Design method for expandable structure of paper-cut metamaterial

Abstract

The invention provides a design method for an expandable structure of a paper-cut metamaterial, and belongs to the technical field of paper-cut metamaterials. The specific design steps comprise: S1, determining basic information of the paper-cut metamaterial, wherein the basic information comprises a closed configuration, an unfolded configuration, shapes of paper-cut units, and a connection mode between the paper-cut units; s2, a closed contour is determined based on the closed configuration, an unfolded contour is determined based on the unfolded configuration, paper-cut units are drawn in the unfolded contour, the multiple paper-cut units are arranged according to a preset mode to form a paper-cut pattern, and the area of the closed contour is the same as that of the unfolded contour; s3, constructing area-preserving transformation mapping from the unfolded contour to the closed contour so as to map the paper-cut pattern in the unfolded contour into the closed contour; and S4, based on a connection mode between the paper-cut units, adding a connection design between the paper-cut units on the paper-cut pattern in the closed contour so as to determine a to-be-cut side line in the paper-cut pattern. The design method provided by the invention is simple, rapid and convenient to operate.

Description

Technical Field

[0001] The present invention belongs to the technical field of paper-cut metamaterials, and particularly relates to a design method for a deployable structure of paper-cut metamaterials. Background Art

[0002] Deployable structures that can achieve large deformations through expansion and folding have extensive applications in fields such as aerospace, intelligent robots, wearable devices, and flexible electronic devices. Among them, paper-cut metamaterials are a type of deployable structure composed of hinges and rotating paper-cut units inspired by traditional paper-cut art, which can achieve arbitrary pre-designed planar and three-dimensional surface deformations through the coordinated rotation of a large number of paper-cut units.

[0003] In current research, due to the very complex geometric constraints and kinematic responses of paper-cut metamaterials, the design of paper-cut metamaterials that can be deployed into arbitrary shapes can only be achieved by means of constraint optimization or establishing a design matrix of a linkage mechanism. However, the calculation processes of these design methods are extremely cumbersome, requiring multiple solutions of a large number of kinematic equations or multiple operations of large matrices. At the same time, the computational amount of these design methods will increase significantly with the increase in the number of paper-cut units, and the design of paper-cut metamaterials with arbitrary deformations can only be achieved by relying on complex computer programs. Summary of the Invention

[0004] The purpose of this application is to provide a design method for a deployable structure of paper-cut metamaterials to solve the above-mentioned technical problems existing in the prior art.

[0005] This application is implemented as follows: The embodiments of this application provide a design method for a deployable structure of paper-cut metamaterials. The specific design steps include: S1: Determine the basic information of the paper-cut metamaterials, where the basic information includes the closed configuration, the deployed configuration, the shape of the paper-cut units, and the connection method between the paper-cut units; S2: Determine the closed contour based on the closed configuration, determine the deployed contour based on the deployed configuration, draw the paper-cut units in the deployed contour, and a plurality of paper-cut units are arranged in a preset manner to form a paper-cut pattern, and the area of the closed contour is the same as the area of the deployed contour; S3: Construct an area-preserving transformation that maps from the deployed contour to the closed contour to map the paper-cut pattern in the deployed contour to the closed contour; S4: Based on the connection method between the paper-cut units, add the connection design between the paper-cut units to the paper-cut pattern in the closed contour to determine the cutting edges to be cut in the paper-cut pattern.

[0006] The technical solution adopted by the present invention can achieve the following beneficial effects: In this application, the unfolding profile and the closing profile are determined according to the required unfolding configuration and closing configuration, and through area-preserving transformation, the paper-cut pattern in the unfolding profile is mapped into the closing profile, so as to obtain the paper-cut metamaterial design that can be deformed from the closing configuration to the unfolding configuration. This method is simple, fast, and easy to operate. At the same time, it can avoid the complex calculation methods involved in the prior art and does not require relying on complex computer programs. Description of the Drawings

[0007] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments of the present invention or the prior art. Obviously, the following described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0008] Figure 1 is the overall flowchart of the design method provided by some embodiments of this application; Figure 2 is a schematic diagram of the closing configuration provided by some embodiments of this application Figure 1 ; Figure 3 is a schematic diagram of the unfolding configuration provided by some embodiments of this application Figure 1 ; Figure 4 is a schematic diagram of the paper-cut pattern and the unfolding profile provided by some embodiments of this application Figure 1 ; Figure 5 is a schematic diagram of the paper-cut pattern and the closing profile provided by some embodiments of this application Figure 1 ; Figure 6 is a schematic diagram of the paper-cut pattern provided by some embodiments of this application Figure 1 ; Figure 7 is a schematic diagram of the paper-cut pattern provided by some embodiments of this application Figure 2 ; Figure 8 is a schematic diagram of the closing configuration of the test piece provided by some embodiments of this application Figure 1 ; Figure 9 is a schematic diagram of the unfolding configuration of the test piece provided by some embodiments of this application Figure 1 ; Figure 10 is a schematic diagram of the closing configuration provided by some embodiments of this application Figure 2 ; Figure 11 is a schematic diagram of the unfolding configuration provided by some embodiments of this application Figure 2 ; Figure 12Schematic diagrams of the paper-cutting pattern and the unfolded contour provided by some embodiments of the present application Figure 2 ; Figure 13 Schematic diagrams of the paper-cutting pattern and the closed contour provided by some embodiments of the present application Figure 2 ; Figure 14 Schematic diagram of the paper-cutting pattern provided by some embodiments of the present application Figure 3 ; Figure 15 Schematic diagram of the paper-cutting pattern provided by some embodiments of the present application Figure 4 ; Figure 16 Schematic diagram of the closed configuration of the test piece provided by some embodiments of the present application Figure 2 ; Figure 17 Schematic diagram of the unfolded configuration of the test piece provided by some embodiments of the present application Figure 2 。 Detailed implementation manners

[0009] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Apparently, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other implementation manners obtained by those of ordinary skill in the art without making creative efforts fall within the scope protected by the present invention.

[0010] The terms "first", "second", etc. in the description and claims of the present application are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present application can be implemented in an order different from those illustrated or described herein.

[0011] Some embodiments of the present application provide a design method for a deployable structure of paper-cutting metamaterials. The specific steps can be referred to Figure 1 as shown, and specifically include: S1: First, determine the basic information of the paper-cutting metamaterial. The basic information includes the closed configuration, the unfolded configuration, the shape of the paper-cutting unit, and the connection method between the paper-cutting units.

[0012] In the paper-cutting metamaterial, the closed configuration and the unfolded configuration are two different geometric states, respectively corresponding to the manifestation forms of the paper-cutting metamaterial under different conditions.

[0013] The closed configuration usually refers to the state in which the material remains compact, folded or contracted without external force or under specific excitation conditions. In this state, the material may have a higher density and a smaller volume, which is suitable for storage or transportation. Refer to Figure 8 andFigure 16 As shown, the material is in a closed configuration.

[0014] The expanded configuration generally refers to the state in which the material can expand or extend to a larger volume or area after being subjected to an external force or a specific stimulus (such as a temperature change). In this state, the material may have a lower density and a larger surface area, which is suitable for applications that require a larger space. Refer to Figure 9 and Figure 17 As shown, the material is in an expanded configuration.

[0015] The conversion between the closed configuration and the expanded configuration can be achieved by mechanical force, thermal excitation or other external stimuli, and this conversion is usually reversible, enabling the paper-cut metamaterial to flexibly switch between different configurations to adapt to different application scenarios.

[0016] In some preferred embodiments, the shape of the paper-cut unit is a regular polygon, such as an equilateral triangle, a square, a regular hexagon, etc.

[0017] S2: Determine the closed contour based on the closed configuration, determine the expanded contour based on the expanded configuration, and the area of the expanded contour is the same as the area of the closed contour. Draw paper-cut units in the expanded contour, and a plurality of paper-cut units are arranged in a preset manner to form a paper-cut pattern. The paper-cut pattern is formed by arranging a plurality of paper-cut units according to a certain rule, and different paper-cut patterns can be formed according to the shape, size and arrangement method of the paper-cut units.

