Martensitic phase transformation (PT) is a first-order, displacive and diffusionless PT which plays an important role in the formation of nano and microstructures and mechanical properties in many materials such as smart alloys. In this project, the coupled system of phase field and large strain based elasticity equations is solved using the nonlinear finite element method (NFEM) to simulate the single-variant martensitic PT in nanoparticles under different mechanical and thermal loadings in 2D and in the Cartesian coordinate. First, the NFEM, implementing both the explicit and implicit methods, was used to solve the time dependent phase field or Ginzburg-Landau (GL) equation without mechanics. The numerical procedure and the self-developed code were verified using the exisiting analytical solutions. Next, the large strain based stationary elasticity equations were solved using the NFEM and the developed code was verified by comparing the results obtained form the code and those from Abaqus, Ansys and Comsol codes. The equilibrium equation was satisfied using the principle of virtual work based on both the total and updated Lagrangean descriptions. Finally, the GL and the large strain based elasticity equations were coupled through the elastic energy and the transformation strain tensor and were solved using the NFEM based on both the explicit and implicit methods and both the the total and updated Lagrangean descriptions. Several examples of the cubic to tetragonal PT in NiAl were simulated and the results were compared with those from the Comsol code. Due to the importance of structural defects and in particular, voids, in kinetics, thermodynamics and nanostructure, and the complication of their analysis, and also to illustrate the ability of developed codes, examples of martensitic PTs in a sample with a single hole with different sizes were solved. Also, various phase field boundary conditions such as variable surface energy, isolated boundary and constant phase were applied and the results were compared. Keywords: Phase field, Martensitic phase transformation, Nano dimensions, Nonlinear finite element, Large strains
