Crystal is the solid whose atomic structures are determined by lattices. One type of special crystal is Martensitic crystal, which can undergo reversible, diffusionless, structural phase transformations. We call this kind of transformations are martensitic transformations. It is observed in various metals, alloys, ceramics and even biological systems. For instance, it has the role in strengthening steel. The martensitic microstructure is the fine-scale mixtures of coherent phases of martensitic crystals. A very good example of martensitic crystal is some shape-memory alloys.

I am interested in the martensitic microstructure produced in the continuum transformation, in which the high temperature austenite phase transforms to the low-temperature martensite phase. Specifically I will investigate the 2-D vectorial problem with surface energy, in which the situation along the interface will be considered. The well-known two-tell problem with different choices of energy density function will be simulated in my project. My program will be open to other proper energy density functions by simply changing the function definition.

Mid-term Progress Report