[0018] S3: Construct an area-preserving transformation that maps from the expanded contour to the closed contour to map the paper-cut pattern in the expanded contour to the closed contour. The area-preserving transformation mapping is a special mapping that keeps the area of the region unchanged, so that the finally obtained closed configuration corresponds to the preset expanded configuration in step S1 after expansion.

[0019] S4: Based on the connection method between the paper-cut units, add the connection method between the paper-cut units to the paper-cut pattern in the closed contour to determine the cutting edges to be cut in the paper-cut pattern. This step is mainly to determine the connection positions of the paper-cut units in the paper-cut pattern, which is convenient for subsequent cutting of the paper-cut pattern, so that the paper-cut units can rotate and transform positions relative to each other while maintaining the connection to deform from the closed configuration to the expanded configuration.

[0020] The embodiments provided in this application determine the closed contour and the expanded contour based on the closed configuration and the expanded configuration, set the paper-cut pattern in the expanded contour, and map the paper-cut pattern in the expanded contour to the closed contour through an area-preserving transformation, so as to obtain a paper-cut metamaterial design that can deform from the closed configuration to the expanded configuration, so that the paper-cut metamaterial obtained according to the closed contour can expand from the closed configuration to form the preset expanded configuration in step S1.

[0021] Compared with the complex operation methods involved in the prior art, the method provided by the embodiments of the present application is more convenient, simpler and faster, without overly complex operations and without relying on complex computer programs, providing a simpler and faster new method and new idea for the design of the deployable structure of the paper-cut metamaterial.

[0022] In step S2, it is necessary to determine the closed contour based on the closed configuration. First, it is necessary to extract the contour line of the closed configuration. The edge of the closed configuration is not necessarily a regular line. For irregular lines, processing is required to facilitate area-preserving transformation and mapping of the paper-cut pattern.

[0023] Set the lines of the contour line of the closed configuration as straight lines or smooth curves to form a closed contour. The contour line of the closed configuration consists of multiple lines. For lines that are already straight lines or smooth curves, no modification is required. For irregular lines, such as continuous broken lines or lines with corners, they all need to be redrawn and set as straight lines or smooth curves.

[0024] At the same time, when redrawing the contour line to form a closed contour, there are limitations. It is necessary to note that the closed contour can overlap with the contour line of the closed configuration or the closed contour can be sleeved outside the contour line of the closed configuration.

[0025] Overlap means that the contour line of the closed configuration is a regular line and no additional setting is required. The closed contour can be sleeved outside the contour line of the closed configuration means that the contour line is redrawn, and the contour line of the closed configuration can be completely inside the closed contour, avoiding the situation that the designed closed configuration is smaller than the preset closed configuration in step S1. Here, being completely inside means that the contour line of the closed configuration is completely inside the outer contour of the closed contour.

[0026] In step S2, the principle of determining the unfolded contour based on the unfolded configuration is similar to the principle of the closed contour.

[0027] First, it is necessary to extract the contour line of the unfolded configuration, and set the side lines of the contour line of the unfolded configuration as straight lines or smooth curves to form an unfolded transition contour line. For facilitating subsequent drawing of the paper-cut pattern and area-preserving transformation. The unfolded transition contour line can overlap with the contour line of the unfolded configuration or the unfolded transition contour line can be sleeved outside the contour line of the unfolded configuration.

[0028] Due to the large size difference between the unfolded configuration and the closed configuration, it is necessary to proportionally reduce the unfolded transition contour line to form the unfolded contour, so that the area of the unfolded contour is the same as the area of the closed contour. This facilitates subsequent area-preserving transformation and mapping the paper-cut pattern on the unfolded contour to the closed contour. The areas of the unfolded contour and the closed contour refer to the areas of the regions enclosed by their outer contours.

[0029] When performing the area-preserving transformation in step S3, it is necessary to determine the expression of the area-preserving transformation based on the shapes of the unfolded contour and the closed contour. In some embodiments, as shown in Figure 3 , the unfolded contour is a rectangle, and as shown in Figure 2 , the closed contour is a sine wave. At this time, the expression of the area-preserving transformation can be determined. In other embodiments, as shown in Figure 11 , the unfolded contour is a rectangle with a clockwise rotation inside, and as shown in Figure 10 , the closed contour is a rectangle. At this time, the expression of the area-preserving transformation can be determined.

