Name: Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing (Video) | JoVE Journal
Uploaded: 2024-06-28T14:30:00.000+00:00
Duration: 9 min 39 s
Description: Discover ultrasonic characterization of viscoelastic properties in additively manufactured polymers using numerical modeling and DMA testing. This method enhances metamaterial design for acoustic applications.

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S.B. and A.O.K. acknowledge the financial support for the OCENW.M.21.186 project provided by the Dutch Research Council (NWO).

Characterizing Viscoelastic Properties of 3D-Printed Polymer Metamaterials

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<li>de Oliveira, V. B. S., Schalcher, L. F. C., dos Santos, J. M. C., Miranda Jr, E. J. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Wave+attenuation+in+1-D+viscoelastic+phononic+crystal+rods+using+different+polymers%5BTitle%5D)+AND+%22Mater+Res%22%5BJournal%5D)">Wave attenuation in 1-D viscoelastic phononic crystal rods using different polymers.</a> Mater Res. 26, 10.1590/1980-5373-mr-2022-0534 (2023).</li>
<li>Xiao, Y., Wen, J., Wen, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Broadband+locally+resonant+beams+containing+multiple+periodic+arrays+of+attached+resonators%5BTitle%5D)+AND+%22Phys+Lett+A%22%5BJournal%5D)">Broadband locally resonant beams containing multiple periodic arrays of attached resonators.</a> Phys Lett A. 376 (16), 1384-1390 (2012).</li>
<li>Kulpe, J. A., Sabra, K. G., Leamy, M. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Bloch-wave+expansion+technique+for+predicting+wave+reflection+and+transmission+in+two-dimensional+phononic+crystals%5BTitle%5D)+AND+%22J+Acoust+Soc+Am%22%5BJournal%5D)">Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals.</a> J Acoust Soc Am. 135 (4), 1808-1819 (2014).</li>
<li>Guo, Z., Sheng, M., Pan, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Flexural+wave+attenuation+in+a+sandwich+beam+with+viscoelastic+periodic+cores%5BTitle%5D)+AND+%22J+Sound+Vib%22%5BJournal%5D)">Flexural wave attenuation in a sandwich beam with viscoelastic periodic cores.</a> J Sound Vib. 400, 227-247 (2017).</li>
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<li>Matlack, K. H., Bauhofer, A., Krödel, S., Palermo, A., Daraio, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Composite+3D-printed+metastructures+for+low-frequency+and+broadband+vibration+absorption%5BTitle%5D)+AND+%22Proc+Natl+Acad+Sci+U+S+A%22%5BJournal%5D)">Composite 3D-printed metastructures for low-frequency and broadband vibration absorption.</a> Proc Natl Acad Sci U S A. 113 (30), 8386-8390 (2016).</li>
<li>Van Belle, L., Claeys, C., Deckers, E., Desmet, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((On+the+impact+of+damping+on+the+dispersion+curves+of+a+locally+resonant+metamaterial%3A+Modelling+and+experimental+validation%5BTitle%5D)+AND+%22J+Sound+Vib%22%5BJournal%5D)">On the impact of damping on the dispersion curves of a locally resonant metamaterial: Modelling and experimental validation.</a> J Sound Vib. 409, 1-23 (2017).</li>
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<li>Samykano, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Mechanical+property+of+FDM+printed+ABS%3A+influence+of+printing+parameters%5BTitle%5D)+AND+%22Int+J+Adv+Manuf+Technol%22%5BJournal%5D)">Mechanical property of FDM printed ABS: influence of printing parameters.</a> Int J Adv Manuf Technol. 102 (9-12), 2779-2796 (2019).</li>
<li>Hussein, M. I., Leamy, M. J., Ruzzene, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Dynamics+of+Phononic+Materials+and+Structures%3A+Historical+Origins%2C+Recent+Progress%2C+and+Future+Outlook%5BTitle%5D)+AND+%22Appl+Mech+Rev%22%5BJournal%5D)">Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook.</a> Appl Mech Rev. 66 (4), 040802(2014).</li>
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All authors declare that they have no conflicts of interest.

