A method for testing poisson's ratio of metamaterials

Abstract

The application provides a kind of metamaterial poisson's ratio test method, including steps as follows: S1, the section of test sample is marked;S2, test sample is installed on the mechanical testing machine, and camera is installed in front of test sample;S3, check the ratio of camera pixel and test sample mark point displacement;S4, test sample is mechanically adjusted;S5, test sample is continuously loaded from 0 to specified position x0 at constant speed, and stop loading, camera carries out k times image sampling, after sampling is completed, continue to carry out displacement loading to y0+Δy, and camera carries out m times image sampling;S6, according to y0 and y0+Δy image, respectively calculate the lateral and vertical displacement of the unit cell in the central region of metamaterial at two position points, and calculate poisson's ratio.The application uses the way of camera shooting when test sample is static, eliminates the displacement hysteresis problem caused by the damping characteristics of viscoelastic material, and improves the stability of poisson's ratio test.

Description

Technical Field

[0001] This invention relates to the field of Poisson's ratio measurement technology, and in particular to a method for testing the Poisson's ratio of metamaterials. Background Technology

[0002] Metamaterials possess extraordinary physical properties not found in natural materials, allowing them to overcome certain apparent laws of nature and thus achieve functionalities beyond those inherent in nature. Poisson's ratio is a fundamental physical property parameter characterizing the mechanical properties of metamaterials, and accurate measurement of this parameter is crucial for evaluating their characteristics.

[0003] Traditional testing methods for Poisson's ratio and modulus of elasticity have relevant specifications and standards. For example, GB / T22315-2008 proposes calculating Poisson's ratio by measuring the lateral and vertical deformation of a material under compression or during compression using an extensometer. It also proposes using acoustic resonance to test the shear modulus and loading modulus to calculate Poisson's ratio. These standards generally require the specimen to have high rigidity and be a solid material. For porous and flexible materials such as metamaterials, traditional methods are not well-suited. CN115165570A proposes a method for measuring the Poisson's ratio and Young's modulus of irregularly shaped materials. This method involves mounting the specimen on a universal testing machine equipped with a camera above it and performing a uniaxial loading test. The Poisson's ratio and Young's modulus are measured by acquiring the expansion or contraction of the specimen's cross-sectional image and the vertical loading during the loading process. The Poisson's ratio of metamaterials is generally the ratio of lateral to vertical deformation of a cell under periodic boundary conditions. However, actual fabricated samples are typically finite structures, making it impossible to achieve periodic boundary conditions. In academic research, to measure the Poisson's ratio of metamaterials, multi-row, multi-column metamaterial samples are usually prepared, and the cells in the central region of the sample are selected as the data extraction object. This reduces the influence of the free boundary of the outer contour of the sample, approximating periodic boundary conditions and maximizing the accuracy of the Poisson's ratio test. However, the optical method described in the aforementioned patent, which calculates the Poisson's ratio by acquiring the image changes of the outermost contour of the sample, cannot obtain the deformation state of the central region of the sample, and therefore is not suitable for testing the Poisson's ratio of metamaterials.

[0004] Currently, optical and extensometer methods are commonly used in academia to measure the Poisson's ratio of metamaterials. However, the extensometer method typically only measures the lateral displacement of the outer contour of the sample and cannot fully reflect the Poisson's ratio of the metamaterial. Optical methods, on the other hand, are often more suitable for testing two-dimensional metamaterials. This involves spraying markings onto the sample, recording the loading process with a camera, and then using image processing software to obtain the deformation of the cell boundaries in the central region under load and calculate the Poisson's ratio. Practical experience has shown that the loading process of this method is continuous. During the camera's capture, the pixels still move dynamically. Since the substrate of metamaterials is generally viscoelastic, there is a damping effect, and each pixel often exhibits a time lag in displacement. Furthermore, the amount of lag varies among pixels, leading to significant fluctuations in the test data and poor stability of the Poisson's ratio results. Summary of the Invention

[0005] In view of this, the present invention proposes a method for testing the Poisson's ratio of metamaterials to solve the problem of poor stability of Poisson's ratio results under continuous loading.

