Scott J. Spector           Professor of Mathematics       and Distinguished Scholar Southern Illinois University Ph. D., Carnegie Mellon University, 1978 Continuum Mechanics, Calculus of Variations

My research lies in the areas of continuum mechanics, the calculus of variations and partial differential equations. I am especially interested in the nonlinear theory of elasticity. In recent years I have concentrated on analyzing some mathematical models for the formation of holes in rubbery polymers. Experiments on such elastomers reveal that a major failure mechanism is that of cavity formation and coalescence; when loads are applied small holes appear, grow, and combine to form cracks. A similar material failure can also occur in glass; in certain optical fibers low levels of laser light together with moderate heat will cause a series of cavities to cascade down the core of the fiber, seriously degrading its optical properties. The analysis of such material failures has lead to new and interesting questions concerning: the existence of, and admissibility criterion for, singular solutions to hyperbolic systems of partial differential equations; the existence of singular solutions to certain parabolic systems of partial differential equations; the existence of minimizers with singularities for problems in the calculus of variations; and the regularity and fine properties of singular minimizers.

Selected Publications.

On the Symmetry of Energy Minimising Deformations in Nonlinear Elasticity II: Compressible Materials,  (with  J. Sivaloganathan). ABSTRACT On the Symmetry of Energy Minimising Deformations in Nonlinear Elasticity I: Incompressible Materials,  (with  J. Sivaloganathan). ABSTRACT  Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Anal. Non Linéaire 25 (2008), 201-213 (with  J. Sivaloganathan). ABSTRACT A Variational Approach to Modelling Initiation of Fracture in Nonlinear Elasticity, A Variational Approach to Modelling Initiation of Fracture in Nonlinear Elasticity,  IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics (A. B. Movchan, ed.), Springer, 2004, pp. 295-306 (with J. Sivaloganathan). ABSTRACT Dynamic cavitation with shocks in nonlinear elasticity, Proc. Royal Soc. Edinburgh 127A (1997), 837-857 (with K. A. Pericak-Spector). An existence theory for nonlinear elasticity that allows for cavitation,  Arch. Rational Mech. Anal. 131 (1995), 1-66 (with S. Müller). The formation of filamentary voids in solids,  J. Mech. Phys. Solids 39 (1991), 783-813 (with R. D. James). On copositive matrices and strong ellipticity for isotropic elastic materials,  Arch. Rational Mech. Anal. 84 (1983), 55-68 (with H. C. Simpson).

Biographical Sketch.

Erdös Number .

Four (S. Müller, V. Sverák, D. Preiss, P. Erdös) .

Academic Genealogy.

Mathematics Department Home Page

Last Modified 29 March 2008
© 1997-2008 by Scott J. Spector