Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Computational Mechanics
Erschienen in: Computational Mechanics 4/2015

01.04.2015 | Original Paper

Predicting band structure of 3D mechanical metamaterials with complex geometry via XFEM

verfasst von: Jifeng Zhao, Ying Li, Wing Kam Liu

Erschienen in: Computational Mechanics | Ausgabe 4/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Band structure characterizes the most important property of mechanical metamaterials. However, predicting the band structure of 3D metamaterials with complex microstructures through direct numerical simulation (DNS) is computationally inefficient due to the complexity of meshing. To overcome this issue, an extended finite element method (XFEM)-based method is developed to predict 3D metamaterial band structures. Since the microstructure and material interface are implicitly resolved by the level-set function embedded in the XFEM formulation, a non-conforming (such as uniform) mesh is used in the proposed method to avoid the difficulties in meshing complex geometries. The accuracy and mesh convergence of the proposed method have been validated and verified by studying the band structure of a spherical particle embedded in a cube and comparing the results with DNS. The band structures of 3D metamaterials with different microstructures have been studied using the proposed method with the same finite element mesh, indicating the flexibility of this method. This XFEM-based method opens new opportunities in design and optimization of mechanical metamaterials with target functions, e.g. location and width of the band gap, by eliminating the iterative procedure of re-building and re-meshing microstructures that is required by classical DNS type of methods.
Vorheriger Artikel Multiscale modeling of polycrystalline materials with Jacobian-free multiscale method (JFMM)
Nächster Artikel A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Ambati M, Fang N, Sun C, Zhang X (2007) Surface resonant states and superlensing in acoustic metamaterials. Phys Rev B 75(19):195–447CrossRef
2.
Axmann W, Kuchment P (1999) An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. scalar case. J Comput Phys 150(2):468–481CrossRefMATHMathSciNet
3.
Babuška I, Banerjee U (2012) Stable generalized finite element method (sgfem). Comput Methods Appl Mech Eng 201:91–111CrossRef
4.
Balay S, Abhyankar S, Adams MF, Brown J, Brune P, Buschelman K, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Rupp K, Smith BF, Zhang H (2014) PETSc users manual. Technical Report ANL-95/11 - Revision 3.5, Argonne National Laboratory
5.
Belytschko T, Tabbara M (1993) H-adaptive finite element methods for dynamic problems, with emphasis on localization. Int J Numer Methods Eng 36(24):4245–4265CrossRefMATH
6.
Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. Wiley, ChichesterMATH
7.
Biwa S, Yamamoto S, Kobayashi F, Ohno N (2004) Computational multiple scattering analysis for shear wave propagation in unidirectional composites. Int J Solids Struct 41(2):435–457CrossRefMATH
8.
Cai W, Chettiar UK, Kildishev AV, Shalaev VM (2007) Optical cloaking with metamaterials. Natu Photonics 1(4):224–227CrossRef
9.
Chen H, Chan C (2007) Acoustic cloaking in three dimensions using acoustic metamaterials. Appl Phys Lett 91(18):183–518
10.
Cheng KW, Fries TP (2010) Higher-order xfem for curved strong and weak discontinuities. Int J Numer Methods Eng 82(5):564–590MATHMathSciNet
11.
Cottrell J, Reali A, Bazilevs Y, Hughes T (2006) Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195(41):5257–5296CrossRefMATHMathSciNet
12.
Cottrell JA, Hughes TJ, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, ChichesterCrossRef
13.
Ding Y, Liu Z, Qiu C, Shi J (2007) Metamaterial with simultaneously negative bulk modulus and mass density. Phys Rev Lett 99(9):093–904CrossRef
14.
Dobson DC (1999) An efficient method for band structure calculations in 2d photonic crystals. J Comput Phys 149(2):363–376CrossRefMATH
15.
Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150CrossRefMATHMathSciNet
16.
