Meta sheet capable of independently designing poisson's ratio and coefficient of thermal expansion, and design method for meta sheet

Abstract

The present invention relates to a meta sheet capable of independently designing a Poisson's ratio and a coefficient of thermal expansion, and a design method for the meta sheet. In the meta sheet capable of independently designing a Poisson's ratio and a coefficient of thermal expansion, according to the present invention, polygonal unit structures having beams are continuously arranged and polygonal edges are hinge-connected such that the unit structures are rotated by an external force, thereby allowing expansion or contraction at a predetermined Poisson's ratio, and the beams are formed as double-layer beams in which two materials having different coefficients of thermal expansion are bonded in the longitudinal direction such that bending deformation occurs by heat, thereby allowing expansion or contraction even by external heat.

Description

Meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient and design method of the meta sheet

[0001] The present invention relates to a meta sheet capable of independently designing a Poisson's ratio and a coefficient of thermal expansion, and a design method for the meta sheet, and more particularly, to a meta sheet capable of independently designing a Poisson's ratio and a coefficient of thermal expansion, which can be manufactured by independently controlling the Poisson's ratio (PR) according to the mechanical load and the coefficient of thermal expansion (CTE) according to the thermal load, while expanding or contracting when a mechanical load (external force) or thermal load is applied, and a design method for the meta sheet.

[0002] Poisson's ratio (PR) and coefficient of thermal expansion (CTE) are material properties that are involved in the stress-strain relationship when mechanical load (external force) and thermal load are applied, respectively.

[0003] Figure 1 is a diagram explaining Poisson's ratio and coefficient of thermal expansion.

[0004] Poisson's ratio represents the rate of expansion or contraction in the other axial direction orthogonal to the axial strain. As shown in the left figure of Fig. 1 (a), when a compressive force is applied in the y-axis direction, it usually expands in the x-axis direction and has a positive Poisson's ratio value. However, due to structural design such as an organic structure, when a compressive force is applied in the y-axis direction, it can contract in the x-axis direction and have a negative Poisson's ratio, as shown in the right figure of Fig. 1 (a).

[0005] As shown in (b) of Fig. 1, the coefficient of thermal expansion is defined as the ratio of thermal expansion of an object according to temperature under a constant pressure.

[0006] Previously, structures capable of simultaneously controlling Poisson's ratio and thermal expansion coefficient had the same or coupled mechanism for controlling Poisson's ratio and the mechanism for controlling thermal expansion coefficient, making it difficult to design a structure having a desired Poisson's ratio and thermal expansion coefficient, and the designable area was narrow, limiting the range of applications.

[0007] Accordingly, the present invention proposes a meta sheet and a design method thereof that can independently control and design the Poisson's ratio and thermal expansion coefficient.

[0008] <Prior Art Literature>

[0009] Patent Document

[0010] Republic of Korea Publication Patent No. 10-2024-0080775

[0011] The problem to be solved by the present invention is to provide a meta sheet in which polygonal unit structures formed of beams are continuously arranged and the polygonal corners are hinge-connected to form a meta sheet so that the meta sheet can expand or contract at a predetermined Poisson's ratio by an external force, and a design method for the meta sheet in which the beam is formed as a double-layer beam with two materials having different coefficients of thermal expansion so that bending deformation occurs due to heat so that the meta sheet can expand or contract even by external heat, and in which the Poisson's ratio and the coefficient of thermal expansion can be independently designed by controlling the thickness of the hinge and the thickness of the double-layer beam.

[0012] The problems to be solved by the present invention are not limited to the problems mentioned above, and other problems not mentioned can be clearly understood by a person having ordinary skill in the technical field to which the present invention belongs from the description below.

[0013] The above object can be achieved by a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient, which has the characteristics of expanding or contracting by external heat, by continuously arranging polygonal unit structures in accordance with the present invention, wherein the polygonal corners are hinge-connected to rotate the unit structures by an external force, and the beam is formed as a double-layer beam in which two materials having different thermal expansion coefficients are bonded in the longitudinal direction, and thus undergoes bending deformation due to heat.

[0014] Here, the polygon may be any one of a square, a rectangle, and a parallelogram.

[0015] Here, the Poisson's ratio can be controlled by adjusting the thickness of the hinge.

[0016] Here, the thermal expansion coefficient of the meta sheet can be controlled by adjusting the thickness of the double-layer beam.

[0017] Here, it is preferable that the double-layer beam is made up of two different materials arranged alternately in the longitudinal direction.

