Mathematical Sciences: Studies in Continuum Mechanics and Materials Sciences

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9531221 Gurtin This project is a continuation of a research effort toward developing, analyzing, and unifying mathematical models that characterize material behavior at a phenomenological level. The long-term goal of this project is a continuum-mechanical framework for the study of materials that provides a basis for general theories and leads to boundary-value problems of physical relevance. The following specific studies are planned: (i) the development of a small-strain theory of incoherent phase transitions that results in free-boundary problems amenable to analysis and computation; (ii) the development of a theory of deformational phase transitions appropriate to fully faceted crystals; (iii) the analysis of models that generalize motion by curvature. The goal of this project is a continuum mechanical framework for the study of materials. This framework should provide a basis for the development of general theories that lead to new ways of understanding defects and microstructures and provide an ability to predict macroscopic properties as well as detailed behavior at the microscopic level.