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David R. Owen, Professor Emeritus
Ph.D., Brown University
E-mail: do04@andrew.cmu.edu
Office: Wean Hall 8130
Phone: 412-268-2679


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 elastic-plastic materials has concentrated on studying systems of ordinary differential equations that describe "elastic-plastic 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:

  • Deseri, L. and D. R. Owen (2000), "Active Slip-Band Separation and the Energetics of Slip in Single Crystals, " Int. J. Plasticity 16, 14111418.
  • Del Piero, G. and Owen, D.R. (2000), Structured Deformations, XXII Scuola Estiva di Fisica Matematica, Ravello, September 1997.
  • Choksi, R., Del Piero, G., Fonseca, I., and Owen, D.R. (1999), "Structured Deformations as Energy Minimizers in Models of Fracture and Hysteresis, " Math. Mech. Solids 4, 321356.
  • Greenberg, J. M., and Owen, D. R. (1998), "Antiplane Shear Flows in Visco-Plastic Solids Exhibiting Isotropic and Kinematic Hardening," SIAM J. Appl. Math. 58, 6, 19962023.
  • Del Piero, G., and Owen, D. R. (1995), "Integral-Gradient Formulae for Structured Deformations," Arch. Rational Mech. Anal. 131, 121138.
  • Del Piero, G., and Owen, D. R. (1993), " Structured Deformations of Continua," Arch. Rational Mech. Anal. 124, 99155.
  • Owen, D.R., Schaeffer, J., and Wang, K. (1992), "A Gronwall Inequality for Weakly Lipschitzian Mappings," Arch. Rational Mech. Anal. 120, 191200.