall, the second horizontal wall, the first sloped wall, the second sloped wall, the third sloped wall, the fourth sloped wall, the first vertical wall, the second vertical wall, the first horizontally extending wall, and the second horizontally extending wall are all the same.
According to some embodiments of the invention, the first horizontal wall, the second horizontal wall, the first sloped wall, the second sloped wall, the third sloped wall, the fourth sloped wall, the first vertical wall, the second vertical wall, the first horizontally extending wall, and the second horizontally extending wall each have a wall thickness of 2 mm.
According to some embodiments of the invention, the unit cell structure has a thickness of 5 mm.
According to some embodiments of the invention, the first horizontal wall and the first sloped wall are equal in length, the first horizontally extending wall is half the length of the first sloped wall, and the first vertical wall is half the length of the first sloped wall.
According to some embodiments of the invention, the first sloped wall has a length of 10 mm.
On the other hand, the embodiment of the present invention further provides a zero poisson ratio honeycomb structure, which includes the unit cell structure described in the above aspect, and the zero poisson ratio honeycomb structure is formed by repeatedly arranging a plurality of unit cell structures along the direction of the first horizontal wall and the direction of the first vertical wall, wherein,
when the unit cell structures are repeatedly arranged along the direction of the first horizontal wall, the first horizontal extension wall of the next unit cell structure is connected with the intersection point of the first horizontal wall and the fourth inclined wall of the previous unit cell structure; the second horizontal extension wall of the next unit cell structure is connected with the intersection point of the second horizontal wall and the third inclined wall of the previous unit cell structure;
when the unit cell structures are repeatedly arranged along the direction of the first vertical wall, the first horizontal wall of the next unit cell structure is attached to the second horizontal wall of the previous unit cell structure in parallel, and the first horizontal extension wall of the next unit cell structure is attached to the second horizontal extension wall of the previous unit cell structure in parallel.
The zero-Poisson ratio honeycomb structure provided by the embodiment of the invention at least has the following beneficial effects: the zero Poisson ratio honeycomb structure is formed by repeatedly arranging unit cell structures along the direction of the first horizontal wall and the direction of the first vertical wall, wherein the first horizontal extension wall of the next unit cell structure is connected with the intersection point of the first horizontal wall and the fourth inclined wall of the previous unit cell structure, and the second horizontal extension wall is connected with the intersection point of the second horizontal wall and the third inclined wall of the previous unit cell structure; the first horizontal wall of the next unit cell structure is attached to the second horizontal wall of the previous unit cell structure in parallel, and the first horizontal extension wall is attached to the second horizontal extension wall of the previous unit cell structure in parallel; the array connection mode of the unit cell structure improves the limit of the point-to-point connection mode on the in-plane bending deformation capacity of the honeycomb structure, and simultaneously reduces the complexity of the whole structure, so that the structure is more convenient to assemble.
According to some embodiments of the invention, the zero-poisson-ratio honeycomb structure has 5 of the unit cell structures connected in sequence in each row in the direction of the first horizontal wall, and the zero-poisson-ratio honeycomb structure has 5 of the unit cell structures connected in sequence in each row in the direction of the first vertical wall.