Eleftheriades GV, Balmain KG (2005) Negative-refraction metamaterials: fundamental principles and applications. Wiley, New YorkCrossRef
17.
Fang N, Lee H, Sun C, Zhang X (2005) Sub-diffraction-limited optical imaging with a silver superlens. Science 308(5721):534–537CrossRef
18.
Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C, Zhang X (2006) Ultrasonic metamaterials with negative modulus. Nat Mater 5(6):452–456CrossRef
19.
Fries TP (2008) A corrected xfem approximation without problems in blending elements. Int J Numer Methods Eng 75(5):503–532CrossRefMATHMathSciNet
20.
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
21.
22.
Huang H, Sun C, Huang G (2009) On the negative effective mass density in acoustic metamaterials. Int J Eng Sci 47(4):610–617CrossRefMathSciNet
23.
Hughes TJ, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39):4135–4195CrossRefMATHMathSciNet
24.
Hussein MI (2009) Reduced bloch mode expansion for periodic media band structure calculations. Proc R Soc A 465(2109):2825–2848CrossRefMATHMathSciNet
25.
Jia Y, Anitescu C, Ghorashi SS, Rabczuk T (2014) Extended isogeometric analysis for material interface problems. IMA J Appl Math p. hxu004
26.
Jun S, Cho YS (2003) Deformation-induced bandgap tuning of 2d silicon-based photonic crystals. Opt Express 11(21):2769–2774CrossRef
27.
Jun S, Cho YS, Im S (2003) Moving least-square method for the band-structure calculation of 2d photonic crystals. Opt Express 11(6):541–551CrossRef
28.
Kittel C, McEuen P (1976) Introduction to solid state physics, vol 8. Wiley, New York
29.
Kobayashi F, Biwa S, Ohno N (2004) Wave transmission characteristics in periodic media of finite length: multilayers and fiber arrays. Int J Solids Struct 41(26):7361–7375CrossRefMATH
30.
Lai Y, Wu Y, Sheng P, Zhang ZQ (2011) Hybrid elastic solids. Nat Mater 10(8):620–624CrossRef
31.
Laude V, Wilm M, Benchabane S, Khelif A (2005) Full band gap for surface acoustic waves in a piezoelectric phononic crystal. Phys Rev E 71(3):036–607CrossRef
32.
Lee B, To A (2009) Enhanced absorption in one-dimensional phononic crystals with interfacial acoustic waves. Appl Phys Lett 95(3):031–911
33.
Lee SH, Park CM, Seo YM, Wang ZG, Kim CK (2010) Composite acoustic medium with simultaneously negative density and modulus. Phys Rev Lett 104(5):054–301CrossRef
34.
Li J, Chan C (2004) Double-negative acoustic metamaterial. Phys Rev E 70(5):055–602
35.
Liu WK, Li S, Belytschko T (1997) Moving least-square reproducing kernel methods (i) methodology and convergence. Comput Methods Appl Mech Eng 143(1):113–154CrossRefMATHMathSciNet
36.
Liu Z, Zhang X, Mao Y, Zhu Y, Yang Z, Chan C, Sheng P (2000) Locally resonant sonic materials. Science 289(5485):1734–1736CrossRef
37.
Liu Z, Chan C, Sheng P (2002) Three-component elastic wave band-gap material. Phys Rev B 65(16):116–165
38.
Liu Z, Chan C, Sheng P (2005) Analytic model of phononic crystals with local resonances. Phys Rev B 71(1):014–103
39.
Martin A, Kadic M, Schittny R, Bückmann T, Wegener M (2012) Phonon band structures of three-dimensional pentamode metamaterials. Phys Rev B 86(15):116–155CrossRef
40.
Matsuki T, Yamada T, Izui K, Nishiwaki S (2014) Topology optimization for locally resonant sonic materials. Appl Phys Lett 104(19):191–905CrossRef
41.
Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P (2012) Dark acoustic metamaterials as super absorbers for low-frequency sound. Nat Commun 3:756CrossRef
42.
Milton GW, Cherkaev AV (1995) Which elasticity tensors are realizable? J Eng Mater Technol 117(4):483–493CrossRef
43.
Moës N, Cloirec M, Cartraud P, Remacle JF (2003) A computational approach to handle complex microstructure geometries. Comput Methods Appl Mech Eng 192(28):3163–3177CrossRefMATH
44.
Pendry JB (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85(18):3966CrossRef
45.
Qiu M, He S (2000) A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions. J Appl Phys 87(12):8268–8275CrossRef
46.
Rabczuk T, Belytschko T (2005) Adaptivity for structured meshfree particle methods in 2d and 3d. Int J Numer Methods Eng 63(11):1559–1582CrossRefMATHMathSciNet
47.