The 3D printing procedure described in section 1 applies to most table-size FDM 3D printers. Yet, 3D printing from ABS can be tricky because this polymer is sensitive to temperature changes. Uneven heating or cooling can cause shrinkage of already printed parts, leading to warping, cracking, or delamination. To prevent these issues, it is suggested first to identify proper print settings based on a datasheet from the supplier. Next, it is advised to avoid strong temperature variations near the printed part during the printing process. It can be achieved by enclosing the 3D printer with a box or a chamber to maintain a stable warm environment.
Thermogravimetric analysis (TGA) is aimed here to identify the temperature at which the material decomposition initiates, as this temperature governs the maximum safe temperature for differential scanning calorimetry (DSC). TGA operates on the principle of measuring the mass loss of a material as a function of temperature. The DSC, in turn, measures key thermal parameters of a material, including the glass-transition temperature, melting point, and recrystallization temperatures. It operates based on the principle of detecting energy changes associated with phase transitions. Thus, TGA and DSC tests serve as complementary techniques to DMA.
It is crucial to analyze Tm from the DSC plot carefully, as subjecting the dynamic mechanical analyzer to a melted sample can damage the thermocouple of the instrument. Before loading the sample, one needs to ensure that the pan remains uncontaminated. Contamination of the sample with foreign substances can affect the thermal properties and introduce artifacts in the TGA and DSC curves. Careful identification of Tg and Tm is crucial as they serve as important parameters for DMA.
DMA measures the variation of material properties of the test sample with temperature, within the user-specified frequency range. The DMA instrument can do such measurements within the frequency range of 0.01-600 Hz. Variation of material properties of rheological simple polymers at frequency values outside this range can be predicted using the time-temperature superposition7. In this way, one obtains the viscoelastic properties of materials - loss modulus and complex viscosity. However, operating at temperatures near Tm can damage the dynamic mechanical analyzer and must be avoided. Besides, operating at temperatures near Tg, may result in inconsistent and unreliable results. Also, note that proper sample alignment is essential, ensuring that the sample is straight and has smooth, parallel edges without surface defects. The thermocouple must not touch the clamps at any point of the measurement to avoid damage.
The almost flat trends for the storage and loss moduli curves in Figure 4 reveal that the FDM-printed ABS primarily exhibits elastic behavior at room temperature. The flatness of the curve for the tangent of phase angle(&#948;), which is the ratio of storage modulus to loss modulus, indicates that the Tg of the material does not lie within the measured temperature range. Besides, the data for the two test samples with different orientations of the print pattern are indistinguishable, suggesting no significant effect of the print pattern on the moduli. It can be attributed to exceptionally low viscous losses in ABS and 100% infill density, which mask any effect of patterning. Note, however, that these results are more an exemption rather than a rule for 3D printed polymers as the viscous losses in other filaments are non-negligible. These losses emphasize the importance of conducting the DMA for 3D-printed polymers.
Tensile testing is a widely adopted technique for the mechanical characterization of materials. It provides quasi-static mechanical moduli, e.g., Young&#39;s modulus and Poisson&#39;s ratio, for a material of the test sample, often of a bone-like shape (Figure 1B). The digital image correlation (DIC) technique can be added to ensure the proper positioning of a test sample and to capture images of its deformed surface at each loading step, as well as to process the images to analyze strain and displacement fields. Although the integration of DIC yields a higher level of accuracy in results, it can lead to several challenges if not handled properly. It is important to apply a good speckle pattern, with a 3D residuum less than 0.4/pixel, while sample preparation for DIC. Ensure that the sample is well-focused and use proper calibration plates that fit best the field of view of the camera. The Young&#39;s modulus determined from tensile testing in this study, 0.543 GPa, agrees well with the value reported (0.751 GPa) by Samykano et al.26. UTM used for testing may have limitations in terms of accuracy, resolution, or capacity, which can affect the quality and reliability of the results. Incorrect sample preparation, including improper mounting or machining, can cause errors in the measurement. Slippage of the sample can be avoided by using abrasive papers for better contact between the sample and the jaws of the UTM. Additionally, many materials have anisotropic mechanical properties. Lack of attention to anisotropic behavior can lead to inaccurate predictions.
