Scott Spector | Mathematics | SIU

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Scott Spector

Emeritus

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Professor and Distinguished Scholar; Ph.D., Carnegie Mellon University, 1978. Elasticity and continuum mechanics.

Research Interests

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. 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 minimizers with singularities for problems in the calculus of variations; and the regularity and fine properties of singular minimizers.

Selected Publications

  1. Energy minimising properties of the radial cavitation solution in incompressible nonlinear elasticity, J. Elasticity 93 (2008), 177-187 (with J. Sivaloganathan).
  2. On bifurcation in finite elasticity: Buckling of a rectangular rod, J. Elasticity 92 (2008), 277-326 (with H. C. Simpson).
  3. Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Anal. Non Linéaire 25 (2008), 201-213 (with J. Sivaloganathan).
  4. Dynamic cavitation with shocks in nonlinear elasticity, Proc. Royal Soc. Edinburgh 127A (1997), 837-857 (with K. A. Pericak-Spector).
  5. An existence theory for nonlinear elasticity that allows for cavitation, Arch. Rational Mech. Anal. 131 (1995), 1-66 (with S. Müller).
  6. On copositive matrices and strong ellipticity for isotropic elastic materials, Arch. Rational Mech. Anal. 84 (1983), 55-68 (with H. C. Simpson).