Computational modeling of coupled dynamic phase transformations in shape memory alloys

In spite of several modeling approaches to understand the shape memory alloy (SMA) behaviour, many difficulties exist because of the various limitations of the existing free energy models. Associated phase kinetics coupled with the thermoelastodynamics is still not fully tractable. A new dynamic model of 3D SMA is developed in this paper, which employs an improved version of the microscopic Landau theory. Essential properties of the single and multi-variant martensitic phase transformations are recovered using consistent steps, which eliminates the problem of non-uniqueness of energy partitioning and relaxes the over-sensitivity of the free energy due to many unknown material constants in previously reported models. The newly developed microscopic model is incorporate in a variationally formulated finite element framework. Newmark´s time integration scheme is adopted and the condition for consistent iteration to solve the strongly nonlinear system at each time step is highlighted. Banded assembly of the discretized system matrix is performed in parallel. A parallel PCG method with Jacobi preconditioner is employed to solve the system at each time step.