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@ARTICLE{,
    author = {Rezaee-Hajidehi, Mohsen and Tůma, Karel and Stupkiewicz, Stanis{\l}aw},
  keywords = {finite element method, Micromorphic regularization, Phase transformation, Softening, Strain localization},
     title = {Gradient-enhanced thermomechanical 3D model for simulation of transformation patterns in pseudoelastic shape memory alloys},
   journal = {International Journal of Plasticity},
      year = {2019},
      issn = {0749-6419},
       url = {http://www.sciencedirect.com/science/article/pii/S0749641919302037},
       doi = {https://doi.org/10.1016/j.ijplas.2019.08.014},
  abstract = {Stress-induced martensitic transformation in polycrystalline NiTi under tension often proceeds through formation and propagation of macroscopic phase transformation fronts, i.e., diffuse interfaces that separate the transformed and untransformed domains. A gradient-enhanced 3D finite-strain model of pseudoelasticity is developed in this work with the aim to describe the related phenomena. The underlying softening response is regularized by enhancing the Helmholtz free energy of a non-gradient model with a gradient term expressed in terms of the martensite volume fraction. To facilitate finite-element implementation, a micromorphic-type regularization is then introduced following the approach developed recently in the 1D small-strain context. The complete evolution problem is formulated within the incremental energy minimization framework, and the resulting non-smooth minimization problem is solved by employing the augmented Lagrangian technique. In order to account for the thermomechanical coupling effects, a general thermomechanical framework, which is consistent with the second law of thermodynamics and considers all related couplings, is also developed. Finite-element simulations of representative 3D problems show that the model is capable of representing the loading-rate effects in a NiTi dog-bone specimen and complex transformation patterns in a NiTi tube under tension. A parametric study is also carried out to investigate the effect of various parameters on the characteristics of the macroscopic transformation front.}
}