Numerical simulations to estimate bandgaps are essential to properly define the work frequencies for pitch-catch transmission tests4,8,27. The calculated data shown in Figure 7B are expectable for the analyzed metamaterial configuration shown in Figure 7A. Specifically, the transmission curve outside the bandgap frequency oscillates around a constant value with the oscillation peaks corresponding to natural frequencies of the finite-size periodic medium27. Within the bandgap, the transmission is strongly reduced validating the capability of this metamaterial to attenuate acoustic waves.
The reported simulation procedure (section 5) is general and not restricted to the analyzed geometry or specific viscoelastic behavior. Other metamaterial structures made of various viscoelastic materials can be successfully tested in the transmission analysis7,8,20,22,24. The material behavior is limited to linear elastic of viscoelastic as nonlinear materials cannot be analyz in the frequency domain4. Note that the transmission analysis in other finite-element packages may require other implementation steps and different terminology or commands for similar actions. Also, periodic boundary conditions and PML may be absent which requires searching for alternatives to reduce spurious wave reflections from the domain boundaries.
The pitch-catch transmission tests aim to estimate the portion of the acoustic wave energy transmitted through a (meta)material sample and identify (validate) bandgap frequencies. It is convenient to set up such a test based on preliminary numerical transmission data, which allows for identifying an operating frequency range that, in turn, enables the selection of a proper excitation source8,20,22,24. Typical equipment for transmission tests includes a signal generator to generate an excitation signal, an amplifier to increase the intensity of the signal, piezo elements (e.g., a piezoelectric disc or piezoceramic transducer) to transform electric signals into mechanical motions and vice versa, and a data acquisition system for recording transmitted signals7. One piezo element is tightly connected to a tested sample to excite a signal, while the other(s) is (are) used to receive a transmitted signal. The second piezo element is replaced here by a laser Doppler vibrometer (LDV) for non-contact measurements that deliver a better quality of recorded signals due to the extremely high sensitivity of the laser.
The averaged measured transmitted signal is in good agreement with the numerical predictions (Figure 7B and Figure 9B), as can be expected for a sample with extremely low viscous losses. The shown frequency-domain data are superimposed by noise owing to the high sensitivity of the laser. The advantages and flexibility of using LDV for data acquisition are clear. In addition to non-contact measurements and accurate data, the LDV enables measuring the signal at the excitation side by focusing the laser on the sample in the vicinity of a piezoelectric disk. This offers a possibility to evaluate the ratio of transmitted to the input signals as in numerical simulation which is especially useful for complex-structured metamaterials that exhibit an elevated level of internal wave reflections.
It can be concluded that the proposed protocol for characterizing viscoelastic metamaterials can be helpful for researchers working in this rapidly developing field to acquire data for a broad range of additively manufactured materials and to use these data in the analysis of metamaterials dynamics. Since exceptional damping properties offered by polymers due to viscoelastic effects make them a preferred choice over metallic or ceramic metamaterials, a deeper understanding of these effects is essential to further increase the applications of metamaterials in acoustic waveguiding, cloaking, underwater acoustics, sound absorption, medical imaging, energy harvesting, and many others.

Polymers reveal viscoelastic response to a greater or smaller extent. This means that in addition to elastic behavior described by elastic (storage) moduli, they have viscous (loss) components. Viscous losses cause delay in the development of stress under applied strain and vice versa. Under dynamic excitation, out-of-phase stress components are dissipated through heat, thus reducing the energy of acoustic waves propagating in a viscoelastic medium. This phenomenon is referred to as viscous damping.
Viscosity originates at a molecular level due to relative motions or local rotations of bonds in polymer chains and, thus, is governed by the chemical composition, structure, and connections of polymer chains. Molecular mobility depends on temperature and deformation rate, resulting in temperature- and time-driven behavior of viscoelastic materials. All this makes viscoelasticity an inherently complex phenomenon that has a unique signature for each material. One feasible way to approximate such behavior implies modeling a viscoelastic material as a mechanical system composed of (Hookean) springs and (Newtonian) dashpots1. Although this approach fully neglects the molecular structure of a material and all the complexity of a real relaxation process, it can provide adequate results for hard polymers with comparatively low viscous losses2.
