  A Ginzburg-Landau model for the macroscopic behaviour of a shape memory alloy
is proposed. The model is one-dimensional in essence, in that we consider the
effect of the martensitic phase transition in terms of a uniaxial deformation
along a fixed direction and we use a scalar order parameter whose equilibrium
values describe the austenitic phase and the two martensitic variants. The
model relies on a Ginzburg-Landau free energy defined as a function of
macroscopically measurable quantities, and accounts for thermal effects;
couplings between the various relevant physical aspects are established
according to thermodynamic consistency. The theoretical model has been
implemented within a finite-element framework and a number of numerical tests
are presented which investigate the mechanical behaviour of the model under
different conditions; the results obtained are analysed in relation to
experimental evidences available in literature. In particular, the influence of
the strain-rate and of the ambient conditions on the response of the model is
highlighted.