According to some embodiments of the invention, the zero poisson's ratio honeycomb structure is prepared by a 3D printing process.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a diagram of a conventional cell structure and its stressed deformation according to an embodiment of the present invention;
FIG. 2 is a schematic plan view of a unit cell structure according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the unit cell structure deformation under stress according to an embodiment of the present invention;
FIG. 4 is a perspective view of a unit cell structure provided in an embodiment of the present invention;
FIG. 5 is a perspective view of a single cell structure provided with chamfers according to an embodiment of the present invention;
FIG. 6 is a schematic plan view of a zero Poisson's ratio honeycomb structure provided by an embodiment of the present invention;
fig. 7 is a schematic diagram of the in-plane stability of a zero poisson's ratio honeycomb structure provided by the embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating the parameterization of unit cell structure size according to the embodiment of the present invention;
fig. 9 is a schematic diagram of a theoretical calculation model of the equivalent elastic modulus in the Y direction according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of a theoretical calculation model of equivalent elastic modulus in the X direction according to an embodiment of the present invention;
FIG. 11 is a schematic diagram of a theoretical calculation model of in-plane shear modulus according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of a simplified model of theoretical calculation of in-plane shear modulus according to an embodiment of the present invention;
FIG. 13 is a graph illustrating the effect of the declination angle θ of the sloped wall on the equivalent elastic modulus in the X direction at different first horizontal wall lengths α L according to an embodiment of the present invention;
FIG. 14 is a graph illustrating the effect of the slope angle θ of the sloped wall on the equivalent elastic modulus in the X direction at different wall thicknesses t according to an embodiment of the present invention;
FIG. 15 is a graph illustrating the effect of the slope angle θ of the sloped wall on the equivalent elastic modulus in the Y direction at different wall thicknesses t according to an embodiment of the present invention;
FIG. 16 is a graph illustrating the effect of the slope angle θ on the equivalent elastic modulus across a surface at different first horizontal wall lengths α L for a sloped wall according to an embodiment of the present invention;
FIG. 17 is a graph illustrating the effect of skew angle θ on the equivalent elastic modulus across a surface at different wall thicknesses t according to an embodiment of the present invention.
Reference numerals: a first horizontal wall 1, a second horizontal wall 2, a first inclined wall 3, a second inclined wall 4, a third inclined wall 5, a fourth inclined wall 6, a first vertical wall 7, a second vertical wall 8, a first horizontally extending wall 9, a second horizontally extending wall 10.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention and are not to be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. The terms first, second and the like in the description and in the claims, and the drawings described above, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, unless explicitly defined otherwise, terms such as set, mounted, connected, etc., should be interpreted broadly, such as a fixed connection or a movable connection, and may be a detachable connection or a non-detachable connection, or an integral connection; either directly or indirectly through intervening media, or through both elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
Fig. 1 shows a conventional unit cell structure and a schematic diagram of a stressed deformation thereof, an embodiment of the present invention provides a new unit cell structure and a zero poisson ratio honeycomb structure, fig. 2 shows a schematic diagram of a plane structure of the unit cell structure provided by the embodiment of the present invention, and referring to fig. 2, the unit cell structure includes a first horizontal wall 1, a second horizontal wall 2, a first inclined wall 3, a second inclined wall 4, a third inclined wall 5, a fourth inclined wall 6, a first vertical wall 7, a second vertical wall 8, a first horizontally extending wall 9, and a second horizontally extending wall 10, wherein the first horizontal wall 1, the first inclined wall 3, the first vertical wall 7, the second inclined wall 4, the second horizontal wall 2, the third inclined wall 5, the second vertical wall 8, and the fourth inclined wall 6 are sequentially connected end to form a closed shape. The first horizontally extending wall 9 is connected with the intersection point of the first horizontal wall 1 and the first inclined wall 3, the second horizontally extending wall 10 is connected with the intersection point of the second inclined wall 4 and the second horizontal wall 2, the first horizontally extending wall 9 and the first horizontal wall 1 are positioned on the same straight line, and the second horizontally extending wall 10 and the second horizontal wall 2 are positioned on the same straight line. The first horizontal wall 1 and the second horizontal wall 2 are parallel to each other, the first vertical wall 7 and the second vertical wall 8 are parallel to each other, the first inclined wall 3 and the fourth inclined wall 6 are parallel to each other, the second inclined wall 4 and the third inclined wall 5 are parallel to each other, and the first horizontal wall 1 and the first vertical wall 7 are perpendicular to each other. The first inclined wall 3, the second inclined wall 4, the third inclined wall 5 and the fourth inclined wall 6 are equal in length, the first horizontal wall 1 and the second horizontal wall 2 are equal in length, the first vertical wall 7 and the second vertical wall 8 are equal in length, and the first horizontally extending wall 9 and the second horizontally extending wall 10 are equal in length.
