Evaluation of different SMA models performances in the nonlinear dynamics of pseudoelastic oscillators via a comprehensive modeling framework

Abstract The nonlinear dynamics of Shape Memory Alloys (SMA) oscillators with pseudoelastic behaviour has been studied extensively in the last years by using different constitutive models for the restoring force. The response of SMA devices is rather complex and is characterized by several aspects that, usually, are not taken into account within a single model. For this reason, the constitutive models that are typically used to study the nonlinear dynamics are often of a rather simplified nature that neglects one or more aspects. This works investigates the extent to which the choice of a more or less refined constitutive model can affect the evaluation of the nonlinear dynamic behaviour of a SMA oscillator. In order to compare different constitutive models, a comprehensive thermomechanical modelling framework capable to simulate different constitutive assumptions is proposed first. Then, numerical simulations are carried out to compare the different dynamical responses. The obtained results show that, for single trajectories with specific features, different models can give similar dynamical information, although with the exception of different transient behaviour. However, when the overall scenario of local dynamics is investigated by computing frequency-response curves, it becomes evident that the simplified models, and in particular those with polynomial restoring force, fail to capture main aspects such as the location of the jumps and the order of magnitude of response peaks. Moreover, they generally lead to significant errors in the estimation of the dissipated energy, which is crucial for the quantification of the structural damping. The results of this work should then be helpful to guide the choice of SMA models to be used in nonlinear dynamic applications.

[1]  Marcelo A. Savi,et al.  Chaos in a shape memory two-bar truss , 2002 .

[2]  Huibin Xu,et al.  On the pseudo-elastic hysteresis , 1991 .

[3]  Stefan Seelecke,et al.  Thermodynamic aspects of shape memory alloys , 2001 .

[4]  Marcelo A. Savi,et al.  Nonlinear dynamics and chaos in shape memory alloy systems , 2015 .

[5]  Davide Bernardini,et al.  Thermomechanical modelling, nonlinear dynamics and chaos in shape memory oscillators , 2005 .

[6]  José Manoel Balthazar,et al.  Non-linear dynamics of a thermomechanical pseudoelastic oscillator excited by non-ideal energy sources , 2015 .

[7]  Marcelo A. Savi,et al.  An overview of constitutive models for shape memory alloys , 2006 .

[8]  Marcelo A. Savi,et al.  Tensile-compressive asymmetry influence on shape memory alloy system dynamics , 2008 .

[9]  Danuta Sado,et al.  Pseudoelastic effect in autoparametric non-ideal vibrating system with SMA spring , 2012 .

[10]  Renata Erica Morace,et al.  Analysis of thermomechanical behaviour of Nitinol wires with high strain rates , 2005 .

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

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

[13]  W. Zaki,et al.  A review of constitutive models and modeling techniques for shape memory alloys , 2016 .

[14]  B. R. Pontes,et al.  Analytical study of the nonlinear behavior of a shape memory oscillator: Part I—primary resonance and free response at low temperatures , 2010 .

[15]  Davide Bernardini,et al.  New micromechanical estimates of the interaction energy for shape memory alloys modeled by a two-phases microstructure* , 2016 .

[16]  Cyril Touzé,et al.  Non-linear dynamic thermomechanical behaviour of shape memory alloys , 2012 .

[17]  José Manoel Balthazar,et al.  Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source , 2009 .

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

[19]  Dimitris C. Lagoudas,et al.  Pseudoelastic SMA Spring Elements for Passive Vibration Isolation: Part I – Modeling , 2004 .

[20]  Davide Bernardini,et al.  Chaos Robustness and Strength in thermomechanical Shape Memory oscillators Part I: a Predictive Theoretical Framework for the Pseudoelastic Behavior , 2011, Int. J. Bifurc. Chaos.

[21]  Qingping Sun,et al.  Jump phenomena of rotational angle and temperature of NiTi wire in nonlinear torsional vibration , 2015 .

[22]  Davide Bernardini,et al.  Chaos Robustness and Strength in thermomechanical Shape Memory oscillators Part II: numerical and Theoretical Evaluation , 2011, Int. J. Bifurc. Chaos.

[23]  Corneliu Cismasiu,et al.  Numerical simulation of superelastic shape memory alloys subjected to dynamic loads , 2008 .

[24]  F. Falk.  Model free energy, mechanics, and thermodynamics of shape memory alloys , 1980 .

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

[26]  Elena Sitnikova,et al.  Vibration reduction of the impact system by an SMA restraint: numerical studies , 2010 .

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

[28]  Behrouz Asgarian,et al.  A simple hybrid damping device with energy‐dissipating and re‐centering characteristics for special structures , 2014 .

[29]  Dimitris C. Lagoudas,et al.  Numerical Investigation of an Adaptive Vibration Absorber Using Shape Memory Alloys , 2011 .