[0018] The above object can be achieved by a design method of a meta-sheet capable of independent design of a Poisson's ratio and a coefficient of thermal expansion, characterized in that, according to the present invention, the method comprises the steps of: setting a target size of the meta-sheet, a target Poisson's ratio of the meta-sheet, and a target coefficient of thermal expansion of the meta-sheet for the meta-sheet of the structure; setting a shape of a unit structure and a connection angle between the unit structures based on the target Poisson's ratio and the target coefficient of thermal expansion to generate an initial design of the meta-sheet; obtaining the Poisson's ratio and the coefficient of thermal expansion for the meta-sheet of the initial design through a dynamic simulation program; and obtaining a thickness value of the hinge and a thickness value of the double-layer beam so as to reach the target Poisson's ratio and the target coefficient of thermal expansion by adjusting the thickness of the hinge or the thickness of the double-layer beam.

[0019] Here, it is desirable that the thickness of the initial hinge be set small compared to the thickness of the initial double-layer beam.

[0020] As described above, according to the meta sheet of the present invention, which can independently design the Poisson's ratio and the coefficient of thermal expansion, and the design method of the meta sheet, there is an advantage in that the meta sheet can be manufactured by independently controlling the Poisson's ratio according to the mechanical load and the coefficient of thermal expansion according to the thermal load while expanding or contracting according to the mechanical load or the thermal load.

[0021] Another advantage is that metasheets can be manufactured with both a negative and a positive Poisson's ratio, and with both an isotropic and anisotropic coefficients of thermal expansion. This means that the design possibilities are wide, allowing for a wide range of applications.

[0022] The effects of the present invention are not limited to the effects described above, and should be understood to include all effects that can be inferred from the detailed description of the present invention or the composition of the invention described in the claims.

[0023] Figure 1 is a diagram explaining Poisson's ratio and coefficient of thermal expansion.

[0024] FIG. 2 illustrates a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient according to one embodiment of the present invention.

[0025] Figure 3 is a drawing showing shrinkage deformation due to axial compressive force in Figure 2.

[0026] Figure 4 is a drawing showing shrinkage deformation due to thermal stress in Figure 2.

[0027] FIG. 5 illustrates experimental results showing that the meta sheet according to the present invention can independently control the Poisson's ratio without affecting the coefficient of thermal expansion depending on the thickness (h) of the hinge.

[0028] FIG. 6 illustrates experimental results showing that the meta sheet according to the present invention can independently control the coefficient of thermal expansion without affecting the Poisson's ratio depending on the thickness (H) of the double-layer beam.

[0029] Figure 7 shows the experimental results according to the design modification of the meta sheet according to the present invention.

[0030] Figure 8 shows experimental results showing that the meta sheet according to the present invention can have anisotropic thermal expansion coefficient.

[0031] FIG. 9 is a drawing illustrating a design method of a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient according to one embodiment of the present invention.

[0032] Specific details of the embodiments are included in the detailed description and drawings.

[0033] The advantages and features of the present invention, and the methods for achieving them, will become clearer with reference to the embodiments described in detail below together with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but can be implemented in various different forms. These embodiments are provided only to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined only by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

[0034] Hereinafter, the present invention will be described with reference to drawings for explaining a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient and a design method of the meta sheet according to embodiments of the present invention.

[0035] FIG. 2 illustrates a meta-sheet capable of independently designing a Poisson's ratio and a coefficient of thermal expansion according to an embodiment of the present invention, FIG. 3 is a diagram illustrating shrinkage deformation due to axial compressive force in FIG. 2, FIG. 4 is a diagram illustrating shrinkage deformation due to thermal stress in FIG. 2, FIG. 5 illustrates experimental results showing that the meta-sheet according to the present invention can independently control the Poisson's ratio without affecting the coefficient of thermal expansion depending on the thickness (h) of the hinge, FIG. 6 illustrates experimental results showing that the meta-sheet according to the present invention can independently control the coefficient of thermal expansion without affecting the Poisson's ratio depending on the thickness (H) of the double-layer beam, FIG. 7 illustrates experimental results according to design variations of the meta-sheet according to the present invention, and FIG. 8 illustrates experimental results showing that the meta-sheet according to the present invention can have an anisotropic coefficient of thermal expansion.

[0036] According to one embodiment of the present invention, a meta sheet (hereinafter referred to as a “meta sheet”) capable of independent design of Poisson’s ratio (PR) and coefficient of thermal expansion (CTE) is formed by continuously arranging polygonal unit structures as illustrated, and the polygonal corners are hinge-connected to neighboring unit structures.