Referring to fig. 2, a closed shape formed by sequentially connecting a first horizontal wall 1, a first inclined wall 3, a first vertical wall 7, a second inclined wall 4, a second horizontal wall 2, a third inclined wall 5, a second vertical wall 8 and a fourth inclined wall 6 end to end is an octagon, wherein the first inclined wall, the first vertical wall and the second inclined wall form a first side of the octagon, and the third inclined wall, the second vertical wall and the fourth inclined wall form a second side of the octagon. For a conventional symmetrical octagon, the first and second sides should project to opposite sides and be symmetrical to each other with respect to a perpendicular bisector of the first and second horizontal walls, whereas in the present application, the first and second sides project to the same side, forming a sealing shape in the form of an anti-symmetrical octagon.
Fig. 3 shows a schematic diagram of the unit cell structure stressed deformation of the present application, and fig. 1 shows a schematic diagram of the traditional hexagonal unit cell structure stressed deformation, wherein the outline marked by the dotted line is the deformation trend of the unit cell structure after being pressed. This application has reduced the holistic rigidity of single cell structure through introducing first vertical wall 7 and second vertical wall 8, consequently under the same load, compares with traditional hexagon single cell structure, and this single cell structure has better deformability, can satisfy bigger deformation demand.
Further, in some embodiments, the wall thicknesses of the first horizontal wall 1, the second horizontal wall 2, the first sloped wall 3, the second sloped wall 4, the third sloped wall 5, the fourth sloped wall 6, the first vertical wall 7, the second vertical wall 8, the first horizontally extending wall 9, and the second horizontally extending wall 10 in the unit cell structure are designed to be the same value. For example, in an embodiment of the present application, the wall thickness of each wall is 2mm, and in other embodiments, the wall thickness of each wall may be designed to be other values such as 1mm or 3mm, which is not limited herein. Besides, in other embodiments, the wall thickness of each wall can be designed to be different values according to needs, for example, the first horizontal wall 1, the second horizontal wall 2, the first horizontally extending wall 9 and the second horizontally extending wall 10 are designed to be the same first wall thickness, the first inclined wall 3, the first vertical wall 7, the second inclined wall 4, the third inclined wall 5, the second vertical wall 8 and the fourth inclined wall 6 are designed to be the same second wall thickness, and the first wall thickness and the second wall thickness can be different, which is not listed herein.
Fig. 4 is a perspective view of a unit cell structure provided in the embodiment of the present application, and referring to fig. 4, the unit cell structure extends along a direction perpendicular to the plane of fig. 2 (i.e., along the Z direction in the figure) to obtain a thickness of the unit cell structure, and the thickness of the unit cell structure is denoted by b. By way of example, in one embodiment of the present application, the thickness of the unit cell structure is 5mm, and in other embodiments, the thickness of the unit cell structure may also be other values such as 6mm, 10mm, and so on, which is not limited herein.
The zero-Poisson ratio honeycomb structure provided by the application is formed by repeatedly arranging a plurality of unit cell structures along the direction of the first horizontal wall 1 and the direction of the first vertical wall 7. Fig. 6 shows a schematic plan view of a zero poisson ratio honeycomb structure provided in the embodiment of the present application, and referring to fig. 6, a direction of the first horizontal wall 1 is marked as an X direction, a direction of the first vertical wall 7 is marked as a Y direction, and a plurality of unit cell structures are sequentially connected along the X direction and the Y direction respectively and repeatedly arranged to form the zero poisson ratio honeycomb structure. By way of example, in one embodiment of the present application, the scale of the zero poisson's ratio honeycomb structure is 5 × 5, that is, 5 cell structures are connected in sequence in each row along the direction of the first horizontal wall 1 (i.e., the X direction), and 5 cell structures are connected in sequence in each row along the direction of the first vertical wall 7 (i.e., the Y direction).
