Skip to main content
Erschienen in: Archive of Applied Mechanics 3/2019

21.01.2019 | Original

Damage propagation in 2d beam lattices: 2. Design of an isotropic fault-tolerant lattice

verfasst von: Andrej Cherkaev, Michael Ryvkin

Erschienen in: Archive of Applied Mechanics | Ausgabe 3/2019

Einloggen

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

search-config
loading …

Abstract

The paper demonstrates a rational design of an isotropic heterogeneous beam lattice that is fault-tolerant and energy-absorbing. Combining triangular and hexagonal structures, we calculate elastic moduli of obtained hybrid heterogeneous structures; simulate the development of flaws in that composite lattice subjected to a uniform uniaxial deformation; investigate its damage evolution; measure various characteristics of damage that estimate fault tolerance; discuss the trade-off between stiffness and fault tolerance. A design is found that develops a cloud of small evenly spread flaws instead of a crack.

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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Ajdari, A., Jahromi, B.H., Papadopoulos, J., Nayeb-Hashemi, H., Vaziri, A.: Hierarchical honeycombs with tailorable properties. Int. J. Solids Struct. 49(11–12), 1413–1419 (2012)CrossRef Ajdari, A., Jahromi, B.H., Papadopoulos, J., Nayeb-Hashemi, H., Vaziri, A.: Hierarchical honeycombs with tailorable properties. Int. J. Solids Struct. 49(11–12), 1413–1419 (2012)CrossRef
2.
Zurück zum Zitat Berger, J.B., Wadley, H.N., McMeeking, R.M.: Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness. Nature 543(7646), 533–537 (2017)CrossRef Berger, J.B., Wadley, H.N., McMeeking, R.M.: Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness. Nature 543(7646), 533–537 (2017)CrossRef
4.
Zurück zum Zitat Cherkaev, E., Cherkaev, A.: Principal compliance and robust optimal design. J. Elast. 72, 71–98 (2003). (also in: The Rational Spirit in Modern Continuum Mechanics, Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III, 2003) MathSciNetCrossRefMATH Cherkaev, E., Cherkaev, A.: Principal compliance and robust optimal design. J. Elast. 72, 71–98 (2003). (also in: The Rational Spirit in Modern Continuum Mechanics, Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III, 2003) MathSciNetCrossRefMATH
5.
Zurück zum Zitat Cherkaev, E., Cherkaev, A.: Minimax optimization problem of structural design. Comput. Struct. 86, 1426–1435 (2008)CrossRefMATH Cherkaev, E., Cherkaev, A.: Minimax optimization problem of structural design. Comput. Struct. 86, 1426–1435 (2008)CrossRefMATH
6.
Zurück zum Zitat Cherkaev, A., Cherkaev, E., Leelavanichkul, S.: Principle of optimization of structures against an impact. J. Phys. Confer. Ser. 319(1), 1–16 (2011)MATH Cherkaev, A., Cherkaev, E., Leelavanichkul, S.: Principle of optimization of structures against an impact. J. Phys. Confer. Ser. 319(1), 1–16 (2011)MATH
7.
Zurück zum Zitat Cherkaev, A., Leelavanichkul, S.: An impact protective structure with bistable links. Int. J. Damage Mech. 21(5), 697–711 (2012)CrossRef Cherkaev, A., Leelavanichkul, S.: An impact protective structure with bistable links. Int. J. Damage Mech. 21(5), 697–711 (2012)CrossRef
8.
Zurück zum Zitat Cherkaev, A., Cherkaev, E., Slepyan, L.: Transition waves in bistable structures. I: delocalization of damage. J. Mech. Phys. Solids 53(2), 383–405 (2005)MathSciNetCrossRefMATH Cherkaev, A., Cherkaev, E., Slepyan, L.: Transition waves in bistable structures. I: delocalization of damage. J. Mech. Phys. Solids 53(2), 383–405 (2005)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Cherkaev, E., Cherkaev, A., Slepyan, L.: Dynamics of structures with bistable links. In: Vibration Problems ICOVP 2005, vol. 111, pp. 111–122. Springer (2007) Cherkaev, E., Cherkaev, A., Slepyan, L.: Dynamics of structures with bistable links. In: Vibration Problems ICOVP 2005, vol. 111, pp. 111–122. Springer (2007)
10.
