Thermomechanical modelling, nonlinear dynamics and chaos in shape memory oscillators

A constitutive model for the restoring force in pseudo-elastic shape memory oscillators is proposed. The model is developed in a thermomechanical 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 response 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.

[1]  D. E. Carlson,et al.  An introduction to thermomechanics , 1983 .

[2]  K. Shimizu,et al.  Pseudoelasticity and shape memory effects in alloys , 1986 .

[3]  Thomas J. Pence,et al.  A Thermomechanical Model for a One Variant Shape Memory Material , 1994 .

[4]  M. Berveiller,et al.  Continuum mechanical aspects of phase transformations in solids , 1994, Archive of Applied Mechanics.

[5]  P. Müller.  Calculation of Lyapunov exponents for dynamic systems with discontinuities , 1995 .

[6]  G. Rega,et al.  Bifurcation structure at 1/3-subharmonic resonance in an asymmetric nonlinear elastic oscillator , 1996 .

[7]  Z. C. Feng,et al.  Dynamics of a Mechanical System with a Shape Memory Alloy Bar , 1996 .

[8]  Arun R. Srinivasa,et al.  On the thermomechanics of shape memory wires , 1999 .

[9]  D. Bernardini.  Models of hysteresis in the framework of thermomechanics with internal variables , 2001 .

[10]  M. Schwartz.  Encyclopedia of smart materials , 2002 .

[11]  Davide Bernardini,et al.  Models for one-variant shape memory materials based on dissipation functions , 2002 .

[12]  Marcelo Amorim Savi,et al.  Chaos and Hyperchaos in Shape Memory Systems , 2002, Int. J. Bifurc. Chaos.

[13]  Arata Masuda,et al.  An overview of vibration and seismic applications of NiTi shape memory alloy , 2002 .

[14]  Fabrizio Vestroni,et al.  Non-isothermal oscillations of pseudoelastic devices , 2003 .

[15]  Marcelo A. Savi,et al.  Nonlinear dynamics and chaos in coupled shape memory oscillators , 2003 .

[16]  Fabrizio Vestroni,et al.  Nonlinear thermomechanical oscillations of shape-memory devices , 2004 .

[17]  T. Pence,et al.  Uniaxial Modeling of Multivariant Shape-Memory Materials with Internal Sublooping using Dissipation Functions , 2005 .