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Abstract
Materials with both excellent frequency selective characteristic and ultralight mechanical properties are highly urgent demanded for its potential applications such as absorbing materials, artificial magnetic conductors, antenna and so on. However, although the research about materials with only excellent frequency selective characteristic or ultralight mechanical properties is advanced, in most cases, it is still a challenge that making a material possesses excellent frequency selective characteristic and ultralight mechanical properties simultaneously. So how to make the two properties achieving a high level simultaneously is a hot topic which remains to be solved. Herein, we proposed a novel and feasible strategy for achieving simultaneously excellent frequency selective characteristic and ultralight mechanical properties material. According to our strategy, the composite we designed behaviors as a FSS which can realize highly efficiency stop bands in 16.09-16.4GHz and 17.11-17.36GHz. At the same time, the composite can be regarded as an ultralight mechanical metamaterial. The relativity density of the composite can reduce to 431.99 Kg/m3, which have a distinct advantage compared with the dielectric layers that conversional FSS used. Moreover, Its elasticity modulus can reach 112.25 MPa and its bending stiffness can reach 90.54 N/mm. These performances show that although the density of the composite is reduced, the composite can still keep well mechanical properties. The strategy we proposed gives a good solution to the problem existing in the materials which desire both excellent frequency selective characteristic and ultralight mechanical properties. The composite is a designing example which can be applied in engineering. So the strategy is a guideline for researchers to achieve composite which owns both excellent frequency selective characteristic and ultralight mechanical properties.
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1. Introduction
The frequency selective characteristics and excellent mechanical properties are the two significant evaluation indices for the materials design, fabrication, measurement and application. There is no doubt that the demands and applications of this kind of materials is increasing, especially in absorbing materials, artificial magnetic conductors and so on. But for most now available materials, the frequency selective characteristics and excellent mechanical properties are a pair of contradictions. It is remained to be solved that keeping high efficiency frequency selective characteristics and owning good mechanical properties at the same time in composites. For many existing materials, when materials have well frequency selective characteristics, its total weight or thickness will become larger, which lead to its mechanical performance can not come up to the expectation. While the material owning the advantages of load-bearing or lightweight, it can not behavior well frequency selective performance. So it is a meaningful investigation that solving the contradiction in designing materials to achieving two excellent properties in a composite. In this paper, we proposed a novel strategy to achieving frequency selective characteristics and excellent mechanical properties simultaneously in composites. The composite is a combination of frequency selective surface and mechanical metamaterial.
Frequency selective surface (FSS) has been studied for the past decades [1], which is a kind of periodic structures that can be used to select incoming electromagnetic waves with different operating frequencies, polarizations, and incident angles. Conventionally, FSSs are composed of one- or two-dimensional arrays of metallic resonant structures, either as apertures in a conducting sheet or as metallic patches on a substrate. metallic patches/apertures have influences on the effects of the FSS. So the geometric shape of metallic patches/apertures are researched. Rectangles, circles, circular rings, cross shapes, Jerusalem cross shapes, are the most common shapes FSS used. With the development of printed circuit board technology, the fabrication of FSS become easily and make it possible to produce many complex structures. In order to obtain wider working bands, lower insertion loss, better angle stability, multi-layer and more complex structure FSS come into being. R.Mittr et al. proposed method to analysis the multi-layer FSS. Although the multilayer FSS may have more excellent frequency selective characteristics, the weight of the FSS may also increasing. Or rather, FSS is produced for electromagnetic using, most of them do not considering mechanical properties. With its rapidly and widely investigated, it is founded that FSS can be used in absorbing materials [2,3], artificial magnetic conductors [4,5] to applied in microwave communication, aeronautics and astronautics and many other important fields. The large weight may constrain the applications of FSS in practice. As we all known, the most of FSSs need dielectric layers which usually made by FR4 (the density about 1700∼1900kg/m3), F4B(the density about 2100∼2300 kg/m3), RT/duroid 6002 (the density about 2100 kg/m3), TP(the density about 2000kg/m3), TF(the density about 3000 kg/m3), etc. It is certain that if we want to utilize FSS to engineering application, only excellent frequency selective characteristics sometimes can not satisfy the application environment.
