An improved, fully symmetric, finite-strain phenomenological constitutive model for shape memory alloys

The ever increasing number of shape memory alloy applications has motivated the development of appropriate constitutive models taking into account large rotations and moderate or finite strains. Up to now proposed finite-strain constitutive models usually contain an asymmetric tensor in the definition of the limit (yield) function. To this end, in the present work, we propose an improved alternative constitutive model in which all quantities are symmetric. To conserve the volume during inelastic deformation, an exponential mapping is used to arrive at the time-discrete form of the evolution equation. Such a symmetric model simplifies the constitutive relations and as a result of less nonlinearity in the equations to be solved, numerical efficiency increases. Implementing the proposed constitutive model within a user-defined subroutine UMAT in the nonlinear finite element software ABAQUS/Standard, we solve different boundary value problems. Comparing the solution CPU times for symmetric and asymmetric cases, we show the effectiveness of the proposed constitutive model as well as of the solution algorithm. The presented procedure can also be used for other finite-strain constitutive models in plasticity and shape memory alloy constitutive modeling.