Recent Applications of Level Set Methods in Material Science: Dislocation Models of Grain Boundaries & Equilibrium/Optimal Microstructures

Department of Mathematics, San Jose State University, San Jose, CA, March 22, 2007



The level set method continues to be a popular computational and analytical tool for studying many interesting problems in material science and engineering. In this seminar, we discuss recent applications of level set methods to two long-standing problems in material science. First, we present a level set formalism for describing dislocation models of low-angle grain boundaries. Using a dislocation dynamics simulation based on this formalism, we examine the microstructure of equilibrium grain boundaries and investigate the motion of grain boundaries under applied stresses. Next, we present a variational level set approach to theoretically and computationally study triply-periodic, two-phase equilibrium microstructures. Here, we focus on systems where only the interfacial energy between the two phases contributes to the free energy and where the volume fraction of the two phases is constrained. We demonstrate, theoretically, that equilibrium microstructures are those where the interface between the phases possesses a constant mean curvature. We then computationally study the stability of microstructures whose phases are separated by well-known minimal surfaces and explore the properties of equilibrium microstructures when the volume fractions are unequal.