Zurück zum Zitat Cherkaev, A., Ryvkin, M.: Damage propagation in 2d beam lattices: 1. Uncertainty and assumptions. Arch. Mech. (2017). (in print) Cherkaev, A., Ryvkin, M.: Damage propagation in 2d beam lattices: 1. Uncertainty and assumptions. Arch. Mech. (2017). (in print)
11.
Zurück zum Zitat Cherkaev, A., Slepyan, L.: Waiting element structures and stability under extension. Int. J. Damage Mech. 4(1), 58–82 (1995)CrossRef Cherkaev, A., Slepyan, L.: Waiting element structures and stability under extension. Int. J. Damage Mech. 4(1), 58–82 (1995)CrossRef
12.
Zurück zum Zitat Cherkaev, A., Vladimir Vinogradov, V., Leelavanishkul, S.: The waves of damage in elastic–plastic lattices with waiting links: design and simulation. Mech. Mater. 38, 748–756 (2005)CrossRef Cherkaev, A., Vladimir Vinogradov, V., Leelavanishkul, S.: The waves of damage in elastic–plastic lattices with waiting links: design and simulation. Mech. Mater. 38, 748–756 (2005)CrossRef
13.
Zurück zum Zitat Cherkaev, A.A., Zhornitskaya, L.: Protective structures with waiting links and their damage evolution. Multibody Syst. Dyn. J. 13(1), 53–67 (2005)CrossRefMATH Cherkaev, A.A., Zhornitskaya, L.: Protective structures with waiting links and their damage evolution. Multibody Syst. Dyn. J. 13(1), 53–67 (2005)CrossRefMATH
14.
Zurück zum Zitat Diaz, A.R., Bendsoe, M.P.: Shape optimization of multipurpose structures by homogenization method. Struct. Optim. 4, 17–22 (1992)CrossRef Diaz, A.R., Bendsoe, M.P.: Shape optimization of multipurpose structures by homogenization method. Struct. Optim. 4, 17–22 (1992)CrossRef
15.
Zurück zum Zitat Diaz, A.R., Soto C.A.: Lattice models for crash resistant design and optimization. In: Proceedings of 3rd World Congress of Structural and Multidisciplinary Optimization, Buffalo, New York, USA, 17–21 May 1999 Diaz, A.R., Soto C.A.: Lattice models for crash resistant design and optimization. In: Proceedings of 3rd World Congress of Structural and Multidisciplinary Optimization, Buffalo, New York, USA, 17–21 May 1999
16.
Zurück zum Zitat Fleck, N.A., Qiu, X.: The damage tolerance of elastic–brittle, two-dimensional isotropic lattices. J. Mech. Phys. Solids 55(3), 562–588 (2007)MathSciNetCrossRefMATH Fleck, N.A., Qiu, X.: The damage tolerance of elastic–brittle, two-dimensional isotropic lattices. J. Mech. Phys. Solids 55(3), 562–588 (2007)MathSciNetCrossRefMATH
17.
18.
Zurück zum Zitat Fuchs, M.B., Farhi, E.: Shape of stiffest controlled structures under unknown loads. Comput. Struct. 79(18), 1661–1670 (2001)CrossRef Fuchs, M.B., Farhi, E.: Shape of stiffest controlled structures under unknown loads. Comput. Struct. 79(18), 1661–1670 (2001)CrossRef
19.
Zurück zum Zitat Grenestedt, J.: Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids. J. Mech. Phys. Solids 46(1), 29–50 (1998)CrossRefMATH Grenestedt, J.: Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids. J. Mech. Phys. Solids 46(1), 29–50 (1998)CrossRefMATH
20.
Zurück zum Zitat Holnicki-Szulc, J., Knap, L.: Optimal design of adaptive structures for the best crashworthiness. In: Proceedings of 3rd World Congress of Structural and Multidisciplinary Optimization, Buffalo, New York, USA, pp. 17–21 (1999) Holnicki-Szulc, J., Knap, L.: Optimal design of adaptive structures for the best crashworthiness. In: Proceedings of 3rd World Congress of Structural and Multidisciplinary Optimization, Buffalo, New York, USA, pp. 17–21 (1999)
21.
Zurück zum Zitat Holnicki, J., Knap, L.: Adaptive crashworthiness concept. Int. J. Impact Eng. 30(6), 639–663 (2004)CrossRef Holnicki, J., Knap, L.: Adaptive crashworthiness concept. Int. J. Impact Eng. 30(6), 639–663 (2004)CrossRef
22.
Zurück zum Zitat Kucherov, L., Ryvkin, M.: Flaw nucleation in a brittle open-cell Kelvin foam. Int. J. Fract. 175(1), 79–86 (2012)CrossRef Kucherov, L., Ryvkin, M.: Flaw nucleation in a brittle open-cell Kelvin foam. Int. J. Fract. 175(1), 79–86 (2012)CrossRef
23.
Zurück zum Zitat Leelavanichkul, S., Cherkaev, A., Adams, D., Solzbacher, F.: Energy absorption of a helicoidal bistable structure. J. Mech. Mater. Struct. 5(2), 305–321 (2009)CrossRef Leelavanichkul, S., Cherkaev, A., Adams, D., Solzbacher, F.: Energy absorption of a helicoidal bistable structure. J. Mech. Mater. Struct. 5(2), 305–321 (2009)CrossRef