[0037] In the present invention, the term "hinge connection" may mean that two edges are connected by a material having a predetermined thickness (h) and a predetermined length (w), as illustrated. Furthermore, the hinge connection portion may be formed by extending and connecting one of the materials forming the double-layer beam described below, or may be formed by forming an independent material.

[0038] At this time, the unit structure may be a square as shown, or may be a rectangle or parallelogram with different vertical lengths (A) and horizontal lengths (B). In addition, it is not limited to a square and may be formed into other polygons such as triangles.

[0039] When a compressive force is applied in the x-axis direction in an initial state where the angle between neighboring unit structures is set to Θ as shown in Fig. 2, the hinge connection portion connecting the unit structures acts as a hinge as shown in Fig. 3, causing the unit structures to rotate and thus contract in the y-axis direction. That is, the structure shown can have a negative Poisson's ratio value. At this time, as described below, if the shape of the unit structures, the initial connection angle Θ, etc. are appropriately selected, a meta sheet having a positive Poisson's ratio value can be formed.

[0040] At this time, in the present invention, the beam forming the unit structure may be formed as a double-layer beam in which two materials (a first material and a second material) having different coefficients of thermal expansion are bonded in the longitudinal direction. Therefore, when the double-layer beam experiences a temperature change, bending deformation occurs as illustrated in the dotted box in Fig. 4 due to the difference in coefficients of thermal expansion of the two materials. At this time, in the double-layer beam of the present embodiment, it is preferable that the two materials are alternately arranged in the longitudinal direction. That is, when the double-layer beam is divided into equal parts in the longitudinal direction, the positions between the first material and the second material in the divided areas are reversed. Therefore, in the present embodiment, since the first material has a large coefficient of thermal expansion, the divided left area of ​​the double-layer beam may bend convexly upward as the temperature increases, and the divided right area of ​​the double-layer beam may bend convexly downward as the temperature increases.

[0041] Double-layer beams can be made by 3D printing two materials with different coefficients of thermal expansion, but they can also be made through semiconductor processes.

[0042] Since the double-layer beams forming each side of the unit structure undergo bending deformation simultaneously as the temperature increases, the unit structure can be rotated. Therefore, the meta sheet according to the present invention can shrink or expand in the x and y directions as the temperature increases. FIG. 4 illustrates an example of shrinkage, but if the bending direction of the double-layer beam or the shape of the unit structure and the initial connection angle Θ are appropriately designed, a structure in which the meta sheet expands due to heat can also be formed. In addition, as described below, the meta sheet can be designed to have different anisotropic properties in terms of x-direction and y-direction thermal expansion characteristics as the temperature increases. For example, when the temperature increases, it can shrink in the x-direction and expand in the y-direction.

[0043] In this way, the meta sheet according to the present invention can contract or expand under mechanical load and thermal load. In particular, depending on the design of the meta sheet, it can have a negative or positive Poisson's ratio, and can expand or contract isotropically or anisotropically due to heat.

[0044] Since the deformation mechanism due to mechanical load is based on the rotation of the hinge, and the deformation mechanism due to thermal load is based on the rotation of the double-layer beam, the deformation mechanisms due to mechanical load and the deformation mechanisms due to thermal load are each separated. Therefore, by appropriately adjusting the variable values ​​affecting each mechanism, the Poisson's ratio and the thermal expansion coefficient of the meta-sheet can be independently controlled and designed. In other words, the Poisson's ratio of the meta-sheet can be controlled while the thermal expansion coefficient of the meta-sheet is fixed, and also the thermal expansion coefficient can be controlled while the Poisson's ratio of the meta-sheet is fixed.

[0045] In Fig. 5, according to the present invention, a meta sheet having a predetermined shape (differentiating A / B) is manufactured, but the thickness (h) of the hinge is different, and the deformation due to heat is measured as in Fig. 5 (d), or the deformation due to external force is measured by applying a compressive force in the y-axis direction as in Fig. 5 (e). Figs. 5 (a) and (b) show the deformation results due to heat, and it can be seen that there is almost no change in the thermal loss coefficient of the meta sheet depending on the thickness of the hinge. In addition, Fig. 5 (c) shows the deformation results due to a compressive force, and it can be seen that the Poisson's ratio value changes depending on the thickness of the hinge.

[0046] Therefore, in order to control only the Poisson's ratio of the metasheet while keeping the thermal expansion coefficient of the metasheet fixed, the hinge thickness (h) can be changed. Since the hinge thickness does not affect the deformation mechanism due to thermal load based on the bending of the double-layer beam, the value of the thermal expansion coefficient of the metasheet does not change even if the hinge thickness is changed.