[0030] It should be noted that the unfolded contour and the closed contour corresponding to the unfolded configuration and the closed configuration do not specifically refer to the outer contour of the paper-cut material. As shown in Figure 11 , in addition to its outer contour, the unfolded configuration also includes the contour line formed by the paper-cut units rotating clockwise around its center. The rotation is relative to the closed configuration shown in Figure 10 .

[0031] In step S2, arranging multiple paper-cut units in a preset manner to form a paper-cut pattern includes: First, divide the multiple paper-cut units into multiple groups of paper-cut unit groups. Any paper-cut unit group includes multiple paper-cut units arranged in a first direction, and the multiple groups of paper-cut unit groups are arranged in a second direction. The first direction is perpendicular to the second direction. At the same time, two vertices of any one paper-cut unit are in one-to-one contact with two vertices of any one of the surrounding paper-cut units, and the side lines between the two vertices of the two paper-cut units are in contact with each other to avoid gaps between adjacent paper-cut units.

[0032] Multiple paper-cut units are arranged in the unfolded contour. There should be no gaps between the paper-cut units. Moreover, in order to deform smoothly in the unfolded configuration and the closed configuration, the vertices of adjacent paper-cut units need to be in contact with each other. Therefore, for any one paper-cut unit, as long as it is a paper-cut unit located around it, two of its vertices need to be docked with the other paper-cut unit, and the side lines between the two docked vertices also need to be in contact with each other to ensure the regular arrangement of the paper-cut units.

[0033] When there are other paper-cutting units around a paper-cutting unit, each vertex and each side of this paper-cutting unit are in contact with other paper-cutting units. When the paper-cutting unit is located at the edge position of the paper-cutting pattern, there are only some positions around the paper-cutting unit where other paper-cutting units exist, and this paper-cutting unit needs to be in contact with the sides and vertices of other paper-cutting units located around it.

[0034] Reference Figure 4 and Figure 12 As shown, the unfolded contour is rectangular, the paper-cutting unit is an equilateral triangle, and the paper-cutting units are neatly arranged within the unfolded contour. At the same time, the paper-cutting units cannot completely fill the unfolded contour, and there will be some gaps unfilled at the outer edge position of the unfolded contour. In some other embodiments, when the unfolded contour is rectangular, if the paper-cutting unit is a regular quadrilateral, the paper-cutting units can completely fill the unfolded contour, avoiding gaps at the edge of the unfolded contour.

[0035] After mapping the paper-cutting pattern in the unfolded contour into the closed contour, step S4 needs to be executed. Adding the connection design between the paper-cutting units on the paper-cutting pattern in the closed contour in step S4 to determine the cutting edges to be cut in the paper-cutting pattern includes: A connection part is set between any paper-cutting unit and the paper-cutting unit adjacent to its side. The connection part serves to connect two adjacent paper-cutting units. In the embodiments provided in the present application, the setting position of the connection part needs to be restricted to ensure that the closed configuration can be smoothly deformed into the unfolded configuration.

[0036] Specifically, the connection part is set in contact with one of the vertices. The connection part needs to be set at the vertex position, and the number of connection parts in contact with any vertex of any paper-cutting unit is less than or equal to one.

[0037] At most one connection part can correspond to one vertex of the paper-cutting unit. One vertex corresponds to two sides of the paper-cutting unit. When neither of these two sides is in contact with other paper-cutting units, this vertex will not be in contact with the connection part; when one of these two sides is in contact with other paper-cutting units, a connection part is set on this side, and this connection part is in contact with this vertex; when both of these two sides are in contact with other paper-cutting units, connection parts are set on both of these two sides, but this vertex can only be in contact with one of the connection parts, and the other connection part needs to be in contact with the corresponding other vertex of the side where it is located. With such a setting, it can be ensured that there is a reasonable connection design between any paper-cutting unit and the paper-cutting units around it, so as to ensure that the closed configuration can be smoothly deformed into the unfolded configuration after being stressed.

