[en] Characterizing the mechanics of periodic scaffolds used for bone tissue repair, while maintaining their structural integrity, is a challenging problem. By leveraging concepts arising from the bulk phononic crystal community, here we investigate the reflection of elastic waves propagating through a water-immersed biphasic architectured medium in the ultrasonic regime. Towards this goal, Bloch–Floquet analysis is applied on a 2D unit cell made of a soft inclusion embedded in a hard matrix, to recover its corresponding phononic band structure. Exploring the modal conversion at the boundary between the homogeneous incident medium and the architectured one allows identifying a bandgap within the considered frequency range, which exhibits a significant sensitivity to varying volume fraction of the soft phase. Conducting further numerical analyzes, which account for the viscoelasticity of the two constituent phases, along with the finite-size and bounded nature of the architectured medium, shows that a sudden amplitude rise of the reflection coefficient takes place at a frequency that is closely related to the upper limit of this bandgap. This hypothesis is experimentally verified on 3D-printed bio-mimicking samples, which exhibit an in-plane periodicity at a length scale of a few hundred micrometers. Altogether, the reported results suggest that tracking prohibited frequency bands via the measurement of the reflection coefficient allows for the monitoring of micro-architectured media like scaffolds.
Disciplines :
Materials science & engineering
Author, co-author :
Gattin, Max; Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, Créteil, France
Bochud, Nicolas ; Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, Créteil, France
Grossman, Quentin ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Ruffoni, Davide ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Mécanique des matériaux biologiques et bioinspirés
Rosi, Giuseppe ; Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, Créteil, France
Naili, Salah ; Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, Créteil, France
Language :
English
Title :
Ultrasound monitoring of multiphase architectured media: Bandgap tracking via the measurement of the reflection coefficient
The authors are in debt to Pierre Margerit (Arts et Métiers Institute of Technology, CNRS, CNAM, PIMM, HESAM Université, Paris, France) for the fruitful discussions regarding the Bloch wave analysis. This work was partially supported by the “Bonus Qualité Recherche” for young researchers (Faculté des Sciences et Technologie, Université Paris-Est Créteil, France) and the CNRS/IRP Coss&Vita between the Fédération Francilienne de Mécanique (F2M, CNRS FR2609, France) and the International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS, Università dell'Aquila, Italy).The authors are in debt to Pierre Margerit (Arts et Métiers Institute of Technology, CNRS, CNAM, PIMM, HESAM Université, Paris, France) for the fruitful discussions regarding the Bloch wave analysis. This work was partially supported by the “Bonus Qualité Recherche” for young researchers (Faculté des Sciences et Technologie, Université Paris-Est Créteil , France) and the CNRS/IRP Coss&Vita between the Fédération Francilienne de Mécanique (F2M, CNRS FR2609, France) and the International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS, Università dell'Aquila, Italy).
Cleemput, S., Huys, S.E., Cleymaet, R., Cools, W., Mommaerts, M.Y., Additively manufactured titanium scaffolds and osteointegration-meta-analyses and moderator-analyses of in vivo biomechanical testing. Biomater Res, 25, 2021, 18.
Tajvar, S., Hadjizadeh, A., Samandari, S.S., Scaffold degradation in bone tissue engineering: an overview. Int Biodeterior Biodegrad, 180, 2023, 105599.
Bawolin, N., Li, M., Chen, X., Zhang, W., Modeling material-degradation-induced elastic property of tissue engineering scaffolds. J Biomech Eng, 132, 2010.
Jin, H., Zhuo, Y., Sun, Y., Fu, H., Han, Z., Microstructure design and degradation performance in vitro of three-dimensional printed bioscaffold for bone tissue engineering. Adv Mech Eng, 11, 2019, 1687814019883784.
Kruisová, A., Ševčík, M., Seiner, H., Sedlák, P., Román-Manso, B., Miranzo, P., et al. Ultrasonic bandgaps in 3D-printed periodic ceramic microlattices. Ultrasonics 82 (2018), 91–100.