[0047] When the hinge thickness is thin, the unit structure acts as a rigid body, and when a compressive force is applied, deformation occurs mainly only in the hinge portion. However, as the hinge thickness increases, deformation of the edges forming the unit structure also occurs, so the Poisson's ratio value changes as the hinge thickness changes.

[0048] In Fig. 6, according to the present invention, a meta sheet having a predetermined shape (differentiating A / B) was manufactured, and the thickness (H) of the double-layer beam was different, and the deformation due to heat was measured as in Fig. 6 (d), or the deformation due to external force was measured by applying a compressive force in the y-axis direction as in Fig. 6 (e). Figs. 6 (a) and (b) show the deformation results due to heat, and it can be confirmed that the strain of the meta sheet varies depending on the thickness of the double-layer beam. In addition, Fig. 6 (c) shows the deformation results due to a compressive force, and it can be confirmed that the Poisson's ratio value hardly changes depending on the thickness of the double-layer beam.

[0049] Therefore, in order to control only the thermal expansion coefficient of the meta-sheet while fixing the Poisson's ratio of the meta-sheet, the thickness (H) of the double-layer beam can be changed. Preferably, the thickness (H) of the double-layer beam can be controlled when the thickness (H) of the double-layer beam is sufficiently thicker than the hinge thickness (h). If the thickness (H) of the double-layer beam changes, the degree of bending of the double-layer beam changes, and accordingly, the amount of rotation of the unit structure also changes, thereby allowing the thermal expansion coefficient of the meta-sheet to be controlled. In a situation where the thickness (H) of the double-layer beam is sufficiently thick, deformation mainly occurs only at the hinge portion, so the Poisson's ratio can be maintained almost constant even when the value of H changes.

[0050] Figures 7 (a) and (b) show the experimental results of the thermal expansion coefficient of the meta-sheet manufactured with different initial connection angles (Θ) between unit structures and different thicknesses (H) of the double-layer beam when the positions of the first and second materials are swapped. When the arrangements of the two materials constituting the double-layer beam are reversed, the bending direction according to the temperature is reversed. It can be confirmed that the meta-sheet thermally expands as the temperature increases due to the changed bending direction of the double-layer beam, and it can be confirmed that the range of change in the thermal expansion coefficient of the meta-sheet according to the thickness of the double-layer beam is different depending on the initial connection angle between the unit structures. In addition, it can be confirmed that the thermal expansion coefficient of the meta-sheet becomes smaller as the thickness of the double-layer beam increases.

[0051] Figures 7(c) and (d) show the experimental results of the Poisson's ratio of the meta-sheet according to the shape (A / B) of the unit structure and the initial connection angle (Θ) between the unit structures. It can be confirmed that the Poisson's ratio value of the meta-sheet changes variously depending on the shape of the unit structure and the initial connection angle between the unit structures. In addition, it can be confirmed that a meta-sheet having a negative or positive Poisson's ratio value can be produced depending on the shape of the unit structure and the initial connection angle between the unit structures.

[0052] In Fig. 8, it can be confirmed that the x-direction thermal expansion coefficient and the y-direction thermal expansion coefficient can be controlled anisotropically differently according to the initial design of the meta sheet according to the present invention. In Fig. 8 (a), the upper graph is a graph showing the x-direction thermal expansion coefficient according to the shape (A / B) of the unit structure and the initial connection angle (Θ) between the unit structures, and the lower graph is a graph showing the y-direction thermal expansion coefficient. For example, when A / B = 1.8 and Θ is 80 degrees, it can be confirmed that the x-direction thermal expansion coefficient is negative (blue) and the y-direction thermal expansion coefficient is positive (red). When A / B = 0.8 and Θ is 80 degrees, it can be confirmed that the x-direction thermal expansion coefficient is positive (red) and the y-direction thermal expansion coefficient is negative (blue). That is, Fig. 8 has the characteristic of anisotropic thermal expansion coefficient. Therefore, the meta sheet according to the present invention can adjust the thermal expansion coefficient values ​​in the x and y directions differently and in various ways by appropriately adjusting the shape (A / B) of the unit structure and the initial connection angle (Θ) between the unit structures.

[0053] Hereinafter, a design method of a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient according to the present invention will be described.

[0054] FIG. 9 is a drawing illustrating a design method of a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient according to one embodiment of the present invention.

[0055] The design method of a meta sheet according to the present invention calculates the Poisson's ratio and thermal expansion coefficient of the meta sheet through a structural dynamic analysis of the meta sheet according to design variables, and can derive a final design plan through an independent control mechanism of the Poisson's ratio and thermal expansion coefficient.

