Mathematical modeling of shock induced martensitic phase transitions

Abstract

Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by "rarefaction discontinuities". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure.