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


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.


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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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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