[0056] First, as shown in ① of Fig. 9, the size of the meta sheet, the target Poisson's ratio (PR) of the meta sheet, and the target coefficient of thermal expansion (CTE) of the meta sheet are set for the meta sheet of the aforementioned structure.

[0057] Next, as illustrated in ② of Fig. 9, the initial design of the meta sheet is generated by setting the shape of the unit structure and the connection angle between the unit structures based on the target Poisson's ratio and the target thermal expansion coefficient. As described above, the characteristics of the thermal expansion coefficient may vary with a negative or positive Poisson's ratio value depending on the shape of the unit structure and the connection angle between the unit structures. Therefore, the initial design can be generated by setting the shape of the unit structure and the connection angle between the unit structures close to the target Poisson's ratio and the target thermal expansion coefficient. At this time, it is preferable that the hinge thickness be set sufficiently smaller than the thickness of the double-layer beam.

[0058] Next, the Poisson's ratio and thermal expansion coefficient are calculated using a dynamic simulation program for the initial design generated based on the target Poisson's ratio and target thermal expansion coefficient. Using a known dynamic simulation program, the Poisson's ratio can be calculated through the deformation induced by applying external force to the initial design structure, and the thermal expansion coefficient can be calculated through the deformation induced by applying heat to the initial design structure.

[0059] Next, as illustrated in ③ of Fig. 9, the Poisson's ratio and thermal expansion coefficient of the initial design are compared with the target Poisson's ratio and thermal expansion coefficient, and the design variables are adjusted using the independent adjustment mechanism described above. As described above, the design variables may be the thickness (h) of the hinge and the thickness (H) of the double-layer beam.

[0060] For example, by increasing the hinge thickness (h) value as shown, the Poisson's ratio is adjusted while keeping the thermal expansion coefficient the same, and then the thickness of the double-layer beam is adjusted while keeping the Poisson's ratio the same so that the target value can be reached.

[0061] In this way, after designing the final design of the meta sheet using a dynamics simulation program, the meta sheet can be manufactured accordingly and the simulation results can be verified through actual experiments.

[0062]

[0063] Although the embodiments of the present invention have been described with reference to the attached drawings, those skilled in the art will appreciate that the present invention can be implemented in other specific forms without altering the technical concept or essential features thereof. Therefore, the embodiments described above should be understood to be illustrative in all respects and not restrictive.

Claims

1. Polygons formed by beams are continuously arranged as unit structures, and the corners of the polygons are hinged so that the unit structures rotate by an external force and expand or contract at a predetermined Poisson's ratio. The above beam is a meta sheet that can be independently designed for Poisson's ratio and thermal expansion coefficient, which is formed as a double-layer beam in which two materials with different thermal expansion coefficients are bonded in the longitudinal direction, and thus has the characteristics of expanding or contracting even when subjected to external heat due to bending deformation caused by heat.

2. In paragraph 1, A meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient, wherein the above polygon is any one of a square, a rectangle, and a parallelogram.

3. In paragraph 1, A meta sheet capable of independent design of the Poisson's ratio and thermal expansion coefficient, characterized in that the Poisson's ratio is controlled by adjusting the thickness of the hinge.

4. In paragraph 1, A meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient, characterized in that the thermal expansion coefficient of the meta sheet is controlled by adjusting the thickness of the double-layer beam.

5. In paragraph 1, The above double-layer beam is a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient, characterized in that two different materials are alternately arranged in the longitudinal direction.

6. A step of setting a target size of the meta sheet, a target Poisson's ratio of the meta sheet, and a target thermal expansion coefficient of the meta sheet for the meta sheet of the structure of claim 1; A step of creating an initial design of a meta sheet by setting the shape of the unit structure and the connection angle between the unit structures based on the target Poisson's ratio and the target thermal expansion coefficient; A step of obtaining the Poisson's ratio and thermal expansion coefficient for the meta sheet of the initial design using a dynamic simulation program; and A design method for a meta sheet capable of independent design of a Poisson's ratio and a thermal expansion coefficient, characterized in that it includes a step of obtaining a thickness value of the hinge and a thickness value of the double-layer beam so as to reach a target Poisson's ratio and a target thermal expansion coefficient by adjusting the thickness of the hinge or the thickness of the double-layer beam.

7. In paragraph 6, A design method for a meta sheet capable of independent design of Poisson's ratio and thermal expansion coefficient, characterized in that the thickness of the initial hinge is set to be smaller than the thickness of the initial double-layer beam.

Images