Kinetics of lattice phase transitions

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VainchteinDMS-1007908 This project focuses on development and analysis ofphysically-motivated models of materials undergoing martensiticphase transition, a diffusionless deformation of a crystallattice from the high-symmetry parent austenite phase to thelow-symmetry martensite phase, which can exist in severalsymmetry-related twin variants. Under mechanical or thermalloading, these materials form finely layered twinningmicrostructures. The unique properties of martensites, such astheir ability to accommodate large deformations and the markedhysteresis they exhibit under cyclic loading, are determined bythe kinetics of phase and twin boundaries. Understanding howdynamics of the interfaces depends on their orientation,microstructural configuration, and properties of the crystallattice involves challenging open problems in modeling ofmartensites. The project seeks to advance the understanding ofthese phenomena from the perspective of mesoscopic latticemodels. Building on her prior work, the investigator focuses onseveral prototypical discrete models with the goal of capturingthe essential features of interface kinetics and microstructureevolution and an emphasis on higher-dimensional phenomena andrate effects. The main ingredients of the models are nonconvexinteractions between nearest neighbors allowing for the existenceof two stable homogeneous states and the long-range interactions. Among the outcomes of this project are prediction of nucleatedmicrostructural patterns and derivation of interfacial kineticlaws that can be used to solve problems involving temporal andspatial inhomogeneities. The results are compared toexperimental observations and molecular dynamics simulations. By focusing on the interface kinetics, this project helpsdetermine how the dissipative properties of martensites andrelated active materials depend on the material structure and theloading conditions. This is important in emerging civil,aerospace and industrial applications that require significantpassive damping, such as damage and vibration control incomposite structures and attenuation of earthquake- andwind-induced vibrations in buildings and bridges. Results ofthis project may also help design new materials with desiredproperties. Mathematical methods developed during the projectcan be used to solve similar problems encountered in dislocationtheory, fracture mechanics, DNA modeling, image recognition, andnumerical analysis. The broader impacts of this program are alsoachieved through training of graduate and undergraduate studentsin an interdisciplinary research program, as well as educationaland high-school outreach activities.