When the unit cell structures are repeatedly arranged along the direction of the first horizontal wall 1, that is, along the X direction, the connection mode of the front and rear unit cell structures is as follows: the first horizontal extension wall 9 of the next unit cell structure is connected with the intersection point of the first horizontal wall 1 of the previous unit cell structure and the fourth inclined wall 6, and the second horizontal extension wall 10 of the next unit cell structure is connected with the intersection point of the second horizontal wall 2 of the previous unit cell structure and the third inclined wall 5; after the front unit cell structure and the rear unit cell structure are connected, a fourth inclined wall 6 of the front unit cell structure is parallel to a first inclined wall 3 of the rear unit cell structure, a second vertical wall 8 of the front unit cell structure is parallel to a first vertical wall 7 of the rear unit cell structure, and a third inclined wall 5 of the front unit cell structure is parallel to a second inclined wall 4 of the rear unit cell structure. When the unit cell structures are repeatedly arranged along the direction of the first vertical wall 7, namely, along the Y direction, the connection mode of the front unit cell structure and the rear unit cell structure is as follows: the first horizontal wall 1 of the next unit cell structure is attached to the second horizontal wall 2 of the previous unit cell structure in parallel, and the first horizontal extension wall 9 of the next unit cell structure is attached to the second horizontal extension wall 10 of the previous unit cell structure in parallel.
The unit cell structures of the traditional honeycomb structure are generally connected in a point-to-point mode, the connection mode is weak, and the integral deformability of the honeycomb structure is influenced. In the zero-Poisson ratio honeycomb structure, the arrangement of the unit cell structures in the Y direction is the connection between the edges, the connection mode improves the limit of the point-point connection mode on the in-plane bending deformation capacity, and simultaneously reduces the complexity of the whole structure, so that the structure assembly is more convenient. In addition, referring to fig. 6, the unit cell structure of the present application is provided with a first horizontally extending wall 9 and a second horizontally extending wall 10 in the X direction, so that the fourth inclined wall 6, the second vertical wall 8, and the third inclined wall 5 of the previous unit cell structure in the honeycomb structure after the array are sequentially connected end to end with the second horizontally extending wall 10, the second inclined wall 4, the first vertical wall 7, the first inclined wall 3, and the first horizontally extending wall 9 of the next unit cell structure, and a closed shape with an inverse symmetrical octagon shape is formed again. The antisymmetric octagon closed shapes formed between the previous unit cell structure and the next unit cell structure and the antisymmetric octagon closed shapes contained in the unit cell structure are sequentially arranged at intervals on the X axis, so that the whole structure is simpler and more regular.
In the stress deformation process of the zero-Poisson ratio honeycomb structure, a stress concentration phenomenon occurs at a place where the local shape is changed rapidly, and the risk of reducing the strength of the whole structure exists. In order to improve the stress concentration problem of the structure, the single cell structure is improved by the application, chamfers are arranged at the joint of the first horizontal wall 1 and the first inclined wall 3, the joint of the first inclined wall 3 and the first vertical wall 7, the joint of the first vertical wall 7 and the second inclined wall 4, the joint of the second inclined wall 4 and the second horizontal wall 2, the joint of the second horizontal wall 2 and the third inclined wall 5, and the joint of the third inclined wall 5 and the second vertical wall 8, the joint of the second vertical wall 8 and the fourth inclined wall 6, the joint of the fourth inclined wall 6 and the first horizontal wall 1, the joint of the first horizontally extending wall 9 and the first inclined wall 3, and the joint of the second horizontally extending wall 10 and the second inclined wall 4, and fig. 5 shows a three-dimensional diagram of the single cell structure after the chamfers. The added chamfer weakens the sharp change of the shape of the joint of each wall of the unit cell structure, and leads the joint of each wall to be in smooth transition, thereby reducing the stress concentration phenomenon and improving the integral strength of the zero Poisson ratio honeycomb structure. The radius of the chamfer can be adjusted according to the side length of each wall, and a proper value is selected, which is not specifically limited in the application.
