Accurate Response Sensitivity Analysis of a Thermomechanical Constitutive Model for Superelastic SMAs

Quan Gu, Ning Zhang, Bin Wang, Songye Zhu

Research output: Journal article publicationJournal articleAcademic researchpeer-review


Superelastic shape memory alloys (SMAs) have attracted considerable interest in the field of earthquake engineering recently due to their excellent self-centering and moderate energy dissipating capabilities. This unique feature provides promising solutions that can be used in the passive control of structures under strong earthquakes. However, the hysteresis properties of the SMAs have a great influence on the response of the structures. A prominent problem of most previous SMA constitutive models is that they do not consider the strain-rate-dependent effect, especially the mechanical behavior in the typical frequency range of interest for seismic applications. Moreover, the variability effect of the SMA's hysteresis parameters on the performance in seismic applications is not addressed comprehensively. For this reason, it is important to explore the response sensitivity analysis of an improved SMA constitutive model and gain insight into the effects of various thermomechanical parameters. This paper presents an efficient and accurate sensitivity analysis method for the strain-rate-dependent model of SMAs based on the direct differentiation method (DDM). The constitutive model of SMAs involves three coupled quantities, i.e., stress, martensite fraction, and temperature. The model is expressed numerically using the first-order ordinary differential equations and is solved by the fourth-order Runge-Kutta method. Both the consistent tangent modulus and the stress sensitivity of the SMAs are derived and integrated into the DDM framework. The newly developed algorithms are implemented in a general nonlinear finite element analysis program, OpenSees, and are further verified by the time history analyses of a multi-story steel frame designed with SMA braces. The results demonstrate that the developed DDM-based sensitivity algorithm is accurate and efficient and can provide an excellent solution to the response sensitivity analysis of the thermomechanical strain-rate-dependent model of SMAs.

Original languageEnglish
Article number1925
JournalJournal of Engineering Mechanics
Issue number5
Publication statusPublished - 1 May 2021


  • Consistent tangent modulus
  • Direct differentiation method (DDM)
  • Response sensitivity
  • Shape memory alloys (SMAs)
  • Strain-rate-dependent
  • Thermomechanical

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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