Shape memory and phase transitions for auxetic materials

We present a mathematical model describing the auxetic-austenitic phase transition phenomenon by a second order shape memory phase transition. The typical properties of auxetic materials, as the negative Poisson ratio ν, are described by a function of the phase ϕ, called order parameter, which relates the phase transition with a change of the internal order structure of the material. In our model, the auxetic phase is represented by an order parameter ϕ = 1, which provides a negative Poisson's ratio, while the austenitic phase will be denoted by ϕ = 0.