In recent years, mechanical metamaterial is becoming more and more popular for its excellent mechanical properties. Micro-/nanostructured mechanical metamaterials [6], origami-inspired mechanical metamaterials [7,8], ultralight and ultrastiff mechanical metamaterials [9–11], auxetic mechanical metamaterials [12,13] and other impressive work about mechanical metamaterial come into being. In [6], micro-/nano-structured materials as mechanical metamaterials to realize negative dynamic modulus and/or density, superior thermoelectric properties, high specific energy absorption and other functions. In [9], high structural connectivity isotropic microscale unit cells is used to maintain a nearly constant stiffness per unit mass density. In [11], nanoscale ceramics are used to fabricate structural metamaterials which have the properties such as ultralight, strong, energy-absorbing. It can be seen that they all used cellular/lattice structures made of polymers, metals or ceramics to obtain excellent mechanical properties. So the cellular/lattice structures can be used in designing FSS to obtain well mechanical properties. The other thing can be seen is that most of them are nanostructured and they mainly do not have frequency selective characteristics. It is well to be reminded that mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. At this situation, the research of FSS structure come in handy.
In order to introduce excellent mechanical properties to FSS and obtain excellent frequency selective characteristics and mechanical properties simultaneously, we devoted to using FSS composite mechanical metamaterial. Our designing is shown in Fig. 1. The design is targeted at keeping the well frequency selective characteristics and reducing its density. Our designing strategy can realize a combination of frequency selective surface and mechanical metamaterial which behavior both excellent frequency selective characteristics and mechanical performance. The structure which composed by spheres at the cube apexes and body center connected by cylinders whose orientation are along the cube body diagonal. The structure was designed, fabricated and measured. The simulation and experiment results verify that the composite can achieve highly efficiency stop bands in 16.09-16.4 GHz and 17.11-17.36 GHz. What’s more, the mechanical experiment results show that the material owns ultralight mechanical property. Its density can reduce to 431.99 kg/m3. Compared with the conversional FSS(about 2000kg/m3), its density have a distinct advantage. Although the density is reduced, it also can show good mechanical properties. Its elasticity modulus is 112.25 MPa and bending stiffness is 90.54 N/mm. The composite achieves both frequency selective characteristics and mechanical properties. The strategy provides possible to design a novel composite and it is also an alternative path to realize excellent frequency selective characteristics and mechanical properties simultaneously in composites.
2. Designing and preparation of the model
In order to verify our designing strategy, a sample FSS composite mechanical metamaterial is designed. As mentioned above, FSS is always composed of one- or two-dimensional arrays of metallic patches on a substrate or apertures in a conducting sheet. Cellular structures can obtain excellent MP and reduce weight. So we want to using cellular structures to design a FSS. For FSS itself, using another material instead of metal to design is also an effective way to reducing the weight and keep the MP of the FSS. With the material research developed, all-dielectric material is becoming competitive for its own unique advantages such as breakdown, oxidization and corrosion, especially in high-power and high-temperature applications. So in recent years, for its potential engineering application, FSS made by all-dielectric attract many researchers. The application of dielectric materials in filters has been researched for many decades. From Bertoni [14,15] et al. who studied theory of dielectric waveguides, all-dielectric waveguide gratings are once used to be filters and is still used today. Park [16–18] et al. Magnusson [19–24] et al. Bossard [25–30] et al. are the representative researchers of all-dielectric FSS. They realized the all-dielectric FSS at microwave, infrared, terahertz or optical frequency. The method or material they used are mostly based on guided-mode resonance properties of dielectric waveguide gratings, genetic algorithm optimization, liquid crystal, single inhomogeneous dielectric layer et al. Recently, Barton et al. designed all-dielectric (ε≈10) FSS which verified that all-dielectric FSS can be used for high-power applications at microwave frequencies at a peak power of 1.7GW/m2 based on guided-mode resonance [31] or at a high pulsed microwave with a power of 45.26 MW/m2 based on fast Fourier transforms and genetic algorithm optimizations [32]. Li et al. proposed all-dielectric metamaterial FSS at microwave frequencies with stop band [33], pass band [34], or reconfigurable [35] character based on high-permittivity ceramic (ε>100) resonators. For the considering of its MP, [9] and [11] show that composite material have pretty well MP. Consider the all-dielectric FSS processing technology nowadays, 3D printer can use composite materials to easily fabricate large scale samples. So we adopt the 3D printing material polylactic acid (PLA) to fabricate the FSS based on mechanical structure. Thus, an owning excellent mechanical performance all-dielectric FSS composed of 3D printed material PLA is proposed and tested.
