Nonlinear Differential Equations and Applications NoDEA

, Volume 13, Issue 4, pp 385-411

First online:

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

  • M. BrokateAffiliated withZentrum Mathematik, Technische Universität München Email author 
  • , D. RachinskiiAffiliated withDepartment of Applied Mathematics, University College Cork

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The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions.

2000 Mathematics Subject Classification:

47J40 74C05


Hysteresis ratchetting plasticity model periodic solution global stability