The zero-Poisson ratio honeycomb structure provided by the application has a stable zero-Poisson ratio characteristic, namely the whole structure can ensure that the transverse strain and the Poisson ratio are 0 when the whole structure is subjected to uniaxial longitudinal pressure. In the application, the actual deformation effect of the zero-poisson ratio honeycomb structure is verified by adopting an actual compression test. The single cell structure provided by the application only limits the connection relation and the position relation of each wall, the specific length of each wall is not further limited, and the length of each wall can be designed on the premise of meeting the limited connection relation and the position relation according to needs during actual production. By way of example, a zero poisson's ratio honeycomb structure sample used in an actual compression test is specifically described: the scale of the zero poisson ratio honeycomb structure is 5 × 5, that is, 5 unit cell structures are connected in sequence in each row along the direction of the first horizontal wall 1 (i.e., the X direction), and 5 unit cell structures are connected in sequence in each row along the direction of the first vertical wall 7 (i.e., the Y direction). The length of each wall of the unit cell structure is characterized in that: the first horizontal wall 1 and the first inclined wall 3 are equal in length, the first horizontally extending wall 9 is half the length of the first inclined wall 3, and the first vertical wall 7 is half the length of the first inclined wall 3. Further, the length of the first inclined wall 3 is 10mm, the wall thickness of each wall is 2mm, and the thickness of the unit cell structure is 5 mm.
The actual compression test is an axial compression test based on a digital image correlation method (DIC), a zero-Poisson ratio honeycomb structure sample used in the test is prepared by a 3D printing process, and a photocuring molding (SLA)3D printer is specifically selected for preparation. The two ends of the sample piece are provided with clamping heads, so that the sample piece can be clamped on the compression testing machine smoothly. Test to facilitate analysis of strain in a test piece using Digital Image Correlation (DIC), a speckle pattern is marked on the central rectangular area of the sample piece with a black marker for tracking and testing of the visual measurement system. During the test, the displacement loading rate was set at 1mm/min, and an optical measurement system was used to track the strain in the loading direction and transverse direction, with a frame rate of 30 fps. The strain distribution of the acquired zero-Poisson ratio honeycomb structure sample piece is analyzed, and the transverse strain of the sample piece is found to be near 0, namely, the transverse strain of the sample piece is not in the vertical direction of the loading direction, so that the characteristic of zero Poisson ratio is met. Fig. 7 is a schematic diagram of in-plane stability of a sample obtained according to test data, and in a uniaxial compression process, along with increase of compressive strain, the poisson ratio of the sample is gradually stabilized to 0, so that the stable zero poisson ratio characteristic of the zero poisson ratio honeycomb structure provided by the application is further verified.
The zero-Poisson ratio honeycomb structure provided by the application has excellent in-plane mechanical property while keeping stable zero-Poisson ratio characteristic. On the premise of meeting the zero Poisson ratio characteristic, the in-plane mechanical property of the zero Poisson ratio honeycomb structure can be adjusted by adjusting the size and angle parameters of the single cell structure so as to meet the deformation requirements under different conditions. In the present application, parametric analysis is performed on the in-plane mechanical properties of the zero poisson's ratio honeycomb structure, and referring to fig. 8, dimensional parameters of the unit cell structure are parametrically defined, the lengths of the first inclined wall 3, the second inclined wall 4, the third inclined wall 5 and the fourth inclined wall 6 are marked as L, the lengths of the first horizontal wall 1 and the second horizontal wall 2 are marked as al, the included angle between the first inclined wall 3 and the fourth inclined wall 6 is marked as an inclined wall inclination angle θ, the lengths of the first horizontal extension wall 9 and the second horizontal extension wall 10 are marked as Lcos θ, the lengths of the first vertical wall 7 and the second vertical wall 8 are marked as kL, the wall thicknesses of the first horizontal wall 1, the first inclined wall 3, the first vertical wall 7, the second inclined wall 4, the second horizontal wall 2, the third inclined wall 5, the second vertical wall 8, the fourth inclined wall 6, the first horizontal extension wall 9 and the second horizontal extension wall 10 are set to the same value, and labeled t. Here, α is a horizontal cell wall length coefficient, and k is a vertical cell wall length coefficient.
When the zero poisson's ratio honeycomb structure is compressed, a single unit cell structure is taken for analysis. The unit cell structure bears the uniformly distributed stress load in the Y direction, the compression deformation of the first horizontal extension wall 9 and the second horizontal extension wall 10 is neglected, only the bending deformation and the tensile deformation of the octagonal closed space part are considered, and thus the whole model can be simplified into the model in the figure 9: an inclined cantilever beam bearing bending loads M and loads F, and a rod member bearing bending and compressive loads.