The key to obtaining an adequate mechanical model is tuning the parameters of the springs and dashpots to experimental data for the storage and loss moduli of a viscoelastic polymer3,4,5,6,7,8. This work describes a set of methods to determine the viscoelastic moduli of additively manufactured polymers and to use them in characterizing the dynamics of elastic metamaterials. By this, we aim to bridge the gap between material properties and the structure-driven dynamics of metamaterials, enabling a more robust and reliable design of metamaterials for target working frequencies.
Elastic metamaterials are a class of engineered, often periodically structured materials that can manipulate acoustic waves in solids in an unusual yet controllable way9. The wave manipulation is mainly implemented by tailoring bandgaps - the frequency ranges in which wave propagation is prohibited4. The unique dynamics of elastic metamaterials are governed by a fine-tuned architecture represented by complex-shaped unit cells, especially for three-dimensional configurations. Such structural complexity can often be realized only using additive manufacturing which makes viscoelasticity analysis especially relevant for additively manufactured elastic metamaterials. Most current studies, however, have used oversimplified models of viscosity, such as the Maxwell10,11 or Kelvin-Voigt model11. Because these models cannot describe any real viscoelastic material2, the conclusions derived by using them cannot be considered reliable. Therefore, there is a burning need for more realistic models replicating viscoelastic material properties at ultrasonic frequencies. Several studies have addressed this need6,8,12 and reported serious limitations of commercial finite element solvers due to high13 computational load, especially when dealing with complex geometries and/or high frequencies14 and the restriction on considering the relaxation of a single modulus (in reality, both moduli of an isotropic medium under relaxation). Another analysis method, e.g., plane wave expansion, can reduce the computational burden15, but requires an analytical description of the scatterer geometry, limiting its applicability. The extended plane wave expansion approach16,17 addresses this limitation but adds computational complexity. The Bloch wave expansion18 and transfer matrix methods19 can only consider periodic structures of finite dimensions, which can be described analytically. The spectral element approach20,21 offers computational efficiency, but its applicability is limited to very low frequencies below the first bandgap. Thus, in addition to the lack of experimental data for storage and loss moduli at room temperature and high frequencies (above 100 Hz), which are common work conditions for elastic metamaterials20,22,23,24, the analysis of their dynamics remains challenging. This work aims to fill in these gaps by summarizing the experimental (and numerical) techniques for the characterization of additively manufactured viscoelastic polymers and elastic metamaterials made of them.
This approach is illustrated by analyzing a simple one dimensional (1D) continuous analog of a periodic mass-spring model made of commonly used acrylonitrile butadiene styrene (ABS) polymer and produced by a fused-deposition modeling (FDM) 3D-printing (Section 1), for which one can experimentally determine the decomposition and glass transition temperatures (Section 2) and derive the master curves for storage and loss moduli at reference room temperature (Section 3). In addition, the quasi-static mechanical moduli can be estimated in tensile tests (Section 4) and linked to their dynamic counterparts. Next, the numerical method to model the dynamic characteristics of a metamaterial is described (Section 5), and the obtained numerical results are validated experimentally in transmission experiments (Section 6). Finally, the applicability and limitations of the proposed methods based on the findings are discussed.

