Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys

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A thermodynamically-consistent 3 D constitutive model for shape memory polymers (2012, methodology): “However, the numerical manipulation of this procedure follows a standard approach in the literature (Hartl and Lagoudas, 2009), thanks to the well-known Hughes–Winget algorithm (Hughes and Winget, 1980).”
A review of constitutive models and modeling techniques for shape memory alloys (2016, background): “(1996) and Hartl and Lagoudas (2009) depends only on the second invariant J2 of the stress deviator and is given by”
Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys (2010, background): “The choice of the function Hcurð rÞ has been discussed in detail elsewhere (Hartl et al., 2009); here we find it sufficient to state that 4 Not transfor transfor Hcurð rÞ ¼ Hmin; r 6 rcrit; Hmin þ ðHmax HminÞ 1 e kð r rcritÞ ; r > rcrit; ( ð2:11Þ where Hmin corresponds to the observable uniaxial…”