Thereby, the amount of deformation in the Y direction of the honeycomb structure can be obtained:
in the formula, Es is the Young's modulus of the material for manufacturing the unit cell structure, I is the sectional inertia moment of the unit cell structure, and A is the sectional area of the unit cell structure.
The homogenized stress and the homogenized strain in the Y direction of the honeycomb structure are respectively:
combining the definition formula of the young modulus, the equivalent elastic modulus of the honeycomb structure in the Y direction can be obtained as follows:
for the equivalent elastic modulus of the zero poisson ratio honeycomb structure in the horizontal direction (X direction), a theoretical analysis model of the zero poisson ratio honeycomb structure is shown in fig. 10, and two ends of a unit cell structure bear uniformly distributed stress loads. In the calculation process, the influence of the octagonal closed space part on the deformation of the zero Poisson ratio honeycomb structure in the X direction is assumed to be small, so that the influence brought by the octagonal part can be ignored. From the force analysis, the load can be approximately considered to act on both sides of the horizontal cell walls.
The axial pressure F can be obtained according to the stress balance in the horizontal direction as follows:
the deformation of the first horizontal wall 1 and the first horizontally extending wall 9 may be equivalent to an axial compressive deformation, the compressive strain of which may be expressed as:
according to the definition of young's modulus, the equivalent elastic modulus of a zero poisson ratio honeycomb structure in the horizontal direction (X direction) can be expressed as:
the loading scheme for calculating the in-plane shear modulus is shown in fig. 11, the single cell structure bears an evenly distributed in-plane shear stress, only the bending deformation of the octagonal portion of the honeycomb structure is considered, and therefore the solution of the in-plane shear modulus can be simplified to a statically determinate model with the shearing force F, as shown in fig. 12.
The magnitude of the shear force F can be described as:
the displacement of point a in the X direction is first calculated, for which a unit force acting downwards in the X direction is applied at point a. According to the simplified model solved for the in-plane shear modulus, as shown in FIG. 12, M (x) and M (x) of each segment of the octagonal portion of the honeycomb structure can be calculated according to the unit load method and the Mohr integral
The displacement of the honeycomb structure in the X direction can thus be obtained as:
wherein:
the homogenized and dimensionless in-plane shear modulus of the honeycomb structure can thus be obtained as:
and (3) carrying out parametric analysis on the in-plane mechanical parameters of the zero-Poisson-ratio honeycomb structure according to the in-plane mechanical parameter formulas (1) to (3) to obtain the influence of different size parameters of the unit cell structure on the mechanical property of the zero-Poisson-ratio honeycomb structure, as shown in figures 13-17. Wherein, fig. 13 shows the influence of the inclination angle θ of the lower inclined wall with the wall length α L of different first horizontal walls 1 on the equivalent elastic modulus in the X direction; FIG. 14 illustrates the effect of the skew angle θ on the equivalent modulus of elasticity in the X direction at different wall thicknesses t; FIG. 15 shows the effect of the skew angle θ on the equivalent modulus of elasticity in the Y direction at different wall thicknesses t; FIG. 16 shows the effect of the declination angle θ on the internal equivalent modulus of elasticity for different wall lengths α L of the first horizontal wall 1; FIG. 17 illustrates the effect of skew angle θ on the in-plane equivalent modulus of elasticity at different wall thicknesses t; in parametric analysis, the Young modulus of the zero-Poisson ratio honeycomb structure in the X direction and the Y direction is obviously reduced compared with that of the traditional honeycomb structure, and the honeycomb structure can obtain better in-plane flexibility in the X direction and the Y direction and has higher in-plane deformation capability. The theoretical derivation of the internal mechanical property and the parametric analysis can provide guidance for the size parameter selection of the unit cell structure in practical application.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.
