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
Necessary conditions for a minimum
at a radial cavitating singularity in nonlinear elasticity (with J. Sivaloganathan). Submitted.
On cavitation, configurational
forces and implications for fracture in a nonlinearly elastic material, J.
Elasticity 67 (2002), 25-49 (with J. Sivaloganathan).
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).
On copositive matrices and strong
ellipticity for isotropic elastic
materials, Arch. Rational Mech. Anal. 84 (1983), 55-68 (with H. C.
Simpson).