Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions
Source abstract
Abstract
The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In Pham et al. (J. Mech. Phys. Solids 106:80–94, 2017), two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Acoustic Wave Phenomena Research · Composite Material Mechanics · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (27)
Show source-provided references
1. Auriault, J.L., Bonnet, G.: Dynamique des composites élastiques périodiques. Arch. Mech. 37(4–5), 269–284 (1985)
2. Auriault, J.L., Boutin, C.: Long wavelength inner-resonance cut-off frequencies in elastic composite materials. Int. J. Solids Struct. 49(23–24), 3269–3281 (2012). https://doi.org/10.1016/j.ijsolstr.2012.07.00210.1016/j.ijsolstr.2012.07.002 ↗
3. Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. AMS, Providence (2011)
4. Bonnet-Bendhia, A., Drissi, D., Gmati, N.: Simulation of muffler’s transmission losses by a homogenized finite element method. J. Comput. Acoust. 12(3), 447–474 (2004)10.1142/S0218396X04002304 ↗
5. Bouchitté, G., Bourel, C., Felbacq, D.: Homogenization of the 3D Maxwell system near resonances and artificial magnetism. C. R. Math. 347(9–10), 571–576 (2009). https://doi.org/10.1016/j.crma.2009.02.02710.1016/j.crma.2009.02.027 ↗
6. Cornaggia, R., Bellis, C.: Tuning effective dynamical properties of periodic media by FFT-accelerated topological optimization. Int. J. Numer. Methods Eng. (2020). https://doi.org/10.1002/nme.635210.1002/nme.6352 ↗
7. David, M., Pideri, C., Marigo, J.J.: Homogenized interface model describing inhomogeneities located on a surface. J. Elast. 109(2), 153–187 (2012)10.1007/s10659-012-9374-5 ↗
8. Delourme, B.: Modèles asymptotiques des interfaces fines et périodiques en électromagnétisme. PhD thesis—Université, Pierre et Marie Curie—Paris VI (2010)
9. Felbacq, D., Bouchitté, G.: Theory of mesoscopic magnetism in photonic crystals. Phys. Rev. Lett. 94(18), 183902 (2005). https://doi.org/10.1103/physrevlett.94.18390210.1103/physrevlett.94.183902 ↗
10. Lombard, B., Piraux, J.: Numerical treatment of two-dimensional interfaces for acoustic and elastic waves. J. Comput. Phys. 195(1), 90–116 (2004). https://doi.org/10.1016/j.jcp.2003.09.02410.1016/j.jcp.2003.09.024 ↗
11. Lombard, B., Piraux, J., Gélis, C., Virieux, J.: Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves. Geophys. J. Int. 172(1), 252–261 (2008). https://doi.org/10.1111/j.1365-246x.2007.03620.x10.1111/j.1365-246x.2007.03620.x ↗
12. Lombard, B., Maurel, A., Marigo, J.J.: Numerical modeling of the acoustic wave propagation across an homogenized rigid microstructure in the time domain. J. Comput. Phys. 335, 558–577 (2017)10.1016/j.jcp.2017.01.036 ↗
13. Lorcher, F., Munz, C.D.: Lax-Wendroff-type schemes of arbitrary order in several space dimensions. IMA J. Numer. Anal. 27(3), 593–615 (2006). https://doi.org/10.1093/imanum/drl03110.1093/imanum/drl031 ↗
14. Ma, G., Yang, M., Xiao, S., Yang, Z., Sheng, P.: Acoustic metasurface with hybrid resonances. Nat. Mater. 13(9), 873–878 (2014). https://doi.org/10.1038/nmat399410.1038/nmat3994 ↗
15. Marigo, J.J., Maurel, A.: Homogenization models for thin rigid structured surfaces and films. J. Acoust. Soc. Am. 140(1), 260–273 (2016)10.1121/1.4954756 ↗
16. Marigo, J.J., Pideri, C.: The effective behaviour of elastic bodies containing microcracks or microholes localized on a surface. Int. J. Damage Mech. 20, 1151–1177 (2011)10.1177/1056789511406914 ↗
17. Marigo, J.J., Maurel, A., Pham, K., Sbitti, A.: Effective dynamic properites of a row of elastic inclusions: the case of scalar shear waves. J. Elast. 128(2), 265–289 (2017)10.1007/s10659-017-9627-4 ↗
18. Maurel, A., Mercier, J.F., Pham, K., Marigo, J.J., Ourir, A.: Enhanced resonance of sparse arrays of Helmholtz resonators—application to perfect absorption. J. Acoust. Soc. Am. 145(4), 2552–2560 (2019). https://doi.org/10.1121/1.509894810.1121/1.5098948 ↗
19. Maurel, A., Pham, K., Marigo, J.J.: Homogenization of thin 3d periodic structures in the time domain–effective boundary and jump conditions. In: Romero-García, V., Hladky-Hennion, A.C. (eds.) Fundamentals and Applications of Acoustic Metamaterials. Wiley, New York (2019). https://doi.org/10.1002/978111964918210.1002/9781119649182 ↗
20. Pham, K., Maurel, A., Marigo, J.J.: Two scale homogenization of a row of locally resonant inclusions—the case of shear waves. J. Mech. Phys. Solids 106, 80–94 (2017)10.1016/j.jmps.2017.05.001 ↗
21. Sanchez-Hubert, J., Sanchez-Palencia, E.: Introduction aux méthodes asymptotiques et à l’homogénéisation. Collection Mathématiques Appliquées pour la Maîtrise (1992)
22. Schwan, L., Umnova, O., Boutin, C.: Sound absorption and reflection from a resonant metasurface: homogenisation model with experimental validation. Wave Motion 72, 154–172 (2017). https://doi.org/10.1016/j.wavemoti.2017.02.00410.1016/j.wavemoti.2017.02.004 ↗
23. Schwartzkopff, T., Dumbser, M., Munz, C.D.: Fast high order ADER schemes for linear hyperbolic equations. J. Comput. Phys. 197(2), 532–539 (2004). https://doi.org/10.1016/j.jcp.2003.12.00710.1016/j.jcp.2003.12.007 ↗
24. Sheng, P., Zhang, X., Liu, Z., Chan, C.: Locally resonant sonic materials. Physica B, Condens. Matter 338(1–4), 201–205 (2003). https://doi.org/10.1016/s0921-4526(03)00487-310.1016/s0921-4526(03)00487-3 ↗
25. Touboul, M., Lombard, B., Bellis, C.: Time-domain simulation of wave propagation across resonant meta-interfaces. J. Comput. Phys. 414, 109474 (2020). https://doi.org/10.1016/j.jcp.2020.10947410.1016/j.jcp.2020.109474 ↗
26. Zhikov, V.V.: On an extension of the method of two-scale convergence and its applications. Sb. Math. 191(7), 973–1014 (2000). https://doi.org/10.1070/sm2000v191n07abeh00049110.1070/sm2000v191n07abeh000491 ↗
27. Zhikov, V.V.: On spectrum gaps of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(05), 773–791 (2005). https://doi.org/10.1090/s1061-0022-05-00878-210.1090/s1061-0022-05-00878-2 ↗