Claims (10)
1. A unit cell structure, characterized in that it comprises: the device comprises a first horizontal wall, a second horizontal wall, a first inclined wall, a second inclined wall, a third inclined wall, a fourth inclined wall, a first vertical wall, a second vertical wall, a first horizontally extending wall and a second horizontally extending wall, wherein the first horizontal wall, the first inclined wall, the first vertical wall, the second inclined wall, the second horizontal wall, the third inclined wall, the second vertical wall and the fourth inclined wall are sequentially connected end to form a closed shape, and the closed shape is an anti-symmetric octagon;
the first horizontally extending wall is connected with the intersection point of the first horizontal wall and the first inclined wall, the second horizontally extending wall is connected with the intersection point of the second inclined wall and the second horizontal wall, the first horizontally extending wall and the first horizontal wall are positioned on the same straight line, and the second horizontally extending wall and the second horizontal wall are positioned on the same straight line;
the first horizontal wall and the second horizontal wall are parallel to each other, the first vertical wall and the second vertical wall are parallel to each other, the first sloped wall and the fourth sloped wall are parallel to each other, the second sloped wall and the third sloped wall are parallel to each other, and the first horizontal wall and the first vertical wall are perpendicular to each other;
the first inclined wall, the second inclined wall, the third inclined wall and the fourth inclined wall are equal in length, the first horizontal wall and the second horizontal wall are equal in length, the first vertical wall and the second vertical wall are equal in length, and the first horizontally extending wall and the second horizontally extending wall are equal in length.
2. The unit cell structure of claim 1, wherein a junction of the first horizontal wall and the first sloped wall, a junction of the first sloped wall and the first vertical wall, a junction of the first vertical wall and the second sloped wall, a junction of the second sloped wall and the second horizontal wall, a junction of the second horizontal wall and the third sloped wall, and a junction of the third sloped wall and the second vertical wall, and wherein a junction of the second vertical wall and the fourth sloped wall, a junction of the fourth sloped wall and the first horizontal wall, a junction of the first horizontally extending wall and the first sloped wall, and a junction of the second horizontally extending wall and the second sloped wall are all chamfered.
3. The unit cell structure according to claim 1, wherein the first horizontal wall, the second horizontal wall, the first sloped wall, the second sloped wall, the third sloped wall, the fourth sloped wall, the first vertical wall, the second vertical wall, the first horizontally extending wall, and the second horizontally extending wall all have the same wall thickness.
4. The unit cell structure according to claim 1, wherein the wall thickness of each of the first horizontal wall, the second horizontal wall, the first sloped wall, the second sloped wall, the third sloped wall, the fourth sloped wall, the first vertical wall, the second vertical wall, the first horizontally extending wall, and the second horizontally extending wall is 2 mm.
5. The unit cell structure according to claim 1, characterised in that the thickness of the unit cell structure is 5 mm.
6. The unit cell structure according to claim 1, wherein the first horizontal wall and the first sloped wall are equal in length, the first horizontally extending wall has a length that is half the length of the first sloped wall, and the first vertical wall has a length that is half the length of the first sloped wall.
7. The unit cell structure according to claim 6, wherein the first sloped wall is 10mm in length.
8. A zero Poisson ratio honeycomb structure comprising the unit cell structure of any one of claims 1 to 7, the zero Poisson ratio honeycomb structure being formed by repeatedly arranging a plurality of the unit cell structures in a direction of the first horizontal wall and a direction of the first vertical wall, wherein,
when the unit cell structures are repeatedly arranged along the direction of the first horizontal wall, the first horizontal extension wall of the next unit cell structure is connected with the intersection point of the first horizontal wall and the fourth inclined wall of the previous unit cell structure; the second horizontal extension wall of the next unit cell structure is connected with the intersection point of the second horizontal wall and the third inclined wall of the previous unit cell structure;
when the unit cell structures are repeatedly arranged along the direction of the first vertical wall, the first horizontal wall of the next unit cell structure is attached to the second horizontal wall of the previous unit cell structure in parallel, and the first horizontal extension wall of the next unit cell structure is attached to the second horizontal extension wall of the previous unit cell structure in parallel.
9. The zero-poisson-ratio honeycomb structure of claim 8, wherein 5 of the unit cell structures are connected in sequence in each row along the direction of the first horizontal wall, and 5 of the unit cell structures are connected in sequence in each row along the direction of the first vertical wall.
10. The zero-poisson-ratio honeycomb structure of claim 8, wherein the zero-poisson-ratio honeycomb structure is prepared by a 3D printing process.
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