Figure 2(a)-(h) show the progress of model design and preparation. Figure 2.(a) shows the basic lattice of the structure. Actually, the space shape of the basic lattice is a cube. Eight spheres at the cube apexes and one sphere at the body center. The radius of the sphere is R = 4 mm. The spheres are connected by cylinders whose orientations are along the cube body diagonal. The radius of the cylinder is r = 2.25 mm. The size of the whole structure is 16mm×16mm×16 mm. Based on this lattice, the all-dielectric FSS is composed with this structure periodically arranged in x and y direction, single layer in z direction but we add supplement in z direction. The supplement is eighth sphere. So the size in z direction is 24 mm. As shown in Fig. 2(b), the all-dielectric FSS have three sphere layers in z direction and the basic lattice periodic infinitely in x and y direction. The structure is a space lattice, it can periodically arrange in x, y, z direction, as shown in Fig. 2(c). The lattice periodically arranged in three directions can be used to test its equivalent mechanical performance. The mechanical performance always exists in this space lattice despite the numbers of the layers. Figure 2(d) shows the FSS sample for the testing of bending deformation. This sample is made for research the bending deformation of the FSS shown in Fig. 2(a). In order to test the electric and mechanical performance, the sample fabricating divided into three parts. But the samples are all made by 3D printer, shown in Fig. 2(e). The 3D printer we adopted is MakerBot Replicator 2 and the printer material is PLA which permittivity is about 3 at ku band. PLA material with three different colors is adopted to print the samples for distinguish the three samples and experiments. Figure 2(f)(g)(h) show the testing samples for frequency selective performance, compression and bending deformation mechanical performance, respectively. The size of the FSS sample is 240mm×240mm×24 mm (Fig. 2(f)), the quasi-static out-of-plane compression test sample is 64mm×64mm×64 mm (Fig. 2(g)), the three-point bending test sample is 144mm×48mm×24 mm (Fig. 2(h)). The samples with different size or arrangement in space are just for the different requirement of the experiment instrument. But the experiment results are all for the same structure properties characterization. Our design is based on solid structure, and the electromagnetic simulation results are also based on solid structure. If the structure is not solid, which means that the structure is made of air and PLA materials, the compactness and dielectric constant of the structure will be greatly reduced, the electromagnetic resonance mode will change, and the electromagnetic simulation results in this paper will be affected. Therefore, we hope to ensure that the structure is completely made of PLA solid rather than PLA mixed air. When setting 3D printing parameters, we adopt high-quality printing settings and make the filling rate meet 100% as much as possible.
Fig. 2. (a) Basic lattice (b) The design of all-dielectric FSS sample (c) The design of quasi-static out-of-plane compression test sample (d) The design of three-point bending test sample. (e) 3D printer (f) The sample of the FSS (g) The compression testing sample (h) The three-point bending test sample.