[0006] The technical solution of this invention is implemented as follows:

[0007] This invention provides a method for testing the Poisson's ratio of metamaterials, comprising the following steps:

[0008] S1. Mark the cross-section of the test specimen with spray paint;

[0009] S2. Install the test specimen on the mechanical testing machine and install a camera on the front side of the test specimen, so that the shooting direction of the camera is perpendicular to the longitudinal direction of the test specimen.

[0010] S3. Verify the ratio of camera pixel count to the displacement of the test sample marker points;

[0011] S4. Load the test specimen at a constant speed using a mechanical testing machine, load the displacement to the specified position y0, and unload it at the same speed for mechanical adjustment;

[0012] S5. Turn on the camera and reload the test specimen. Load the test specimen continuously from 0 to the specified position y0 at a constant speed and stop loading. The mechanical testing machine remains stationary for a certain period of time. During the stationary period, the camera takes k image samples. After the sampling is completed, continue to perform displacement loading to y0+Δy. The mechanical testing machine remains stationary for a certain period of time. During the stationary period, the camera takes m image samples.

[0013] S6. Based on the y0 and y0+Δy images, calculate the lateral and vertical displacements of the unit cell in the central region of the metamaterial at the two locations, and calculate the Poisson's ratio as the Poisson's ratio at the loaded displacement y0 of the test sample.

[0014] Based on the above technical solution, preferably, in step S1, the cross section of the test specimen is marked by spraying using a strain gauge spraying method.

[0015] Based on the above technical solution, preferably, the ballast surfaces of the mechanical testing machine that come into contact with the test specimen are coated with lubricating oil.

[0016] Based on the above technical solution, the upper and lower surfaces of the test specimen are both perpendicular to its own axis.

[0017] Furthermore, preferably, the ratio of camera pixels to the displacement of the test sample marker points is 1:1.

[0018] Based on the above technical solution, preferably, for a specific image, the intermediate cell of the test sample is selected as the sampling area, and M sampling points are selected in the y-direction and N sampling points are selected in the x-direction, let h1, h2, ..., h M The distance between the longitudinal sampling points is calculated, and the average value h is also calculated. i (i = 1…k), l1, l2, …, l N The distance between the horizontal sampling points is calculated, and the average value l is also calculated. i (i = 1…k), calculate the longitudinal and transverse strains under this image using the following formulas:

[0019]

[0020]

[0021] h0 is the initial longitudinal segment length of the unloaded unit cell in the central region, and l0 is the initial transverse segment length of the unloaded unit cell in the central region. The average longitudinal and transverse strains of the unit cell in the central region are calculated from k images.

[0022]

[0023]

[0024] Based on formulas (3) and (4), the longitudinal and transverse average strains corresponding to the y0 and y0+Δy images are calculated as ε. y ε x 、ε' y 、ε' x Then calculate the Poisson's ratio of the test specimen at displacement y0:

[0025] or

[0026] Based on the above technical solution, preferably, the number of sampling points M and N on one side of the sampling area is greater than or equal to four times the number of selected cell rows and columns, where M is the number of vertical sampling points in the sampling area and N is the number of horizontal sampling points in the sampling area.

[0027] Based on the above technical solution, preferably, the loading process is compression or tension loading. When the metamaterial has a positive Poisson's ratio, ν y0 When the metamaterial has a negative Poisson's ratio, ν is a positive value. y0 It is a negative value.

[0028] Based on the above technical solution, preferably, it also includes step S7, which is: further loading to a larger displacement without unloading, repeating S5 to S6, obtaining the Poisson's ratio of the metamaterial sample at each loading displacement, and plotting the curve of Poisson's ratio changing with loading displacement.

[0029] The present invention has the following advantages over the prior art:

[0030] (1) The method for testing the Poisson's ratio of metamaterials disclosed in this invention uses the method of taking pictures when the test sample is stationary to replace the process of dynamic loading and simultaneous imaging in the traditional method. This eliminates the displacement hysteresis problem caused by the damping characteristics of viscoelastic materials, improves the stability of the Poisson's ratio test, and provides an effective method for accurately evaluating the Poisson's ratio of metamaterials.

