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Computational Mechanics
Erschienen in: Computational Mechanics 1/2019

04.12.2018 | Original Paper

Dynamic homogenization of resonant elastic metamaterials with space/time modulation

verfasst von: Chenchen Liu, Celia Reina

Erschienen in: Computational Mechanics | Ausgabe 1/2019

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Abstract

We present a variational multiscale strategy in the spirit of FE\(^2\) method for simulating the real time evolution of resonant elastic metamaterials with space/time modulation. The implicit time discretization used guarantees the stability of the numerical solution, while the accuracy is quantified by direct comparison with the response obtained via direct numerical simulation. The results showcase a remarkable accuracy of the method, even when the dynamic material properties drastically change over length scales that are equal to the macroscopic mesh size and time scales that are of the same order of magnitude than the external excitations. We further propose a strategy to identify the band gap structure of these metamaterials based on their real time response. The methodology is verified for spatially periodic time invariant systems via classical unit cell analyses in the frequency domain.
Vorheriger Artikel High order exact geometry finite elements for seven-parameter shells with parametric and implicit reference surfaces
Nächster Artikel Variable-order fractional description of compression deformation of amorphous glassy polymers

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Literatur
1.
Bangerth W, Hartmann R, Kanschat G (2007) deal.II—a general-purpose object-oriented finite element library. ACM Trans Math Softw (TOMS) 33(4):24MathSciNetCrossRefMATH
2.
Belytschko T, Hughes T (1983) Computational methods for transient analysis. Elsevier, North-HollandMATH
3.
Celli P, Yousefzadeh B, Daraio C, Gonella S (2018) Exploring heterogeneity and disorder in tunable elastic metamaterials. J Acoust Soc Am 143(3):1917–1917CrossRef
4.
Chen H, Chan C (2007) Acoustic cloaking in three dimensions using acoustic metamaterials. Appl Phys Lett 91(18):183518CrossRef
5.
COMSOL Multiphysics 2017. v. 5.3. COMSOL AB, S.S. (2017)
6.
Cummer SA, Schurig D (2007) One path to acoustic cloaking. New J Phys 9(3):45CrossRef
7.
Deymier PA (2013) Acoustic metamaterials and phononic crystals, vol 173. Springer, BerlinCrossRef
8.
Fish J, Chen W, Nagai G (2002) Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case. Int J Numer Methods Eng 54(3):331–346MathSciNetCrossRefMATH
9.
Fleury R, Sounas DL, Sieck CF, Haberman MR, Alù A (2014) Sound isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343(6170):516–519CrossRef
10.
Gonella S, To AC, Liu WK (2009) Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting. J Mech Phys Solids 57(3):621–633CrossRefMATH
11.
Hu R, Oskay C (2018) Spatial-temporal nonlocal homogenization model for transient anti-plane shear wave propagation in periodic viscoelastic composites. Comput Methods Appl Mech Eng 342:1–31MathSciNetCrossRef
12.
Hughes TJ (2012) The finite element method: linear static and dynamic finite element analysis. Courier Dover Publications, Mineola
13.
Hughes TJ, Pister KS, Taylor RL (1979) Implicit–explicit finite elements in nonlinear transient analysis. Comput Methods Appl Mech Eng 17:159–182CrossRefMATH
14.
Hussein MI, Frazier MJ (2010) Band structure of phononic crystals with general damping. J Appl Phys 108(9):093506CrossRef
15.
Hussein MI, Frazier MJ (2013) Metadamping: an emergent phenomenon in dissipative metamaterials. J Sound Vib 332(20):4767–4774CrossRef
16.
Hussein MI, Leamy MJ, Ruzzene M (2014) Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Appl Mech Rev 66(4):040802CrossRef
17.
Javili A, Chatzigeorgiou G, Steinmann P (2013) Computational homogenization in magneto-mechanics. Int J Solids Struct 50(25–26):4197–4216CrossRef
18.
Khajehtourian R, Hussein MI (2014) Dispersion characteristics of a nonlinear elastic metamaterial. AIP Adv 4(12):124308CrossRef
19.
Krödel S, Thomé N, Daraio C (2015) Wide band-gap seismic metastructures. Extreme Mech Lett 4:111–117CrossRef
20.
Laude V (2015) Phononic crystals: artificial crystals for sonic, acoustic, and elastic waves, vol 26. Walter de Gruyter GmbH & Co KG, BerlinCrossRefMATH
21.
Liu C, Reina C (2016) Discrete averaging relations for micro to macro transition. J Appl Mech 83(8):081006CrossRef
22.
Liu C, Reina C (2017) Variational coarse-graining procedure for dynamic homogenization. J Mech Phys Solids 104:187–206MathSciNetCrossRef
23.
Liu C, Reina C (2018) Broadband locally resonant metamaterials with graded hierarchical architecture. J Appl Phys 123(9):095108CrossRef
24.
Liu Z, Zhang X, Mao Y, Zhu Y, Yang Z, Chan C, Sheng P (2000) Locally resonant sonic materials. Science 289(5485):1734–1736CrossRef
25.
Lv H, Tian X, Wang MY, Li D (2013) Vibration energy harvesting using a phononic crystal with point defect states. Appl Phys Lett 102(3):034103CrossRef
26.
Manimala JM, Sun C (2014) Microstructural design studies for locally dissipative acoustic metamaterials. J Appl Phys 115(2):023518CrossRef
27.