3. Electromagnetic performance(EP) and discussion of the material
The FSS structure is simulated by the frequency-domain solver of CST Microwave Studio, where unit cell boundary conditions are applied on the four boundaries along x and y directions. The S parameters are shown in Fig. 3(a). Figure 3(a) shows that there are double stop bands at 16.09-16.4 GHz and 17.11-17.36 GHz. Because the permittivity of the material is very low, so the FSS behaviors pass band in the most frequencies. In order to analysis the formation of the stop band, we observer the electric and magnetic fields of the three stop band points at 16.245 GHz, 17.247 GHz and 18.78 GHz and the two pass band points at 16.887 GHz and 17.532 GHz. The fields of spheres at cube apexes and body center are observed respectively. As shown in Fig. 3(b), in order to illustrate the distribution of the fields, we defined the plane α1, β1, α2, β2. Figure 3 shows the electric and magnetic fields at different plane and frequencies.
Figure 4(a1) shows the distribution of electric field at 16.245 GHz in α1. Figure 4(b1) shows the distribution of magnetic field at 16.245 GHz in β1. There is an electric dipole in y direction in the body center sphere. The magnetic field in the body center sphere forms a loop which also can verify the existence of the electric dipole. Figure 4(a2) shows the distribution of electric field at 16.245 GHz in α2. The electric fields shows that the electric field loops with opposite orientations are formed in every adjacent two cube apexes spheres in z direction which equivalent to electric dipole. Figure 4(b2) shows the distribution of magnetic field at 16.245 GHz in β2. The magnetic fields at the two cube apex spheres in z direction are opposite and a loop forms in the space between the two cube apexes spheres in z direction. The phenomenon verifies the electric dipole too. So the resonant in 16.245 GHz is an electric resonance. The electric resonant in the body center sphere is an eigenmode, so the stop band forms. Here, it is necessary to explain that the resonance in the body center sphere and in the cube apexes spheres are different. The difference in resonance is because the body center sphere is surrounded by many cylinders which along the body diagonal, while the spheres at cube apexes only connected with limited cylinders. The body center sphere is surrounded by many cylinders, so its resonance behaviors richer and changes faster than the resonance in the cube apexes spheres. So the resonance frequency in the body center sphere is lower than the cube apexes spheres.
Fig. 4. (a1) Electric field of α1 at 16.245 GHz (a2) Electric field of α2 at 16.245 GHz (b1) Magnetic field of β1 at 16.245 GHz (b2) Magnetic field of β2 at 16.245 GHz (c1) Electric field of α1 at 16.887 GHz (c2) Electric field of α2 at 16.887 GHz (d1) Magnetic field of β1 at 16.887 GHz (d2) Magnetic field of β2 at 16.887 GHz (e1) Electric field of α1 at 17.247 GHz (e2) Electric field of α2 at 17.247 GHz (f1) Magnetic field of β1 at 17.247 GHz (f2) Magnetic field of β2 at 17.247 GHz (g1) Electric field of α1 at 17.532 GHz (g2) Electric field of α2 at 17.532 GHz (h1) Magnetic field of β1 at 17.532 GHz (h2) Magnetic field of β2 at 17.532 GHz (i1) Electric field of α1 at 18.78 GHz (i2) Electric field of α2 at 18.78 GHz (j1) Magnetic field of β1 at 18.78 GHz (j2) Magnetic field of β2 at 18.78GHz
Figure 4(c1)(d1)(c2)(d2) show the electric fields and magnetic fields at 16.887 GHz in α1, β1, α2, β2. It can be seen from the figures that the electric fields in the the body center sphere is different from 16.245 GHz. Its resonant mode is changed. But it is still an electric resonance, as shown in Fig. 4(c1)(d1). Because the electric field forms two loops with opposite direction and the main resonance in the sphere is still equivalent to electric dipole. The fields in the cube apexes spheres are basically the same as 16.245 GHz, shown in Fig. 4(c2)(d2). The difference is that the field at 16.887 GHz is stronger than 16.245 GHz. But the resonant mode at 16.245 GHz and 16.887 GHz are the same. The electric loops in the cube apexes spheres at 16.887 GHz are clearer than 16.245 GHz. The new resonant mode in the body center sphere (Fig. 4(c1)(d1)) is actuated by the surrounding cylinders. The cube apex spheres without the surrounding cylinders, so its resonant mode is not change to the new resonance. Figure 4(g1)(h1)(g2)(h2) show the