Modelling shape memory alloys

Modelling shape memory alloys is based on choosing state quantities E which involve the phase volume fractions, on defining the free energy Ψ(E) and the pseudo-potential of dissipation Φ [E, dE/dt, grad T] depending on the thermal heterogeneity characterised by the temperature gradient grad T. The derivatives of Ψ and Φ give the constitutive laws which are used in the momentum and energy conservation laws. It results a set of partial differential equations: we call it the model. It allows to predict the evolution of the state quantities in a structure made of shape memory alloys. It is of paramount importance to measure the physical parameters of the constitutive laws and to prove that the partial differential equations are coherent and have solutions. Thus modelling involves experiments, theory, and mechanics, engineering and mathematics.