[0031] (2) By loading the metamaterial to a specified loading deformation, the testing machine is kept at a stationary position. After the specimen is stable, the cross-sectional image of the specimen is acquired. Then, a small displacement is applied to another displacement point, and the stationary-image acquisition process is repeated. Finally, the Poisson's ratio of the metamaterial under specific equivalent strain is calculated by the lateral and vertical displacements of the cell in the central region of the specimen at the two loading displacement points. This allows for the accurate acquisition of Poisson's ratio data for each equivalent strain of the metamaterial. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a flowchart of the Poisson's ratio testing method for metamaterials disclosed in this invention;

[0034] Figure 2 This is a structural diagram of the optical static measurement method for Poisson's ratio of metamaterials disclosed in this invention;

[0035] Figure 3 This is a schematic diagram of the image acquisition points for the Poisson's ratio metamaterial of the present invention;

[0036] Figure 4 The test specimens used in the embodiments of this invention;

[0037] Figure 5 These are the image sampling points selected for the sample cells in this embodiment of the invention.

[0038] Figure label:

[0039] S, test specimen; P, camera; T, mechanical testing machine. Detailed Implementation

[0040] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0041] like Figure 1 As shown, combined with Figure 2 This invention discloses a method for testing the Poisson's ratio of metamaterials, comprising the following steps:

[0042] S1. Prepare metamaterial test specimens and mark the cross-sections of the test specimens by spraying. In this embodiment, the cross-sections of the test specimens are marked by spraying using a strain gauge spraying method.

[0043] In this embodiment, the marker point is located on one side of the longitudinal direction of the metamaterial, that is, on the side perpendicular to the loading direction of the test sample. With this setting, during the loading process of the test sample, the marker point on the test sample will undergo lateral or longitudinal displacement, which facilitates the subsequent acquisition of displacement data of each point on the cross section of the test sample.

[0044] S2. Install the test specimen on the mechanical testing machine and install a camera on the front side of the test specimen, so that the shooting direction of the camera is perpendicular to the longitudinal direction of the test specimen. Specifically, the shooting direction of the camera is horizontally facing the marked point of the test specimen. This setting can make the displacement image of the marked point acquired by the camera regular, which is convenient for the displacement of the image marked point to be picked up by the software.

[0045] S3. Verify the ratio of camera pixels to the displacement of the test sample marker points, so that the test sample marker image in the camera is roughly consistent with the actual test sample marker point size.

[0046] S4. Place the test specimen on a mechanical testing machine and load it at a constant speed until the displacement reaches the specified position y0. Unload the specimen at the same speed for mechanical adjustment. Repeat this process two to three times to release the mechanical stress on the test specimen.

[0047] S5. Turn on the camera and reload the test specimen. Load the test specimen continuously from 0 to the specified position y0 at a constant speed and stop loading. The mechanical testing machine remains stationary for a certain period of time, preferably 30s. During the stationary period, the camera performs k image samplings (generally k≥10). After sampling, continue to perform displacement loading to y0+Δy, where Δy is a small amount, such as 0.1mm~0.5mm. The mechanical testing machine remains stationary for a certain period of time, preferably 30s. During the stationary period, the camera performs m image samplings (generally m≥10).

[0048] In the above steps, since metamaterials are generally viscoelastic materials, there is displacement hysteresis caused by damping characteristics during loading. Therefore, when the metamaterial is loaded to a certain displacement, the mechanical testing machine remains stationary, which allows the metamaterial to gradually complete the displacement change after stress deformation and stabilize the deformation state of the metamaterial. This ensures that there is no hysteresis in the pixels of the image captured by the camera, thereby obtaining more accurate test data.

[0049] S6. Based on the y0 and y0+Δy images, calculate the lateral and vertical displacements of the unit cell in the central region of the metamaterial at the two locations, and calculate the Poisson's ratio as the Poisson's ratio at the loaded displacement y0 of the test sample.

[0050] Compared to traditional optical methods, this invention uses a method of photographing the test sample while it is stationary, replacing the method of photographing while it is dynamically loaded in traditional methods. This eliminates the displacement hysteresis problem caused by the damping characteristics of viscoelastic materials, improves the stability of Poisson's ratio testing, and provides an effective method for accurately evaluating the Poisson's ratio of metamaterials.

[0051] In the above embodiments, the mechanical testing machine can be a general commercial mechanical loading machine, as long as the loading range and accuracy meet the testing requirements.

