Microstructure and Symmetry Breaking Phase Transition: Analysis and Numerical Simulation

University Of Maryland, College Park, College Park MD

Investigators

Abstract

DMS Award Abstract Award #: 0104118 PI: Dolzmann, Georg Institution: University of Maryland, College Park Program: Applied Math Program Manager: Catherine Mavriplis Title: Microstructure and Symmetry Breaking Phase Transition: Analysis and Numerical Simulation The goal of this project is to understand macroscopic properties of materials undergoing solid to solid phase transitions through modern methods in the calculus of variations. A main objective is to investigate the possible patterns that can form and their impact on the elastic behaviour of the material. On the analytical side, virtually all methods to attack this problem are connected to the deep mathematical concept of quasiconvexity. Even 50 years after Morrey's seminal work, quasiconvexity is despite its fundamental importance still poorly understood, and any progress in this program will contribute to the unraveling of its mysteries. The numerical simulation of microstructure poses a wealth of challenging problems. New insight into the underlying theoretical concepts will enhance the performance of algorithms and lead to their rigorous verification. Successful computations will help to develop new experiments that allow to identify optimal properties of materials. The proposed integrated analytical and numerical approach is designed to advance the understanding and the optimization of new materials which play a crucial role in emerging technological applications, for example of microactuators based on shape memory materials or light guiding devices and bifocal contact lenses made of nematic elastomers. Date: May 11, 2001