<table><tbody><tr><td>Acrylonitrile Butadiene Styrene&amp;nbsp;(ABS)</td><td>BASF</td><td>https://www.xometry.com/resources/3d-printing/abs-3d-printing-filament/</td><td>Print temperature: 225-245 &amp;deg;C</td></tr><tr><td>COMSOL Multiphysics 6.0</td><td>COMSOL</td><td>https://www.comsol.com/product-download/6.0</td><td>Finite element software</td></tr><tr><td>DAQ system for DIC</td><td>Dantec Dynamics</td><td>https://www.dantecdynamics.com/components/daq-controllers/</td><td></td></tr><tr><td>Discovery DSC 25</td><td>TA Instruments</td><td>https://www.tainstruments.com/dsc-25/</td><td>Software: Trios; Pan: Aluminium</td></tr><tr><td>DMA 8000</td><td>Perkin Elmer</td><td>https://www.perkinelmer.com/product/dma-8000-analyzer-qtz-window-ssti-clamp-n5330101</td><td>Software: PerkinElmer</td></tr><tr><td>DN2.813-04 Spectrum hybridNetbox</td><td>Spectrum Instrumentation</td><td>https://spectrum-instrumentation.com/products/details/DN2813-04.php</td><td>4-channel signal generator and digitizer; Software used: SBench6</td></tr><tr><td>FDM 3D printer Ultimaker 3.0</td><td>Ultimaker</td><td>https://ultimaker.com/3d-printers/s-series/ultimaker-s3/</td><td>Slicer: Ultimaker Cura</td></tr><tr><td>Polytec laser unit OFV 534</td><td>Polytec GmbH</td><td>https://www.polytec.com/eu/vibrometry/products</td><td>Laser and laser head, as a set</td></tr><tr><td>Polytec OFV-5000 vibrometer controller</td><td>Polytec GmbH</td><td>https://www.polytec.com/eu/vibrometry/products</td><td>LDV controller</td></tr><tr><td>Power amplifier Type 2718</td><td>Bruel &amp;amp; Kjaer</td><td>https://www.bksv.com/en/instruments/vibration-testing-equipment/vibration-amplifiers/exciters/power-amplifier-type-2718</td><td>Power output capability of 75 VA</td></tr><tr><td>PRYY-0110</td><td>PI Ceramic</td><td>https://www.piceramic.com/en/products/piezoceramic-components/disks-rods-and-cylinders/piezoelectric-discs-1206710</td><td>Ceramic-based, Ag-screened piezoelectric discs</td></tr><tr><td>Q400 DIC</td><td>Limess Messtechnik &amp;amp; Software GmbH</td><td>https://www.limess.com/en/products/q400-digital-image-correlation</td><td>Software: Istra4D</td></tr><tr><td>Thermogravimetric Discovery TGA 550</td><td>TA Instruments</td><td>https://www.tainstruments.com/tga-550/</td><td>Software: Trios; Pan: Aluminium</td></tr><tr><td>UniVert 1kN Tensile testing machine</td><td>Cell Scale biomaterials testing</td><td>https://www.cellscale.com/products/univert/</td><td>Software: UniVert; load cell capacity: 1 kN</td></tr><tr><td>WMA-300 High speed high voltage amplifier</td><td>Falco Systems</td><td>https://www.falco-systems.com/High_voltage_amplifier_WMA-300.html</td><td>50x amplification up to +150 V and -150 V with respect to ground</td></tr></tbody></table>

characterizing dissipative elastic metamaterials produced by additive manufacturing

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

Viscoelastic behavior can be beneficial in enhancing the unprecedented dynamics of polymer metamaterials or, in contrast, negatively impacting their wave control mechanisms. It is, therefore, crucial to properly characterize the viscoelastic properties of a polymer metamaterial at its working frequencies to understand viscoelastic effects. However, the viscoelasticity of polymers is a complex phenomenon, and the data on storage and loss moduli at ultrasonic frequencies are extremely limited, especially for additively manufactured polymers. This work presents a protocol to experimentally characterize the viscoelastic properties of additively manufactured polymers and to use them in the numerical analysis of polymer metamaterials. Specifically, the protocol includes the description of the manufacturing process, experimental procedures to measure the thermal, viscoelastic, and mechanical properties of additively manufactured polymers, and an approach to use these properties in finite-element simulations of the metamaterial dynamics. The numerical results are validated in ultrasonic transmission tests. To exemplify the protocol, the analysis is focused on acrylonitrile butadiene styrene (ABS) and aims at characterizing the dynamic behavior of a simple metamaterial made from it by using fused deposition modeling (FDM) three-dimensional (3D) printing. The proposed protocol will be helpful for many researchers to estimate viscous losses in 3D-printed polymer elastic metamaterials that will improve the understanding of material-property relations for viscoelastic metamaterials and eventually stimulate the use of 3D-printed polymer metamaterial parts in various applications.

The described protocol is illustrated by manufacturing and characterizing bone-shaped and metamaterial samples made of acrylonitrile butadiene styrene (ABS). The geometries of the samples are as follows. The dimensions of the dog bone-shaped samples for the tensile tests follow the designation D638−14. The metamaterial structure represents a continuous analog of a one-dimensional mass-spring model (Supplementary File 1) that is composed of 10 disks of radius 7 mm and 2 mm thickness located periodically at 20 mm, which are joined by thin beams of square cross-section 2 mm x 2 mm. STL file for dog-bone structure used for tensile testing can be found in Supplementary File 2.