electric fields and magnetic fields at 17.532 GHz in α1, β1, α2, β2. It can be seen from Fig. 4(g1)(h1) that in the body center sphere the resonant mode is changed to a new mode and it is a magnetic resonant. Figure 4(g2)(h2) show that the fields in the cube apex spheres are nearly the same as the fields in the body center sphere at 16.245 GHz and it is electric resonant. This is also can verify that because the surrounding cylinders, the resonant mode in the body center sphere is richer and change faster than the resonant mode in the cube apex spheres. Figure 4(e1)(f1)(e2)(f2) show the electric fields and magnetic fields at 17.247 GHz in α1, β1, α2, β2. These fields show that electric dipole and magnetic dipole coexist. One half of the structure forms electric dipole and the other half forms magnetic dipole. This state is intermediate between the state at 16.887 GHz and 17.532 GHz. So the stop band at 17.11GHz-17.36 GHz is formed by the mode transition. Actually, the mode transition is caused by the difference between the body center sphere and cube apex spheres.
Figure 4(i1)(j1)(i2)(j2) show the electric fields and magnetic fields at 18.78 GHz in α1, β1, α2, β2. It can be seen from the figures that the distributions of electric fields and magnetic fields in the body center sphere and other cube apex spheres are the same. The electric field forms a loop, equivalent to a magnetic dipole. The magnetic field oscillates back and forth along x direction. The phenomenon verifies the resonant at 18.78 GHz is magnetic resonance. This resonant mode is also an eigenmode, so a very narrow stop band form near 19 GHz. Through the mode transition between the spheres at the body center sphere and cube apex spheres, we can see that at this frequency, the resonance mode reaches the same. Because the resonant mode in the cube apex spheres are not richer than the sphere at the body center, so the resonant mode in the cube apex spheres after the eigenmode at 17.532 GHz (the same as the resonant mode in the body center sphere at 16.245 GHz), it is directly changes to the eigenmode (shown in Fig. 4(i2)(j2)) at 18.78 GHz and it skip the other resonant modes appear in the body center sphere. So the cube apex spheres do not have the mode transition progress.
Figure 5(a) shows the S21 testing environment. The measurement was carried out in anechoic chamber. Figure 5(b) shows the experimental S21 of the FSS. The experimental result is approximately agreeing with the simulated results. The resonant points of the experimental result are a little blue shift and the effect of the pass band between the double stop bands is not very well. There are many causes contributed to the errors. The size of the printed sample is not well accordance with the size we designed in Fig. 2. The material is shaped via hot melt and the structure is effused layer by layer. So the homogeneous degree may bring error, which result to the permittivity of the structure is not homogeneous too. The maximum size of sample can be fabricated by this type printer is 280mm×153mm×155 mm. So our sample is assembled by three parts. Three same size samples were printed and modified acrylate adhesive was used to paste them. The seams are a little rough and contain modified acrylate adhesive which permittivity is a little different from PLA. These errors can influence the EM transmission/reflection characters of the FSS. The test leads of vector network analyzer bring errors too. So the testing result we observed is a little different with the result simulated in perfect environment.
4. Mechanical performance(MP) and discussion of the material
4.1 Compression tests
Quasi-static out-of-plane compression tests upon the mechanical metamaterial are carried out using a universal material testing machine (INSTRON 3382). SONY vidicon is used to record experiment processes. The experiment setup of compression tests is shown in Fig. 6(a). A compression speed of 1 mm/min was set in all tests. In order to facilitate the compression tests, a PLA sample was employed, as shown in the illustration in Fig. 6(a). By measuring the samples, equivalent mechanical performance of the FSS can be calculated. The tests of three identical samples were performed and the load-displacement data was obtained, which was then converted to stress-strain curves, as shown in Fig. 6(b). Additionally, the experiment processes were recorded, which is shown in Fig. 6(c).