[0052] In the above embodiments, the ballast surfaces in contact with the test specimen by the mechanical testing machine are coated with lubricating oil. This configuration allows the test specimen to deform and extend well in the lateral direction during the loading of the metamaterial, avoiding interference from the roughness of the ballast surface on the lateral deformation displacement of the test specimen and improving the accuracy of the lateral displacement data of the pixels collected by the camera.

[0053] In the above embodiments, the upper and lower surfaces of the test specimen are perpendicular to its own axis. This configuration ensures that the test specimen can always deform in the longitudinal direction during loading, and that the force on each section of the test specimen is uniform during longitudinal loading, thereby ensuring the accuracy of the longitudinal displacement data of the pixels collected by the camera.

[0054] The calculation of Poisson's ratio for the test specimen involves using image acquisition software and a camera to capture the displacement of image marker points. Based on the displacement of the acquired pixels, the lateral and vertical displacements are calculated, and then the Poisson's ratio is determined.

[0055] For details, please refer to the appendix. Figure 3-5 As shown, the intermediate cell of the test sample was selected as the sampling area, and M sampling points were selected in the y-direction (longitudinal direction) and N sampling points were selected in the x-direction (lateral direction). Taking a 5×5 metamaterial unit cell as an example, the intermediate cell of the test sample was selected as the sampling area. Four sampling points were taken from one side boundary of each unit cell. In the 3×3 array unit cell region, a total of 48 sampling points were selected, namely 24 sampling points in the x-direction and 24 sampling points in the y-direction.

[0056] Let h1, h2, ..., h M The line segment formed between longitudinal sampling points (by the attached) Figure 3-5 The line segment formed by the sampling points marked H), l1, l2, ..., l N The line segment formed between the horizontal sampling points (by the attached) Figure 3-5 The line segments formed by the sampling points marked L are first averaged to obtain the average length h of the vertical line segments in a given image. i (i = 1…k) and the average length l of the horizontal line segments i (i=1…k), based on the average length of the line segments, the strain of the unit cell in the central region under a certain image can be obtained. The calculation formula is as follows:

[0057]

[0058]

[0059] h0 is the initial longitudinal segment length of the unloaded unit cell in the central region, and l0 is the initial transverse segment length of the unloaded unit cell in the central region. The average longitudinal and transverse strains are calculated as follows:

[0060]

[0061]

[0062] Based on formulas (3) and (4), the longitudinal and transverse average strains corresponding to the y0 and y0+Δy images are calculated as ε. yε x 、ε' y 、ε' x Then calculate the Poisson's ratio of the test specimen at displacement y0:

[0063] or

[0064] In actual experiments, the number of sampling points M and N on one side of the sampling area is determined based on the number of tagged sample points on the test piece and image recognition technology, and is generally four times the number of cell rows and columns selected. This test method is adaptable to both positive and negative Poisson's ratio metamaterials, and the loading process can be compression or tension. When the metamaterial has a positive Poisson's ratio, ν... y0 When the metamaterial has a negative Poisson's ratio, ν is a positive value. y0 It can be a negative value. Generally, it is recommended that the number of rows and columns of cells be equal. However, if this is not possible, M can be different from N.

[0065] To obtain more detailed Poisson's ratio data for metamaterials, this embodiment further includes step S7 based on the above measurement method. Step S7 involves further loading to a larger displacement without unloading, repeating S5 to S6, and obtaining the Poisson's ratio of the metamaterial sample at each loading displacement. A curve showing the change of Poisson's ratio with loading displacement can then be plotted.

[0066] Using the above technical solution, the testing machine remains stationary when the metamaterial is loaded to a specified deformation. After the specimen stabilizes, an image of the specimen cross-section is acquired. Then, a small displacement is applied to another displacement point, and the stationary-image acquisition process is repeated. Finally, the Poisson's ratio under a specific equivalent strain is calculated by measuring the lateral and vertical displacements of the cell in the central region of the specimen at the two loading displacement points. Repeating the above process yields the Poisson's ratio data for each equivalent strain. Notably, using image capture while the specimen is stationary, instead of the dynamic loading and simultaneous image capture process in traditional methods, eliminates the displacement hysteresis problem caused by the damping characteristics of viscoelastic materials, improves the stability of the Poisson's ratio test, and provides an effective method for accurately evaluating the Poisson's ratio of metamaterials.