3D printing of polymer samples 
The steps of section 1 are followed to manufacture the metamaterial and bone-shaped samples using an FDM two-nozzle 3D printer. In the slicer software, Acrylonitrile Butadiene Styrene (ABS) filament is assigned for nozzle 1, while nozzle 2 is switched off since the samples are produced from a single material without support. The following print settings are used: infill density of 100%, linear infill pattern of 0.2 mm layer height, nozzle temperature of 245 °C, bed temperature of 100 °C, print speed of 40 mm/s, and fan speed of 3%. The sliced geometries are shown in Figure 1A. To keep the parts fixed during the print process, a thin layer of glue on the print bed surface is applied. Once the printing is finished (Figure 1B), the 3D printed structures are removed after the print bed is cooled down to room temperature. The final 3D-printed samples are shown in Figure 1C.
TGA and DSC 
The TGA of the ABS polymer indicates a single-stage decomposition process, see Figure 2A. The measured onset temperature of decomposition is 390 °C, with complete decomposition occurring at around 420 °C. One observes 5% weight loss of the test sample corresponding to 363.6 °C, which served as the upper-temperature limit for the DSC test. DTG results reveal a peak decomposition rate at 404.5 °C. Figure 2B shows the results of the DSC test performed over a temperature range of 40 °C to 270 °C, indicating a glass transition temperature (Tg) of 100.4 °C and a melting temperature (Tm) of 216.5 °C.
DMA 
The glass-transition temperature (Tg) from DSC serves as the upper temperature limit for the DMA test following the objective of this work to characterize ABS at room temperature. The DMA was performed using the DMA 8000, see Figure 3, on three samples, each of linear infill-pattern aligned at 0° (type 1) and 45° (type 2) to the reference <img alt="Spectroscopy system in optical excitation diagram; χ̂ as molecular polarization symbol." src="/files/ftp_upload/66898/66898eq05.jpg" style="margin: auto;" data-altupdatedat="1788304762000" data-alt="Equation 1"> of the 3D printer. A frequency sweep from 0.1 to 100 Hz is employed with temperatures varying between 5 °C and 60 °C. The heating rate was adjusted to 2 °C/min, and the temperature was increased in increments of 5 °C with a 5 min isothermal pause at each step. The curves obtained at 12 different temperatures were shifted to a reference temperature of 25 °C using the Williams-Landel-Ferry (WLF) equation. The conclusive time-temperature superposition outcomes for type 1 and type 2 samples (Figure 4) reveal a flat line for storage modulus and loss modulus in the frequency range of 10-7 to 108 Hz. Some deviations are observed in the loss modulus and tan (δ) at certain points in the TTS curve.
Tensile testing 
Tensile tests were conducted utilizing an ultimate tensile machine (UTM), see Figure 5, with a maximum load capacity of 1 kN. The testing parameters included a maximum force of 980 N and a ramp time of 60 s. A recovery time of 10 s was set, and the tensile test machine recorded 10 data points for force per second. The high-resolution cameras of a DIC system captured 30 images per frame, and the analysis was done focusing on the shaded region identified as polygon 1 in Figure 6A. The average principal strain values within the shaded region are 1.317 (tensile strain) and -0.454 (compressive strain). Figure 6B shows the results for the Poisson's ratio, with an observed average value of 0.37. Figure 6C shows the results for Young's modulus, calculated from the slope of the unloading curve showing elastic regain, which yields a value of 0.543 GPa.
Finite element analysis 
Figure 7A presents the geometry of a metamaterial considered for the transmission analysis, where the "Output plane" indicates the probe to measure transmitted signals. The numerically estimated transmission curve is shown in Figure 7B, for an out-of-plane excitation displacement of 1 μm along <img alt="Static equilibrium equations ΣFx=0; ΣFy=0 with diagram; force analysis; educational physics." src="/files/ftp_upload/66898/66898eq04.jpg" style="margin: auto;" data-altupdatedat="1788304762000" data-alt="Equation 4"> of the incident plane shown for the model in Figure 7A. The drops in transmission level exceeding 20 dB, shown by a shaded region, represent frequency bandgaps at various frequency ranges.
