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.
Energy minimising properties of
the radial cavitation solution in incompressible nonlinear elasticity, J.
Elasticity93 (2008), 177-187 (with J. Sivaloganathan).
On bifurcation in finite elasticity:
Buckling of a rectangular rod, J. Elasticity92
(2008), 277-326 (with H. C. Simpson).
Necessary conditions for a minimum
at a radial cavitating singularity in nonlinear elasticity, Anal. Non
Linéaire25 (2008), 201-213 (with J. Sivaloganathan).
Dynamic cavitation with shocks
in nonlinear elasticity, Proc. Royal Soc. Edinburgh127A
(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).