Fig. 6. The compression tests of the mechanical metamaterial: (a) experiment setup, (b)the stress-strain curves of the samples and (c) the view of different stages.
The stress-strain curves show three stages of the deformation. For the strain at 0-4.8%, the deformation can be considered as linear elastic, where the stress increases linearly with the strain (Stage 1). With the increase of strain, plastic deformation will happen. At this stage, the stress will decrease and then keep in a certain range, along with plastic broken at the connecting points between lattices, as shown in Fig. 6(c) (Stage 2). At the densifying stage, the interspace inside the sample is gradually filled by the PLA material, as shown in Fig. 6(c), and the stress increases rapidly with the strain (Stage 3).
To further investigate the performance of the mechanical metamaterial, we make a comparison with the base material. Three cylindrical standard samples were employed in our compression tests according to ISO 604-2002 standards. The size of the samples and our experiment results are shown in Fig. 7(a) and (b) respectively. Then the elasticity modulus of the base material can be obtained, which is 2353.35 MPa. According to the curves in Fig. 7(b), the elasticity modulus of the mechanical metamaterial also can be calculated, which is 112.25 MPa. In addition, the average weigh and the relative density of different samples were measured, which are shown in Table 1. Comparing these results, we found that the relative density of the mechanical metamaterial can be reduced to about 1/3 of the base material and the elasticity modulus is reduced to approximately 1/20.
Fig. 7. Compression tests of the base material: (a) the size (in mm) of the cylindrical standard samples and (b) the stress-strain curves of tests.
Table 1. The parameters of the mechanical metamaterial and the PLA samples
4.2 Bending tests
In order to investigate the bending deformation of the FSS, three-point bending tests were performed according to standard ASTM: C393. The experiment setup is shown in Fig. 8(a), with a 144mm×48mm×24 mm (Fig. 2(h)) PLA sample installed in the fixture. Three identical samples were employed in our tests and the corresponding load-displacement curves were obtained as shown in Fig. 8(b). For displacement at 0-4.61 mm, the load F increase linearly with displacement l. At this stage, elastic deformation would happen and the sample will gradually become concave, as shown in Fig. 8(c). For displacement at 4.61-10.2 mm, with the increasing of l, the growth of F become gradually slow, which means plastic deformation has happened. After the displacement is more than 10 mm, the fracture will happen and the load F decrease rapidly with the displacement. In this stage, the breakage appears at the center connecting points, as shown in Fig. 8(c) l =18 mm.
Fig. 8. Three-point bending tests of the FSS: (a) experiment setup (b) load-displacement curves of the tests and (c) The view of different stages.
In the elastic bending deformation stage (0- 4.61 mm), we define the bending stiffness ${E^ \ast }$ as:
So, the slope of the load-displacement at 0-4.61 mm can be regarded as the bending stiffness of the FSS, which is 90.54 N/mm.5. Conculsion
In this paper, in order to obtain excellent frequency selective characteristic and mechanical performance at the same time in one material, a new design strategy is proposed. As an example, a 3D all-dielectric microwave band FSS composite mechanical metamaterial is demonstrated. The new composite is made by 3D printer and the material is PLA, which can achieve stop band in Ku band by adjusting its electric and magnetic resonant. In addition, the composite is also mechanical metamaterial, which reduces the weight of the FSS and enhance the mechanical performance of the FSS. This kind material may satisfy stricter environments application. The structure also can be made by other materials if we need. With the develop of FSS, metasurface [36–38], the designing strategy has potential to be extended to realize multiple high-performance materials or devices in the future.
Funding
National Natural Science Foundation of China (12004436); Young Talent fund of University Association for Science and Technology in Shaanxi, China (20210510).
Acknowledgments
The authors are grateful to the supports from the National Natural Science Foundation of China under Grant Nos. 12004436, the Young Talent fund of University Association for Science and Technology in Shaanxi, China under Grant 20210510.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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