Pitch-catch transmission tests 
Figure 8 shows the setup used for the pitch-catch transmission test performed on a simple 1D continuous analog of a periodic mass-spring model made of commonly used ABS polymer (Figure 9A), using non-contact LDV. Figure 9B shows the results of the pitch-catch transmission test in the frequency domain for the 3D-printed ABS sample identical to the one shown in Figure 7A. The ceramic-based Ag-screened piezoelectric disc of radial resonant frequency 200 kHz (diameter 10 mm and thickness 0.2 mm) was used to apply a frequency sweep signal swept from 4 kHz to 40 kHz. The transmitted signal was acquired at the 10th unit cell from the excitation side. The recorded time-domain data were transformed to the frequency domain by applying the Fast Fourier Transform. The processed data reveal a signal drop of more than 20 dB at various frequencies, indicating the frequency bandgaps that are highlighted in blue in Figure 9B.
<img alt="3D printing process with Ultimaker, CAD design to physical object, tensile test sample preparation." class="xfigimg" src="/files/ftp_upload/66898/66898fig01.jpg" data-altupdatedat="1788304762000" data-alt="Figure 1"> 
Figure 1: 3D printing of polymer samples. (A) Sliced geometry in the slicer software. (B) Ongoing 3D printing process. (C) 3D printed ABS sample for tensile testing as per ASTM standard D638. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Thermogravimetric analysis (TGA) and differential thermal analysis (DTA) graph with temperature data." class="xfigimg" src="/files/ftp_upload/66898/66898fig02.jpg" data-altupdatedat="1788304762000" data-alt="Figure 2"> 
Figure 2: Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Thermal characterization results for the ABS polymer in (A) TGA and DTG and (B) DSC tests. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig02large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Nitrogen flow experimental setup with inlet, outlet, dewar; thermocouple, clamps holding sample." class="xfigimg" src="/files/ftp_upload/66898/66898fig03.jpg" data-altupdatedat="1788304762000" data-alt="Figure 3"> 
Figure 3: Dynamic mechanical analysis. (A) DMA instrument and important parts. (B) Image of the single-cantilever test configuration (without sample). (C) Image of a clamped sample in the single-cantilever test configuration. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig03large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Dynamic mechanical analysis graph; storage/loss modulus vs frequency; viscoelastic material testing." class="xfigimg" src="/files/ftp_upload/66898/66898fig04.jpg" data-altupdatedat="1788304762000" data-alt="Figure 4"> 
Figure 4: Time-temperature superposition outcomes. TTS results for ABS polymers 3D printed with a linear infill pattern aligned at 0° (type 1) and 45° (type 2) to the reference <img alt="Spectroscopy system in optical excitation diagram; χ̂ as molecular polarization symbol." src="/files/ftp_upload/66898/66898eq05.jpg" style="margin: auto;" data-altupdatedat="1788304762000" data-alt="Equation 5"> of the 3D printer: storage modulus, loss modulus, and tan(δ). <a href="https://www.jove.com/files/ftp_upload/66898/66898fig04large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Digital Image Correlation setup diagram; high-resolution cameras, UTM, data acquisition for analysis." class="xfigimg" src="/files/ftp_upload/66898/66898fig05.jpg" data-altupdatedat="1788304762000" data-alt="Figure 5"> 
Figure 5: Tensile testing setup. Diagram of the tensile testing setup, including the universal tensile machine (UTM) coupled with a DIC setup. A magnified view of the sample is also shown to highlight the speckle pattern on the sample. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig05large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Static equilibrium, strain measurement, dual-camera setup, strain analysis graph, stress-strain curve." class="xfigimg" src="/files/ftp_upload/66898/66898fig06.jpg" data-altupdatedat="1788304762000" data-alt="Figure 6"> 
Figure 6: Results of tensile testing. (A) Image of the test sample acquired by both cameras of the DIC setup. Polygon 1 is the area considered for calculations; the sample was pulled from left to right. (B) Results for Poisson's ratio. (C) Stress-strain behavior of the 3D printed ABS bone-shaped samples (type 2) tested at 50 mm/min (Test 1) and 5 mm/min (Test 2). Testing was done on four samples. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig06large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Acoustic waveguide diagram; chart of transmission vs. frequency; excitation, acquisition planes." class="xfigimg" src="/files/ftp_upload/66898/66898fig07v2.jpg" data-altupdatedat="1788304762000" data-alt="Figure 7"> 