[0038] After determining the positions of the connection parts between the paper-cutting units, set the edges of the paper-cutting units except for the connection parts as the edges to be cut. During cutting, cut the paper-cutting units along the edges to be cut.

[0039] In some embodiments of the present application, the connection method between the paper-cutting units includes hinge connection provided at the vertices of the paper-cutting units, or flexible connection with a preset width provided at the vertices of the paper-cutting units. The preset width is the width of the connection part between two adjacent paper-cutting units, and the ratio of the preset width to the side length of its corresponding paper-cutting unit is between 4% and 10%.

[0040] After step S4, it further includes step S5: select paper-cutting material, draw the paper-cutting pattern determined in step S4 on the surface of the paper-cutting material, and cut the paper-cutting material along the edges to be cut to form the final product. The finished product after cutting is in a closed configuration, as shown in Figure 8 and Figure 16 shown. After being subjected to an external force, the gap between the paper-cutting units expands, and the whole finished product deforms into an unfolded configuration, as shown in Figure 9 and Figure 17 shown.

[0041] Both the unfolded configuration and the closed configuration provided in step S1 of the embodiments of the present application are approximate shapes. Due to the limitations of the shape and size of the paper-cutting units and the limitations of the size of the connection parts between the paper-cutting units, the configuration after the material is unfolded cannot be fully predicted. Therefore, both the unfolded configuration and the closed configuration in step S1 are approximate shapes. The unfolded configuration of the finished product obtained in step S5 is similar in shape and size to the unfolded configuration in step S1.

[0042] The embodiments of the present application provide two specific implementation manners to better understand the design method provided by the embodiments of the present application.

[0043] In the first implementation manner, the specific design steps are as follows: S1: Determine the basic information of the paper-cutting metamaterial. Among them, the closed configuration is a sinusoidal wave shape as shown in Figure 2 shown, the unfolded configuration is a rectangle as shown in Figure 3 shown. The shape of the paper-cutting unit is selected as an equilateral triangle with a side length of 20 mm, and the connection method between the paper-cutting units is selected as a flexible connection with a connection width of 1.33 mm.

[0044] S2: Determine the closed contour based on the closed configuration and determine the unfolded contour based on the unfolded configuration. In this embodiment, the shape of the closed configuration is the same as the closed contour, and the shape of the unfolded configuration is similar to the unfolded contour. There is no need to reset the lines of the contour. The shape of the closed contour can be referred to Figure 5 shown, and the shape of the unfolded contour can be referred to Figure 4As shown. Draw the paper-cut pattern in the unfolded contour. The paper-cut units are closely arranged in the unfolded contour, with the vertices of adjacent paper-cut units connected to each other and the side lines connected to each other. After the paper-cut pattern is drawn, it can be referred to Figure 4 as shown.

[0045] S3: Construct an area-preserving transformation that maps from the unfolded contour to the closed contour, and thus map the initial regular polygon paper-cut pattern drawn on the unfolded contour into the closed contour. Here, the expression of the area-preserving transformation is: , where is the abscissa after mapping, is the ordinate after mapping. The origin of the coordinate system after mapping is located at the center of the closed contour, is the abscissa before mapping, is the ordinate before mapping. The origin of the coordinate system before mapping is located at the center of the unfolded contour, is the side length of the regular triangle paper-cut unit before mapping, can be 20 millimeters. The paper-cut pattern after mapping can be referred to Figure 5 as shown.

[0046] S4: Based on the flexible connection method selected in step S1, add the connection design of the paper-cut units to the paper-cut pattern after mapping, leaving a minimum connection width of 1.33 millimeters at the connection between the paper-cut units, and obtain the paper-cut metamaterial design that meets the closed configuration and the unfolded configuration, referring to Figure 6 as shown. In addition, in order to more clearly show the connection relationship between the paper-cut units, it can be referred to Figure 7 as shown, Figure 7 the minimum connection width of the paper-cut pattern shown is increased to 3 millimeters.

