Computational methods for martensitic thin films

In this doctoral thesis, we study various theoretical and computational aspects of single-crystal martensitic alloys. Special emphasis is placed on the theory of thin films of such materials. Throughout the thesis, we utilize the geometrically nonlinear theory of martensite to model the diffusionless phase transitions that these materials undergo.; This thesis has four chapters. In the first chapter, we classify and study a particular case of martensitic phase transitions, the tetragonal to monoclinic transformation. This transformation is characterized by a free energy density which is minimized by four symmetry-related transformation strains. We give an analysis of the stability of a laminated microstructure with infinitesimal length scale that oscillates between two compatible variants of martensite corresponding to two energy minimizing strains.; In the second chapter, we employ the theory of thin films of martensitic materials and propose a temperature and pressure operated microvalve. We provide and study a mathematical model for the microvalve and give results of numerical simulations performed to confirm the possibility of functionality of such a device.; In the third chapter, we demonstrate the capabilities of the numerical methods currently used for simulating the behavior of martensitic thin films. We describe an experiment with a thin foil of CuAlNi and provide a corresponding mathematical model. We compare the results of the numerical simulations with the experiment and provide possible explanations for some of the observed phenomena.; Finally, in the fourth chapter, we derive an alternative thin film model for martensitic materials. The free energy is augmented by a higher-order term modelling the interfacial energy. This term allows for sharp interfaces between regions of constant deformation gradient. This is different from the model used in the second chapter of this thesis, where only diffuse interfaces are allowed. The new model should allow for more efficient numerical schemes to simulate the behavior of martensitic thin films.