Stress-induced phase-transition front propagation in thermoelastic solids

A simplest possible mathematical model of martensitic phase transition front propagation is considered in the paper. Martensite and austenite phases are treated as isotropic linear thermoelastic materials. The phase transition front is viewed as an ideal mathematical discontinuity surface. Only one variant of martensite is involved. The problem remains nonlinear even in this simplified description that supposes a numerical solution. A non-equilibrium description of the process is provided by means of non-equilibrium jump relations at the moving phase boundary, which are formulated in terms of contact quantities. The same contact quantities are used in the construction of a finite-volume numerical scheme. The additional constitutive information is introduced by a certain assumption about the entropy production at the phase boundary. Results of numerical simulations show that the proposed approach allows us to capture experimental observations while corresponding to theoretical predictions in spite of the idealization of the process.