Fielder, M., Nair, A.K., Effects of scattering on ultrasound wave transmission through bioinspired scaffolds. J Mech Behav Biomed Mater, 126, 2022, 105065.
Vasileiadis, T., Varghese, J., Babacic, V., Gomis-Bresco, J., Navarro Urrios, D., Graczykowski, B., Progress and perspectives on phononic crystals. J Appl Phys, 129, 2021, 160901.
Oudich, M., Gerard, N.J., Deng, Y., Jing, Y., Tailoring structure-borne sound through bandgap engineering in phononic crystals and metamaterials: a comprehensive review. Adv Funct Mater, 33, 2023, 2206309.
Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzynski, L., Djafari-Rouhani, B., Theory of acoustic band structure of periodic elastic composites. Phys Rev B, 49, 1994, 2313.
Aguzzi, G., Thomsen, H.R., Hejazi Nooghabi, A., Wiltshaw, R., Craster, R.V., Chatzi, E.N., et al. Architected frames for elastic wave attenuation: experimental validation and local tuning via affine transformation. Appl Phys Lett, 121, 2022, 201702.
Declercq, N.F., Chehami, L., Moiseyenko, R.P., The transmission spectrum of sound through a phononic crystal subjected to liquid flow. Appl Phys Lett, 112, 2018, 024102.
Lucklum, R., Mukhin, N., Djafari-Rouhani, B., Pennec, Y., Phononic crystal sensors: a new class of resonant sensors—chances and challenges for the determination of liquid properties. Front Mech Eng, 7, 2021, 705194.
Zhou, X., Assouar, M.B., Oudich, M., Acoustic superfocusing by solid phononic crystals. Appl Phys Lett, 105, 2014, 233506.
Iglesias Martínez, J.A., Moughames, J., Ulliac, G., Kadic, M., Laude, V., Three-dimensional phononic crystal with ultra-wide bandgap at megahertz frequencies. Appl Phys Lett, 118, 2021, 063507.
Ma, F., Huang, Z., Liu, C., Wu, J.H., Acoustic focusing and imaging via phononic crystal and acoustic metamaterials. J Appl Phys, 131, 2022, 011103.
Miniaci, M., Gliozzi, A.S., Morvan, B., Krushynska, A., Bosia, F., Scalerandi, M., et al. Proof of concept for an ultrasensitive technique to detect and localize sources of elastic nonlinearity using phononic crystals. Phys Rev Lett, 118, 2017, 214301.
Smith, E.J., Matlack, K.H., Metal additively manufactured phononic materials as ultrasonic filters in nonlinear ultrasound measurements. J Acoust Soc Am 149 (2021), 3739–3750.
Dhillon, J., Walker, E., Krokhin, A., Neogi, A., Energy trapping in a phononic crystal cavity enhanced by nonreciprocal acoustic wave transmission. Appl Acoust, 203, 2023, 109192.
Abueidda, D.W., Jasiuk, I., Sobh, N.A., Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces. Mater Des 145 (2018), 20–27.
Mukhin, N., Kutia, M., Aman, A., Steinmann, U., Lucklum, R., Two-dimensional phononic crystal based sensor for characterization of mixtures and heterogeneous liquids. Sensors, 22, 2022, 2816.
De Espinosa, F.M., Jimenez, E., Torres, M., Ultrasonic band gap in a periodic two-dimensional composite. Phys Rev Lett, 80, 1998, 1208.
Hsiao, F.-L., Khelif, A., Moubchir, H., Choujaa, A., Chen, C.-C., Laude, V., Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals. J Appl Phys, 101, 2007, 044903.
Jim, K., Leung, C.W., Lau, S., Choy, S., Chan, H., Thermal tuning of phononic bandstructure in ferroelectric ceramic/epoxy phononic crystal. Appl Phys Lett, 94, 2009, 193501.
