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This paper provides a critical review of the advancements made in the application of the variable material properties (VMP) method over the past two decades. The VMP method was originally proposed in 1997 (Jahed and Dubey, 1997, ASME J. Pressure Vessel Technol., 119(3), pp. 264–273; Jahed et al., 1997, Int. J. Pressure Vessels Piping, 71(3), pp. 285–291) and further developed in 2001 (Parker, 2001, ASME J. Pressure Vessel Technol., 123(3), p. 271) as an elastoplastic method for the analysis of axisymmetric problems. The model was originally developed as a boundary value problem to predict the spatial distribution of stress. However, since 1997, it has been extended to include thermal effects to solve thermomechanical residual stresses; time domain to solve creep of disks and cylinders; finite deformation to solve cylinders under large strains; numerical solutions to make them more efficient; and asymmetric hardening behavior to accommodate nonslip deformation modes. These advancements, made over the past 20 years, are reviewed in this paper, and future trends and frontiers are discussed.

The Variable Material Properties (VMP) method of elastoplastic analysis for axisymmetric problems is extended to the applications of the cold expansion problem for magnesium sheets exhibiting asymmetric hardening behavior. To investigate the effect of hardening asymmetry in the stressstrain results, a detailed 3D finite element (FE) model with symmetric material properties was also generated for the cold expansion problem. Comparison between the results of the VMP and the FE model revealed the significant effect of hardening asymmetry.

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