[0047] Through the above steps, a test piece of the paper-cut metamaterial that meets the design can be obtained. According to Figure 6 the paper-cut pattern shown, laser cutting is performed on a 2-millimeter-thick white rubber plate. The closed configuration of the obtained paper-cut sample is Figure 8 the sine wave shape shown, and the unfolded configuration of the obtained paper-cut sample is Figure 9 the rectangle shown. Figure 8 Compared with Figure 5 at the edge of the paper-cut pattern, the void positions where paper-cut units cannot be set will be cut off.

[0048] In the second embodiment, the specific design steps are as follows: S1: Determine the basic information of the paper-cut metamaterial design. The closed configuration is a rectangle as Figure 10 shown, and the unfolded configuration is a rectangle as Figure 11The rectangle shown, but the circular area inside it has rotated clockwise. The shape of the paper-cutting unit is an equilateral triangle with a side length of 20 millimeters. The base material of the paper-cutting unit is a semi-transparent white silicone rubber sheet with a thickness of 2 millimeters, and the connection method of the paper-cutting units is a flexible connection of 1.33 millimeters.

[0049] S2: Determine the closed contour based on the closed configuration and the unfolded contour based on the unfolded configuration. In this embodiment, the shape of the closed configuration is the same as the closed contour, and the shape of the unfolded configuration is similar to the unfolded contour. There is no need to reset the lines of the contour. The shape of the closed contour can be referred to Figure 13 as shown, and the shape of the unfolded contour can be referred to Figure 12 as shown. Draw the paper-cutting pattern in the unfolded contour. The paper-cutting units are closely arranged in the unfolded contour, with the vertices of adjacent paper-cutting units connected to each other and the sides connected to each other. The drawn paper-cutting pattern can be referred to Figure 12 as shown.

[0050] S3: Construct an area-preserving transformation that maps from the unfolded contour to the closed contour, thereby mapping the initial regular polygon paper-cutting pattern drawn on the unfolded contour into the closed contour. Here, mainly the paper-cutting pattern within the circular area of the unfolded contour is mapped into the circular area of the closed contour. Here, the area-preserving transformation of clockwise rotation performed within the circular area with a radius of is: , where is the abscissa after mapping, is the ordinate after mapping. The origin of the mapped coordinate system is located at the center of the closed contour, is the polar radius of the polar coordinate system before mapping, is the polar angle of the polar coordinate before mapping. The origin of the polar coordinate system before mapping is located at the center of the unfolded contour, is the side length of the equilateral triangle paper-cutting unit before mapping, can be 20 millimeters. The paper-cutting pattern after mapping can be referred to Figure 13 as shown.

[0051] S4: Based on the flexible connection method selected in step S1, add the connection design of the paper-cutting units to the mapped paper-cutting pattern, leaving a minimum connection width of 1.33 millimeters at the connection between the paper-cutting units, obtaining a paper-cutting metamaterial design that meets the closed configuration and the unfolded configuration, refer to Figure 14 as shown. In addition, to more clearly show the connection relationship between the paper-cutting units, it can be referred to Figure 15 as shown, Figure 15 and the minimum connection width of the paper-cutting pattern shown is increased to 3 millimeters.

[0052] After the above steps, a test piece of the designed paper-cut metamaterial can be obtained. According to Figure 14 the paper-cut pattern shown, a 2-mm-thick semi-transparent white rubber sheet is laser-cut to obtain a paper-cut sample with a closed configuration of Figure 16 the rectangle shown, and its unfolded configuration is a rectangle with the internal paper-cut units rotated clockwise as shown in Figure 17 . In Figure 16 and Figure 17 , the strip stickers on the test piece change from a linear arrangement to a curved arrangement, demonstrating the overall clockwise rotation of the internal paper-cut units of the test piece after unfolding.

[0053] It should be noted that in this article, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or elements inherent to such a process, method, article or device. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or device including that element.

