Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys

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A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions (2011, methodology): “…of SMA response under cyclic loading has been achieved through the introduction of two separate deformation measures; that is transformation strain and plastic strain (Arghavani et al., 2010; Auricchio et al., 2007; Feng and Sun, 2007; Hartl et al., 2010; Kan and Kang, 2010; Zaki and Moumni, 2007).”
A review of constitutive models and modeling techniques for shape memory alloys (2016, methodology): “The flow rule in (48) cannot be used for stress-free temperature-induced reverse transformation. another expression was therefore introduced by Hartl et al. (2010) inwhich the flow direction is parallel to the transformation strain tensor at reversal ε tr rev. Based on the work of Boyd and Lagoudas…”