Explicit, comprehensive modeling of multi-axial finite strain pseudo-elastic SMAs up to failure

A new elastoplastic J2−flow model with nonlinear combined hardening is proposed for the purpose of achieving an explicit, comprehensive simulation of pseudo-elastic SMAs over the whole range of strain up to failure. To this goal, a new, explicit methodology based on any given uniaxial data is introduced to obtain multi-axial expressions for the constitutive quantities incorporated in this model, in such a unified sense that all three successive deformation stages may be simultaneously represented, including a pseudo-elastic stage with perfect strain recovery, a hardening stage with partial strain recovery, and a softening stage up to failure. As such, any given shapes of uniaxial stress–strain curves from both loading and unloading in these three stages may be automatically reproduced from the proposed model, without involving usual complicated numerical procedures in treating nonlinear rate constitutive equations with a number of switching conditions. Numerical examples with test data are supplied to simulate a complete process including all three stages.