[0054] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A design method for a deployable structure of a paper-cut metamaterial, characterized in that, The specific design steps include: S1: Determine the basic information of the paper-cut metamaterial, where the basic information includes the closed configuration, the unfolded configuration, the shape of the paper-cut unit, and the connection method between the paper-cut units; S2: Determine the closed contour based on the closed configuration, determine the unfolded contour based on the unfolded configuration, draw paper-cut units in the unfolded contour, and a plurality of paper-cut units are arranged in a preset manner to form a paper-cut pattern, where the area of the closed contour is the same as the area of the unfolded contour; S3: Construct an area-preserving transformation that maps from the unfolded contour to the closed contour to map the paper-cut pattern in the unfolded contour to the closed contour; S4: Based on the connection method between the paper-cut units, add the connection design between the paper-cut units to the paper-cut pattern in the closed contour to determine the cutting edges to be cut in the paper-cut pattern.

2. The design method of a deployable structure of a paper-cut metamaterial according to claim 1, wherein In step S2, determining the closed contour based on the closed configuration includes: Extract the contour line of the closed configuration, and set the line of the contour line of the closed configuration to a straight line or a smooth curve to form a closed contour, where the closed contour can overlap with the contour line of the closed configuration or the closed contour can be sleeved outside the contour line of the closed configuration.

3. The design method of a deployable structure of a paper-cut metamaterial according to claim 2, characterized in that, In step S2, determining the unfolded contour based on the unfolded configuration includes: Extract the contour line of the unfolded configuration, set the line of the contour line of the unfolded configuration to a straight line or a smooth curve to form an unfolded transition contour line, where the unfolded transition contour line can overlap with the contour line of the unfolded configuration or the unfolded transition contour line can be sleeved outside the contour line of the unfolded configuration, and proportionally reduce the unfolded transition contour line to form an unfolded contour, and make the area of the unfolded contour the same as the area of the closed contour.

4. The design method of a deployable structure of a paper-cut metamaterial according to claim 1, characterized in that, In step S1, the shape of the paper-cut unit is a regular polygon.

5. A design method for a deployable structure of a paper-cut metamaterial according to claim 4, characterized in that In step S2, the plurality of paper-cut units are arranged in a preset manner to form a paper-cut pattern, which includes: The plurality of paper-cut units are divided into multiple groups of paper-cut unit groups. Any paper-cut unit group includes a plurality of paper-cut units arranged in a first direction. The multiple groups of paper-cut unit groups are arranged in a second direction. The first direction is perpendicular to the second direction, and two vertices of any one of the paper-cut units are in one-to-one contact with two vertices of any one of the paper-cut units surrounding it, and the side line between the two vertices of the two paper-cut units is in contact with each other.

6. The design method of a deployable structure of a paper-cut metamaterial according to claim 1, characterized in that Step S3 also includes: Confirming the expression of the area-preserving transformation based on the shape of the unfolded contour and the shape of the closed contour.

7. A design method for a deployable structure of a paper-cut metamaterial according to claim 5, characterized in that In step S4, adding the connection design between the paper-cut units to the paper-cut pattern in the closed contour to determine the cutting edges to be cut in the paper-cut pattern includes: Set a connection part between any paper-cut unit and the paper-cut unit adjacent to its side line. The connection part is in contact with one of the vertices, and the number of connection parts in contact with any vertex of any paper-cut unit is less than or equal to one. Set the side lines of the paper-cut unit except the connection part as the cutting edges to be cut.

8. The design method of a deployable structure of a paper-cut metamaterial according to claim 1, characterized in that In the step S1, the connection mode between the paper-cutting units includes hinge connection arranged at the vertices of the paper-cutting units or flexible connection with a preset width arranged at the vertices of the paper-cutting units, and the preset width is the width of the connection part between two adjacent paper-cutting units.

9. The design method of a deployable structure of a paper-cut metamaterial according to claim 8, characterized in that The ratio of the preset width to the side length of the corresponding paper-cutting unit is between 4% and 10%.

10. The design method of a deployable structure of a paper-cut metamaterial according to claim 1, characterized in that, After the step S4, the following step S5 is further included: Select paper-cutting materials, draw the paper-cutting pattern determined in the step S4 on the surface of the paper-cutting materials, and cut the paper-cutting materials along the to-be-cut side lines.

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