24.
Zurück zum Zitat Lipperman, F., Ryvkin, M., Fuchs, M.B.: Fracture toughness of two-dimensional cellular material with periodic microstructure. Int. J. Fract. 146, 279–290 (2007)CrossRefMATH Lipperman, F., Ryvkin, M., Fuchs, M.B.: Fracture toughness of two-dimensional cellular material with periodic microstructure. Int. J. Fract. 146, 279–290 (2007)CrossRefMATH
25.
Zurück zum Zitat Lipperman, F., Ryvkin, M., Fuchs, M.B.: Nucleation of cracks in two-dimensional periodic cellular materials. Comput. Mech. 39(2), 127–139 (2007)CrossRefMATH Lipperman, F., Ryvkin, M., Fuchs, M.B.: Nucleation of cracks in two-dimensional periodic cellular materials. Comput. Mech. 39(2), 127–139 (2007)CrossRefMATH
26.
Zurück zum Zitat Lipperman, F., Ryvkin, M., Fuchs, M.B.: Design of crack-resistant two-dimensional periodic cellular materials. J. Mech. Mater. Struct. 4(3), 441–457 (2009)CrossRef Lipperman, F., Ryvkin, M., Fuchs, M.B.: Design of crack-resistant two-dimensional periodic cellular materials. J. Mech. Mater. Struct. 4(3), 441–457 (2009)CrossRef
27.
Zurück zum Zitat Lurie, K.A.: Applied Optimal Control Theory of Distributed Systems, vol. 43. Springer, Berlin (2013)MATH Lurie, K.A.: Applied Optimal Control Theory of Distributed Systems, vol. 43. Springer, Berlin (2013)MATH
28.
Zurück zum Zitat Pedersen, C.B.W.: Topology optimization of 2D-frame structures with path-dependent response. Int. J. Numer. Methods Eng. 57(10), 1471–1501 (2002)CrossRefMATH Pedersen, C.B.W.: Topology optimization of 2D-frame structures with path-dependent response. Int. J. Numer. Methods Eng. 57(10), 1471–1501 (2002)CrossRefMATH
29.
Zurück zum Zitat Quintana-Alonso, I., Fleck, N.A.: Fracture of brittle lattice materials: a review. In: Daniel, I.M., Gdoutos, E.E., Rajapakse, Y.D.S. (eds.) Major Accomplishments in Composite Materials and Sandwich Structures. Springer, Dordrecht (2009) Quintana-Alonso, I., Fleck, N.A.: Fracture of brittle lattice materials: a review. In: Daniel, I.M., Gdoutos, E.E., Rajapakse, Y.D.S. (eds.) Major Accomplishments in Composite Materials and Sandwich Structures. Springer, Dordrecht (2009)
30.
Zurück zum Zitat Salehian, A., Ibrahim, M., Seigler, T.M.: Damping in periodic structures: a continuum modeling approach. AIAA J. 52(3), 569–590 (2014)CrossRef Salehian, A., Ibrahim, M., Seigler, T.M.: Damping in periodic structures: a continuum modeling approach. AIAA J. 52(3), 569–590 (2014)CrossRef
31.
Zurück zum Zitat Slepyan, L., Cherkaev, A., Cherkaev, E.: Transition waves in bistable structures II: analytical solution, wave speed, and energy dissipation. J. Mech. Phys. Solids 53(2), 407–436 (2005)MathSciNetCrossRefMATH Slepyan, L., Cherkaev, A., Cherkaev, E.: Transition waves in bistable structures II: analytical solution, wave speed, and energy dissipation. J. Mech. Phys. Solids 53(2), 407–436 (2005)MathSciNetCrossRefMATH
32.
Zurück zum Zitat Soto, C.A.: Structural topology optimization for crashworthiness. Int. J. Crashworthiness 9(3), 277–283 (2004)CrossRef Soto, C.A.: Structural topology optimization for crashworthiness. Int. J. Crashworthiness 9(3), 277–283 (2004)CrossRef
33.
Zurück zum Zitat Zargarian, A., Esfahanian, M., Kadkhodapour, J., Ziaei-Rad, S.: Numerical simulation of the fatigue behavior of additive manufactured titanium porous lattice structures. Mater. Sci. Eng. C 60, 339–347 (2016)CrossRef Zargarian, A., Esfahanian, M., Kadkhodapour, J., Ziaei-Rad, S.: Numerical simulation of the fatigue behavior of additive manufactured titanium porous lattice structures. Mater. Sci. Eng. C 60, 339–347 (2016)CrossRef
Metadaten
Titel
Damage propagation in 2d beam lattices: 2. Design of an isotropic fault-tolerant lattice
verfasst von
Andrej Cherkaev
Michael Ryvkin
Publikationsdatum
21.01.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 3/2019
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-018-1428-0

Weitere Artikel der Ausgabe 3/2019

Archive of Applied Mechanics 3/2019 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.