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David R. Owen, Professor Emeritus Ph.D., Brown University Email: do04@andrew.cmu.edu Office: Wean Hall 8130 Phone: 4122682679 Research:My research concerns mathematical models for the behavior of continuous bodies. My work on multiscale geometry has centered on the problem of determining classes of deformations broad enough to describe geometric changes at both microscopic and macroscopic scales. This research is the first step in a program of broadening the foundations of continuum mechanics so as to include a wide variety of bodies with microstructure such as liquid crystals, defective crystals, granular materials and mixtures. My work on the analysis of standard models of elasticplastic materials has concentrated on studying systems of ordinary differential equations that describe "elasticplastic oscillators." This study has led to new concepts and theorems on uniqueness and continuous dependence, including the notion of a "weakly Lipschitzian mapping" and a related Gronwall inequality for such mappings. Ideas from this research have led to progress in the study of antiplane shearing flows in viscoplastic solids.Selected Publications:
