Some remarks on the symmetry of singular minimizers in elasticity

Tuesday, July 22, 2008 - 2:15pm - 2:25pm
EE/CS 3-180
Scott Spector (Southern Illinois University)
Experiments on elastomers have shown that triaxial tensions can
induce a material to exhibit holes that were not previously evident.
Analytic work in nonlinear elasticity has established that such
cavity formation may indeed be an elastic phenomenon: sufficiently
large prescribed boundary deformations yield a hole-creating
deformation as the energy minimizer whenever the elastic energy is of slow

In this lecture the speaker will discuss the use of
isoperimetric arguments to establish that a radial deformation, producing a
spherical cavity, is the energy minimizer in a general class of isochoric
deformations that are discontinuous at the center of a ball and produce a
(possibly non-symmetric) cavity in the deformed body. The key ingredient
is a new radial-symmetrization procedure that is appropriate for
problems where the symmetrized mapping must be one-to-one in order to prevent
interpenetration of matter.
MSC Code: