Numerical analysis of a three-dimensional super-elastic constitutive model

This note deals with the efficient approximation of a non-linear constitutive relation arising in the study of the three-dimensional mechanical behaviour of shape memory alloys at constant temperature. In particular, a variable time-step discretization is investigated. For such an algorithm we prove sharp error estimates of optimal order and exactness for a class of experimentally relevant situations. We also report numerical results relative to proportional and non-proportional loading tests which fully confirm the theoretical analysis