Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

Published: June 28, 2024

doi:

Sidharth Beniwal, Ranjita K. Bose, Anastasiia O. Krushynska

¹Engineering and Technology Institute Groningen (ENTEG), Faculty of Science and Engineering,University of Groningen

Summary

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.

Abstract

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.

Introduction

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.

Protocol

1. 3D printing procedure for polymer samples NOTE: The 3D printing of polymer samples on an FDM 3D printer includes a preparatory phase, printing process, and post-processing. Preparation of the model Create a 3D model of a sample geometry in any software supporting computer-aided design (CAD) and export it as an STL, OBJ, or STEP file. NOTE: For metamaterials, the common software is a commercial (COMSOL Multiphysics, Abaqus, SolidWorks, etc.) o…

Representative Results

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 periodic…

Discussion

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 pri…

Declarações

The authors have nothing to disclose.

Acknowledgements

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

Materials

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

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