Reissland J, Klemens PG (2008) The physics of phonons, vol 28. American Institute of Physics, College Park
48.
Roman JE, Campos C, Romero E, Tomas A (2014) SLEPc users manual. Technical Report DSIC-II/24/02 - Revision 3.5, D. Sistemes Informàtics i Computació, Universitat Politècnica de València
49.
Romero E, Roman JE (2014) A parallel implementation of davidson methods for large-scale eigenvalue problems in slepc. ACM Trans Math Softw 40(2):13CrossRefMathSciNet
50.
Sainidou R, Stefanou N, Modinos A (2002) Formation of absolute frequency gaps in three-dimensional solid phononic crystals. Phys Rev B 66(21):212–301CrossRef
51.
Setyawan W, Curtarolo S (2010) High-throughput electronic band structure calculations: challenges and tools. Comput Mater Sci 49(2):299–312CrossRef
52.
Sigalas M, Garcıa N (2000) Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method. J Appl Phys 87(6):3122–3125CrossRef
53.
Soukoulis CM (2001) Photonic crystals and light localization in the 21st century, vol 563. Springer, New YorkCrossRef
54.
Sukumar N, Pask J (2009) Classical and enriched finite element formulations for bloch-periodic boundary conditions. Int J Numer Methods Eng 77(8):1121–1138CrossRefMATHMathSciNet
55.
Tian R, To AC, Liu WK (2011) Conforming local meshfree method. Int J Numer Methods Eng 86(3):335–357CrossRefMATH
56.
Wang Y, Li F, Wang Y, Kishimoto K, Huang W (2009) Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice. Acta Mech Sin 25(1):65–71CrossRefMATHMathSciNet
57.
Wang Y, Luo Z, Zhang N, Kang Z (2014) Topological shape optimization of microstructural metamaterials using a level set method. Comput Mater Sci 87:178–186CrossRef
58.
Wu TT, Huang ZG, Lin S (2004) Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy. Phys Rev B 69(9):094–301CrossRef
59.
Yablonovitch E, Gmitter T (1989) Photonic band structure: the face-centered-cubic case. Phys Rev Lett 63(18):1950CrossRef
60.
Yao J, Liu Z, Liu Y, Wang Y, Sun C, Bartal G, Stacy AM, Zhang X (2008) Optical negative refraction in bulk metamaterials of nanowires. Science 321(5891):930–930CrossRef
61.
Yao S, Zhou X, Hu G (2008) Experimental study on negative effective mass in a 1d mass-spring system. New J Phys 10(4):20–43CrossRef
62.
Yuan R, Singh SS, Chawla N, Oswald J (2014) Efficient methods for implicit geometrical representation of complex material microstructures. Int J Numer Methods Eng 98(2):79–91CrossRefMathSciNet
63.
Zhang H, Smith B, Sternberg M, Zapol P (2007) Sips: shift-and-invert parallel spectral transformations. ACM Trans Math Softw 33(2):9CrossRefMathSciNet
64.
Zhang P, To AC (2013) Broadband wave filtering of bioinspired hierarchical phononic crystal. Appl Phys Lett 102(12):121–910
65.
Zhao H, Liu Y, Wang G, Wen J, Yu D, Han X, Wen X (2005) Resonance modes and gap formation in a two-dimensional solid phononic crystal. Phys Rev B 72(1):012–301
66.
Zhou F, Bao Y, Cao W, Stuart CT, Gu J, Zhang W, Sun C (2011) Hiding a realistic object using a broadband terahertz invisibility cloak. Sci Rep 1:78
Metadaten
Titel
Predicting band structure of 3D mechanical metamaterials with complex geometry via XFEM
verfasst von
Jifeng Zhao
Ying Li
Wing Kam Liu
Publikationsdatum
01.04.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2015
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-015-1129-2

Weitere Artikel der Ausgabe 4/2015

Computational Mechanics 4/2015 Zur Ausgabe

Original Paper

A non-intrusive partitioned approach to couple smoothed particle hydrodynamics and finite element methods for transient fluid-structure interaction problems with large interface motion

Original Paper

Finite rotation FE-simulation and active vibration control of smart composite laminated structures

Original Paper

A modified perturbed Lagrangian formulation for contact problems

Original Paper

A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation

Original Paper

A computational investigation of a model of single-crystal gradient thermoplasticity that accounts for the stored energy of cold work and thermal annealing

Original Paper

A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares

Neuer Inhalt

    Bildnachweise