[0067] The proposed method for testing the Poisson's ratio of metamaterials is simple and convenient, and the Poisson's ratio test results are highly stable. It can accurately obtain the Poisson's ratio data under various equivalent strains of metamaterials. At the same time, the configuration requirements of the camera and mechanical testing machine used are not high, making it easy to promote and use.

[0068] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for testing the Poisson's ratio of metamaterials, characterized in that, The steps include the following: S1. Mark the cross-section of the test specimen; S2. Install the test specimen on the mechanical testing machine and install a camera on the front side of the test specimen, so that the shooting direction of the camera is perpendicular to the longitudinal direction of the test specimen. S3. Verify the ratio of camera pixel count to the displacement of the test sample marker points; S4. Load the test specimen at a constant speed using a mechanical testing machine, load the displacement to the specified position y0, and unload it at the same speed for mechanical adjustment; S5. Turn on the camera and reload the test specimen. Load the test specimen continuously from 0 to the specified position y0 at a constant speed and stop loading. The mechanical testing machine remains stationary for a certain period of time. During the stationary period, the camera takes k image samples. After the sampling is completed, continue to perform displacement loading to y0+Δy. The mechanical testing machine remains stationary for a certain period of time. During the stationary period, the camera takes m image samples. S6. Based on the y0 and y0+Δy images, calculate the lateral and longitudinal displacements of the unit cell in the central region of the metamaterial at the two locations, and calculate the Poisson's ratio as the Poisson's ratio at the loaded displacement y0 of the test sample.

2. The method for testing the Poisson's ratio of metamaterials as described in claim 1, characterized in that: In step S1, the cross section of the test specimen is marked by spraying using a strain gauge spraying method.

3. The method for testing the Poisson's ratio of metamaterials as described in claim 1, characterized in that: All ballast surfaces of the mechanical testing machine that come into contact with the test specimen are coated with lubricating oil.

4. The method for testing the Poisson's ratio of metamaterials as described in claim 1, characterized in that: The upper and lower surfaces of the test specimen are both perpendicular to its own axis.

5. The method for testing the Poisson's ratio of metamaterials as described in claim 4, characterized in that: The ratio of camera pixel distance to the displacement of the test sample marker point is 1:

1.

6. The method for testing the Poisson's ratio of metamaterials as described in claim 1, characterized in that: The intermediate cell of the test sample is selected as the sampling area, and M sampling points are selected in the y-direction and N sampling points are selected in the x-direction. Let h1, h2, ..., h M The distance between the longitudinal sampling points is calculated, and the average value is determined. Let l1, l2, ..., l N The distance between the horizontal sampling points is calculated, and the average value is determined. ,in, i =1… k Calculate the longitudinal and transverse strains in this image using the following formulas: （1） （2） The initial longitudinal line segment length when the central region unit cell is unloaded. Given the initial transverse segment length of the unloaded unit cell in the central region, the mean longitudinal and transverse strains are calculated as follows: （3） （4） Based on formulas (3) and (4), the longitudinal and transverse average strains corresponding to the y0 and y0+Δy images are calculated as follows: , , , Then calculate the Poisson's ratio of the test specimen at displacement y0: （5）。 7. The method for testing the Poisson's ratio of metamaterials as described in claim 6, characterized in that: The number of sampling points M and N on one side of the sampling area is greater than or equal to four times the number of rows and columns of the selected cells. M is the number of sampling points in the y-direction of the sampling area, and N is the number of sampling points in the x-direction of the sampling area.

8. The method for testing the Poisson's ratio of metamaterials as described in claim 6, characterized in that: The loading process is either compression or tension loading. When the metamaterial has a positive Poisson's ratio, When the metamaterial has a negative Poisson's ratio, the value is positive. It is a negative value.

9. The method for testing the Poisson's ratio of metamaterials as described in claim 1, characterized in that: It also includes step S7, which is: under the condition of not unloading, further loading to a larger displacement, repeating S5~S6, obtaining the Poisson's ratio of the metamaterial sample at each loading displacement, and plotting the curve of Poisson's ratio changing with loading displacement.

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