International Journal of Non-Linear Mechanics 37 (2002) 1363–1374 Modeling the dynamic behavior of shape memory alloys Stefan Seelecke Department of Mechanical & Aerospace Engineering, North Carolina State University, Box 7910, Raleigh, NC 27695-7910, USA Abstract The paper studies the single degree of freedom vibration of a rigid mass suspended by a thin-walled shape memory alloy tube under torsional loading. The behavior is analyzed for the cases of quasiplasticity (low temperatures) and pseudoelasticity (high temperatures) on the basis of an improved version of the M uller–Achenbach model. To illustrate the strong hysteresis-induced damping capacity and the non-linear vibration characteristics, both, free and forced vibrations are considered in the rst part of the paper. This is done on the basis of an isothermal version of the model, while the second part of the paper focuses on the eect of non-constant temperature caused by the rate-dependent release and absorption of latent heats. ? 2002 Published by Elsevier Science Ltd. Keywords: Shape memory alloys; Modeling; Damping capacity; Hysteresis; Dynamics 1. Introduction In recent years, shape memory alloys (SMAs) have started to attract increasing attention due to some of their dynamic properties. The hysteretic phase trans- formation between austenite and martensite at high temperature and between dierent twins of the marten- site phase at low temperature constitutes an intrinsic dissipation mechanism, which results in a consider- able damping capacity. Graesser and Cozarelli [1] rst suggested the use of SMAs as novel damping materi- als and Clark et al. [2] demonstrated the feasibility of the concept for a nitinol wire device. Potential appli- cations are seen amongst others in civil structures like buildings and bridges where SMAs can provide an ef- cient seismic base isolation; see [3]. The subject has been quite extensively covered experimentally, and a E-mail address: stefan seelecke@ncsu.edu (S. Seelecke). very good overview can be found in the reports of the European MANSIDE project [4]. The present paper has the objective to present a model, which is able to reproduce the non-linear dynamic eects of SMA materials, including the large damping capacity caused by the hysteresis in the load= deformation curve. The simulation is based on a model originally de- veloped by M uller and Achenbach [5]. The authors use ideas from the theory of thermally activated pro- cesses and statistical thermodynamics to describe the kinetics of the phase transformations, and the model is capable of giving a good qualitative description of the load–deformation behavior of SMA for the en- tire temperature range. In [6], the author has used this model to simulate the torsional vibration of a SMA wire for the rst time. While it reproduces some basic features of the vibration, it also exhibits some disturb- ing details that do not correspond to experimental ob- servations. The pseudoelastic hysteresis loop follows a declining curve under deformation control, which is 0020-7462/02/$ - see front matter ? 2002 Published by Elsevier Science Ltd. PII:S0020-7462(02)00030-6