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**Thermomechanical modelling, nonlinear dynamics and chaos in shape memory oscillators.**
*(English)*
Zbl 1097.74528

Summary: A constitutive model for the restoring force in pseudo-elastic shape memory oscillators is proposed. The model is developed in a thermomechnical framework and allows one to predict the temperature variations that typically arise in shape memory materials under dynamical loading. A peculiar feature of the model is that all the constitutive equations follow from two basic ingredients, the free energy and the dissipation functions, through the restrictions imposed by the balance equations, instead of being directly postulated as in standard internal variable formulations. The model is then implemented and employed to systematically characterize the nonlinear dynamic response of the oscillator. It turns out that non-regular responses occur around the jumps between different branches of frequency – response curves. The features of the responses and the modalities of transition to chaos are described mainly by means of bifurcation diagrams. The effect of the main model parameters (pseudo-elastic loop shape and thermal effects) on the dynamics of the system is also investigated.

### MSC:

74F05 | Thermal effects in solid mechanics |

70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |

74N99 | Phase transformations in solids |

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\textit{D. Bernardini} and \textit{G. Rega}, Math. Comput. Model. Dyn. Syst. 11, No. 3, 291--314 (2005; Zbl 1097.74528)

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