Figure 7: Finite element analysis. (A) A geometric model for numerical calculations of transmission; ax is the unit cell dimension, d is the diameter of the disc, and PML stands for perfectly matched layer. (B) Numerical results for transmission calculations, shaded regions represent frequency bandgap. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig07largev2.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Laser Doppler vibrometry setup; diagram with LDV, laser head, DAQ, computer for vibration analysis." class="xfigimg" src="/files/ftp_upload/66898/66898fig08.jpg" data-altupdatedat="1788304762000" data-alt="Figure 8"> 
Figure 8: Pitch-catch transmission experiment setup. Testing setup for pitch-catch transmission experiments with a non-contact laser Doppler vibrometer used to measure mechanical vibrations transmitted through a sample. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig08large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Piezoelectric disc array setup with frequency transmission graph, illustrating acoustic analysis." class="xfigimg" src="/files/ftp_upload/66898/66898fig09v2.jpg" data-altupdatedat="1788304762000" data-alt="Figure 9"> 
Figure 9: Results of pitch-catch transmission experiment. (A) A photo of the metamaterial structure of unit cell size ax = 20 mm with disk diameter d = 14 mm tested in the pitch-catch transmission experiment. A piezoelectric disc of radial resonant frequency 200 kHz is used to excite structural vibrations and reflective tape is pasted for acquisition at different points (AP1, AP2, AP3, AP4, and AP5) of the structure. (B) Experimental results from pitch-catch transmission test. Recordings for the incident and the transmitted signal were done at the excitation point and the acquisition point 5 (AP5), respectively. Shaded regions represent frequency bandgap estimated experimentally. <a href="https://www.jove.com/files/ftp_upload/66898/66898fig09largev2.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Test configuration</td>
			<td>Test samples</td>
		</tr>
		<tr>
			<td>Single Cantilever</td>
			<td>Most samples, except thin films under 0.1 mm</td>
		</tr>
		<tr>
			<td>Dual Cantilever</td>
			<td>Comparatively soft materials if the single cantilever data are noisy</td>
		</tr>
		<tr>
			<td>Three-point bending</td>
			<td>Very stiff and large samples</td>
		</tr>
		<tr>
			<td>Tension</td>
			<td>Very thin films of thickness &lt;0.2 mm</td>
		</tr>
	</tbody>
</table>
Table 1: Test configurations suitable for different test samples for DMA, classified based on the sample stiffness.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Test configurations</td>
			<td>Length (mm)</td>
			<td>Width (mm)</td>
			<td>Thickness (mm)</td>
		</tr>
		<tr>
			<td>Single Cantilever</td>
			<td>05–25</td>
			<td>04–12</td>
			<td>0.10–4.00</td>
		</tr>
		<tr>
			<td>Dual Cantilever</td>
			<td>25–45</td>
			<td>04–12</td>
			<td>0.10–4.00</td>
		</tr>
		<tr>
			<td>Three Point Bending</td>
			<td>25–45</td>
			<td>04–12</td>
			<td>0.50–4.00</td>
		</tr>
		<tr>
			<td>Tension</td>
			<td>10–25</td>
			<td>04–10</td>
			<td>0.01–0.20</td>
		</tr>
	</tbody>
</table>
Table 2: Dimensions of test samples for different test configurations in the DMA technique.
Supplementary File 1: STL file for 1D periodic structure. <a href="https://www.jove.com/files/ftp_upload/66898/1D%20Periodic%20Structure.zip" target="_blank">Please click here to download this File.</a>
Supplementary File 2: STL file for dog-bone structure used for tensile testing. <a href="https://www.jove.com/files/ftp_upload/66898/Bone_Structure.zip" target="_blank">Please click here to download this File.</a>

Additively manufactured polymers have been widely used for producing elastic metamaterials. The viscoelastic behavior of these polymers at ultrasonic frequencies remains, however, poorly studied. This study reports a protocol to estimate the viscoelastic properties of 3D-printed polymers and show how to use them to analyze the metamaterial dynamics.

Viscoelastic behavior can be beneficial in enhancing the unprecedented dynamics of polymer metamaterials or, in contrast, negatively impacting their wave ...

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