Perier-Metz, C., Duda, G.N., Checa, S., Initial mechanical conditions within an optimized bone scaffold do not ensure bone regeneration–an in silico analysis. Biomech Model Mechanobiol 20 (2021), 1723–1731.
Perier-Metz, C., Duda, G.N., Checa, S., A mechanobiological computer optimization framework to design scaffolds to enhance bone regeneration. Front Bioeng Biotechnol, 10, 2022, 980727.
Martinez-Marquez, D., Delmar, Y., Sun, S., Stewart, R., Exploring macroporosity of additively manufactured titanium metamaterials for bone regeneration with quality by design: a systematic literature review. Materials, 13, 2020, 4794.
Mirzaali, M., Caracciolo, A., Pahlavani, H., Janbaz, S., Vergani, L., Zadpoor, A., Multi-material 3D printed mechanical metamaterials: rational design of elastic properties through spatial distribution of hard and soft phases. Appl Phys Lett, 113, 2018, 241903.
Mirzaali, M., De La Nava, A.H., Gunashekar, D., Nouri-Goushki, M., Veeger, R., Grossman, Q., et al. Mechanics of bioinspired functionally graded soft-hard composites made by multi-material 3D printing. Compos Struct, 237, 2020, 111867.
Gu, Y., Sun, Y., Shujaat, S., Braem, A., Politis, C., Jacobs, R., 3D-printed porous Ti6Al4V scaffolds for long bone repair in animal models: a systematic review. J Orthop Surg Res, 17, 2022, 68.
Aghaei, A., Bochud, N., Rosi, G., Grossman, Q., Ruffoni, D., Naili, S., Ultrasound characterization of bioinspired functionally graded soft-to-hard composites: experiment and modeling. J Acoust Soc Am 151 (2022), 1490–1501.
Gattin, M., Bochud, N., Rosi, G., Grossman, Q., Ruffoni, D., Naili, S., Ultrasound characterization of the viscoelastic properties of additively manufactured photopolymer materials. J Acoust Soc Am 152 (2022), 1901–1912.
Laude, V., Moiseyenko, R.P., Benchabane, S., Declercq, N.F., Bloch wave deafness and modal conversion at a phononic crystal boundary. AIP Adv, 1, 2011, 041402.
Bou Matar, O., Robillard, J., Vasseur, J.O., Hladky-Hennion, A.-C., Deymier, P., Pernod, P., et al. Band gap tunability of magneto-elastic phononic crystal. J Appl Phys, 111, 2012, 054901.
Walker, E., Reyes, D., Rojas, M.M., Krokhin, A., Wang, Z., Neogi, A., Tunable ultrasonic phononic crystal controlled by infrared radiation. Appl Phys Lett, 105, 2014, 143503.
Hou, X., Feng, J., Yuan, X., An, X., Fan, H., Temperature effects on wave attenuation properties of metamaterials: bandgap drift. Therm Sci Eng Prog, 39, 2023, 101724.
Gattin, M., Bochud, N., Rosi, G., Grossman, Q., Ruffoni, D., Naili, S., Ultrasonic bandgaps in viscoelastic 1D-periodic media: mechanical modeling and experimental validation. Ultrasonics, 131, 2023, 106951.
Chen, Y., Yao, H., Wang, L., Acoustic band gaps of three-dimensional periodic polymer cellular solids with cubic symmetry. J Appl Phys, 114, 2013.
Burton, H.E., Eisenstein, N.M., Lawless, B.M., Jamshidi, P., Segarra, M.A., Addison, O., et al. The design of additively manufactured lattices to increase the functionality of medical implants. Mater Sci Eng C 94 (2019), 901–908.
Li, L., Shi, J., Zhang, K., Yang, L., Yu, F., Zhu, L., et al. Early osteointegration evaluation of porous Ti6Al4V scaffolds designed based on triply periodic minimal surface models. J Orthop Transl 19 (2019), 94–105.