Mercer B, Mandadapu KK, Papadopoulos P (2016) Homogenization of high-frequency wave propagation in linearly elastic layered media using a continuum Irving–Kirkwood theory. Int J Solids Struct 96:162–172CrossRef
28.
Miehe C, Schotte J, Lambrecht M (2002) Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals. J Mech Phys Solids 50(10):2123–2167MathSciNetCrossRefMATH
29.
Miehe C, Schröder J, Becker M (2002) Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro-and macro-scales of periodic composites and their interaction. Comput Methods Appl Mech Eng 191(44):4971–5005MathSciNetCrossRefMATH
30.
Miehe C, Schröder J, Schotte J (1999) Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput Methods Appl Mech Eng 171(3–4):387–418MathSciNetCrossRefMATH
31.
Milton GW, Willis JR (2007) On modifications of Newton’s second law and linear continuum elastodynamics. Proc R Soc A Math Phys Eng Sci 463(2079):855–880MathSciNetCrossRefMATH
32.
Molinari A, Mercier S (2001) Micromechanical modelling of porous materials under dynamic loading. J Mech Phys Solids 49(7):1497–1516CrossRefMATH
33.
Nassar H, Chen H, Norris A, Haberman M, Huang G (2017) Non-reciprocal wave propagation in modulated elastic metamaterials. Proc R Soc A 473:20170188MathSciNetCrossRefMATH
34.
Nassar H, He QC, Auffray N (2015) Willis elastodynamic homogenization theory revisited for periodic media. J Mech Phys Solids 77:158–178MathSciNetCrossRefMATH
35.
Nassar H, Xu X, Norris A, Huang G (2017) Modulated phononic crystals: non-reciprocal wave propagation and Willis materials. J Mech Phys Solids 101:10–29MathSciNetCrossRef
36.
Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div 85(3):67–94
37.
Nezamabadi S, Yvonnet J, Zahrouni H, Potier-Ferry M (2009) A multilevel computational strategy for handling microscopic and macroscopic instabilities. Comput Methods Appl Mech Eng 198(27–29):2099–2110CrossRefMATH
38.
Ortiz M, Stainier L (1999) The variational formulation of viscoplastic constitutive updates. Comput Methods Appl Mech Eng 171(3):419–444MathSciNetCrossRefMATH
39.
Özdemir I, Brekelmans W, Geers M (2008) FE-2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids. Comput Methods Appl Mech Eng 198(3):602–613MathSciNetCrossRefMATH
40.
Pham K, Kouznetsova V, Geers M (2013) Transient computational homogenization for heterogeneous materials under dynamic excitation. J Mech Phys Solids 61(11):2125–2146MathSciNetCrossRefMATH
41.
Popa BI, Cummer SA (2014) Non-reciprocal and highly nonlinear active acoustic metamaterials. Nat Commun 5:3398CrossRef
42.
Radovitzky R, Ortiz M (1999) Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput Methods Appl Mech Eng 172(1):203–240MathSciNetCrossRefMATH
43.
Reina C (2011) Multiscale modeling and simulation of damage by void nucleation and growth. Ph.D. thesis, California Institute of Technology
44.
Reina C, Li B, Weinberg K, Ortiz M (2013) A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories. Int J Numer Methods Eng 93(6):575–611MathSciNetCrossRefMATH
45.
Ricker S, Mergheim J, Steinmann P (2009) On the multiscale computation of defect driving forces. Int J Multiscale Comput Eng 7(5):457–474CrossRef
46.
Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Materialia 58(4):1152–1211CrossRef
47.
Schröder J, Labusch M, Keip MA (2016) Algorithmic two-scale transition for magneto-electro-mechanically coupled problems: FE\(^2\)-scheme: localization and homogenization. Comput Methods Appl Mech Eng 302:253–280MathSciNetCrossRefMATH
48.
Sigmund O (2009) Systematic design of metamaterials by topology optimization. In: IUTAM symposium on modelling nanomaterials and nanosystems, pp 151–159. Springer
49.
Subbaraj K, Dokainish M (1989) A survey of direct time-integration methods in computational structural dynamics—II. Implicit methods. Comput Struct 32(6):1387–1401MathSciNetCrossRefMATH
50.
Verhoosel CV, Remmers JJ, Gutiérrez MA, De Borst R (2010) Computational homogenization for adhesive and cohesive failure in quasi-brittle solids. Int J Numer Methods Eng 83(8–9):1155–1179CrossRefMATH
51.
Vila J, Pal RK, Ruzzene M, Trainiti G (2017) A Bloch-based procedure for dispersion analysis of lattices with periodic time-varying properties. J Sound Vib 406:363–377CrossRef
52.
Zanjani MB, Davoyan AR, Engheta N, Lukes JR (2015) NEMS with broken T symmetry: graphene based unidirectional acoustic transmission lines. Sci Rep 5:9926CrossRef
53.
Zanjani MB, Davoyan AR, Mahmoud AM, Engheta N, Lukes JR (2014) One-way phonon isolation in acoustic waveguides. Appl Phys Lett 104(8):081905CrossRef
54.
Zhang P, To AC (2013) Broadband wave filtering of bioinspired hierarchical phononic crystal. Appl Phys Lett 102(12):121910CrossRef
55.
Zhu R, Liu X, Hu G, Sun C, Huang G (2014) A chiral elastic metamaterial beam for broadband vibration suppression. J Sound Vib 333(10):2759–2773CrossRef
56.
Zohdi TI, Wriggers P (2008) An introduction to computational micromechanics. Springer, BerlinMATH
Metadaten
Titel
Dynamic homogenization of resonant elastic metamaterials with space/time modulation
verfasst von
Chenchen Liu
Celia Reina
Publikationsdatum
04.12.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 1/2019
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-018-1662-x

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