Fully coupled thermomechanical modeling of shape memory alloys under multiaxial loadings and implementation by finite element method

  • Y. Mohammad Hashemi
  • M. KadkhodaeiEmail author
  • M. Salehan
Original Article


Different constitutive models along with various numerical implementation approaches have been proposed for shape memory alloys (SMAs) in the last decades. Since 1-D models are only suitable for particular geometries and loading types, due to the broad variety of SMA components in smart structures, 3-D rate-dependent modeling of SMAs is a necessity. In the present research, a fully coupled rate-dependent model to study thermomechanical response of shape memory alloys under multiaxial loadings is presented. The model is implemented into ABAQUS commercial finite element package by developing a user-defined material subroutine. Most of the available works are limited to just mechanical loadings and/or simple geometries, but the current model is able to simulate both shape memory effect and pseudoelasticity. Furthermore, it is capable of being applied to any geometry undergoing thermal/mechanical cycling under a wide range of strain rates spanning quasi-static to high-rate conditions. The obtained numerical results by the model are validated by experimental, analytical, and numerical findings of available three-dimensional case studies in the literature. The predicted results by the current model are shown to be in good agreement with the findings of previous investigations.


Shape memory alloy Multiaxial loading Thermomechanical model Three-dimensional model Finite element method UMAT 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran

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