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DYNAMICS OF STRUCTURES WITH BISTABLE LINKS

  • Andrej Cherkaev
  • Elena Cherkaev
  • Leonid Slepyan
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 111)

Abstract

The paper considers nonlinear structures with bistable links described by irreversible, piecewise linear constitutive relation: the force in the link is a nonmonotonic bistable function of elongation; the corresponding elastic energy is nonconvex. The transition from one stable state to the other is initiated when the force exceeds the threshold; the transition propagates along the chain and excites a complex system of waves. Mechanically, the bistable link may consist of two rods joined at the ends, the longer rod initially being inactive. This rod starts to resist when large enough strain damages the shorter rod. The transition wave is a sequence of breakages, it absorbs the energy of the loading force, transforms it into high frequency vibrations, and distributes the partial damage throughout the structure. In the same time, the partial damage does not lead to failure of the whole structure, because the initially inactive links are activated. The developed model of dynamics of cellular chains allow us to explicitly calculate the speed of the transition wave, conditions for its initiating, and estimate the energy of dissipation. The dissipation or absorption of the energy can be significantly increased in a structure characterized by a nonlinear discontinuous constitutive relation. The considered chain model reveals some phenomena typical for waves of failure or crushing in constructions and materials under collision, waves in a structure specially designed as a dynamic energy absorber and waves of phase transitions in artificial and natural passive and active systems.

Keywords

Transition Wave Damage Parameter Partial Damage Transition Front Basic Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Balk A. M., Cherkaev A. V., Slepyan L. I. (2001a) Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments, J. Mech. Phys. Solids 49 131–148.CrossRefMathSciNetzbMATHADSGoogle Scholar
  2. Balk A. M., Cherkaev A. V., Slepyan L. I. (2001b) Dynamics of chains with non-monotone stress-strain relations. II. Nonlinear waves and waves of phase transition, J. Mech. Phys. Solids 49 149–171.CrossRefMathSciNetzbMATHADSGoogle Scholar
  3. Cherkaev A., Slepyan L. (1995) Waiting element structures and stability under extension, Int. J. Damage Mech. 4 58–82.CrossRefGoogle Scholar
  4. Cherkaev A., Zhornitskaya L. (2004) Dynamics of damage in two-dimensional structures with waiting links, In: Asymptotics, Singularities and Homogenisation in Problems of Mechanics, A.B. Movchan editor 273–284, Kluwer.Google Scholar
  5. Cherkaev A., Cherkaev E., Slepyan, L. (2005) Transition waves in bistable structures I: Delocalization of damage, J. Mech. Phys. Solids 53 383–405.CrossRefMathSciNetzbMATHADSGoogle Scholar
  6. Cherkaev A., Vinogradov V., Leelavanichkul S. (2005a) The waves of damage in elastic-plastic lattices with waiting links: design and simulation, Mechanics of Materials accepted.Google Scholar
  7. Charlotte M., Truskinovsky L. (2002) Linear chains with a hyper-pre-stress, J. Mech. Phys. Solids 50 217–251.CrossRefMathSciNetzbMATHADSGoogle Scholar
  8. Ngan S. C., Truskinovsky L. (1999) Thermal trapping and kinetics of martensitic phase boundaries, J. Mech. Phys. Solids 47 141–172.CrossRefMathSciNetzbMATHGoogle Scholar
  9. Puglisi G., Truskinovsky L. (2000) Mechanics of a discrete chain with bi-stable elements, J. Mech. Phys. Solids 48 1–27.CrossRefMathSciNetzbMATHADSGoogle Scholar
  10. Slepyan L. I., Troyankina L. V. (1984) Fracture wave in a chain structure, J. Appl. Mech. Techn. Phys. 25 921–927.CrossRefADSGoogle Scholar
  11. Slepyan L. I., Troyankina L. V. (1988) Impact waves in a nonlinear chain, In: ‘Strength and Viscoplasticity’ (in Russian), Journal Vol 301–305, Nauka.Google Scholar
  12. Slepyan L. I. (2000) Dynamic factor in impact, phase transition and fracture, J. Mech. Phys. Solids 48 931–964.ADSGoogle Scholar
  13. Slepyan L. I. (2001) Feeding and dissipative waves in fracture and phase transition. II. Phase transition Waves, J. Mech. Phys. Solids 49 513–550.CrossRefMathSciNetADSGoogle Scholar
  14. Slepyan L. I. (2002) Models and Phenomena in Fracture Mechanics, Springer-Verlag.Google Scholar
  15. Slepyan L. I., Ayzenberg-Stepanenko M. V. (2004) Localized transition waves in bistable-bond lattices, J. Mech. Phys. Solids 52 1447–1479.CrossRefMathSciNetzbMATHADSGoogle Scholar
  16. Slepyan L., Cherkaev A., Cherkaev E. (2005) Transition waves in bistable structures II: Analytical solution, wave speed, and energy dissipation, J. Mech. Phys. Solids 53 407–436.CrossRefMathSciNetzbMATHADSGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Andrej Cherkaev
    • 1
  • Elena Cherkaev
    • 1
  • Leonid Slepyan
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Dept. of Solid Mechanics, Materials and SystemsTel Aviv Univ.Israel

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