Abstract: In this talk I will review phase-field modeling approaches for microstructural evolution. The theoretical approach follows from the ideas of Morton Gurtin, using micro-force balances to derive the well-known Landau-Devonshire-Ginzburg equations for ferroelectrics, Landau-Lifshitz-Gilbert equations for FSMAs, and Allen-Cahn type equations for fracture. The finite element method is developed for numerical solutions of the phase-field models to investigate the dependence of various domain structures found in ferroelectrics and ferromagnetic shape memory alloys, and for crack propagation in fracture. Emphasis will be placed upon the role of stresses and mechanical constraints during the evolution of domain structures. I will discuss studies on the evolution of domain structures and the influence of the mechanical constraint supplied by substrates on thin films and nanodots. I will highlight the idea that novel engineering of the mechanical interactions in ferroic materials can allow for a wider range (beyond linear behavior) of thermal, electrical, magnetic, and mechanical behaviors with as yet unforeseen applications. Results from fracture studies will be presented demonstrating the capabilities of the method for representing crack growth bifurcations in two and three dimensions. Preliminary results on fluid driven crack growth with applications to hydraulic fracture will also be discussed.
Biosketch: I received my bachelor’s degrees in mechanical engineering and business from the University of Pennsylvania in 1994. I then went on to earn my MS (1997) and PhD (1999) degrees in mechanical engineering from the University of California at Santa Barbara. After spending a little over a year at Harvard University as a post-doc, I then went to Rice University where I was a member of the Mechanical Engineering and Materials Science faculty from 2000-2006. I now reside in Austin, Texas as a professor in Aerospace Engineering and Engineering Mechanics.
My research focuses on continuum modeling and numerical simulation of the mechanical, electrical, magnetic and thermal behavior of materials. My specific interests are on acitve/smart materials such as ferroelectrics and ferromagnetic shape memory alloys. I also have a broad range of interests in the mechanics of materials, including fracture mechanics, plasticity, micromechanics, composites, and finite element methods.