Friday, February 17, 2006
1:00pm – 2:00pm
Professor Xanthippi Markenscoff
Applied Mechanics
University California - San Diego
“Convection In Mushy Layers With Sidewall Heat Fluxes”
Abstract:
Eshelby's definition of the force on an elastic singularity is generalized > to dynamics
through the Eshelby "cut and reinsert" thought experiment and the resulting expression is
defined as the dynamic J integral, and coincides with an expression that is invariant
under the Noether theorem transformation. Through this thought experiment the dynamic
L and M integrals are also defined as the moment on an an elastic singularity (change of
energy with respect to rotation of the defect) and change of energy with respect to a self
scaling parameter respectively and coincide with the other expressions obtained by
Noether's theorem. The dynamic force on an elastic singularity is surface-independent
and it coincides with the energy-release rate if the singularities are such that the
integrals exist. For a moving dislocation in a generally accelerating motion the self-force
as defined from the above expression of the dynamic J integral > is explicitly calculated ,
as well as the effective mass which is defined as the coefficient of the acceleration in the
self-force expression. The divergent integrals are smoothed out by a ramp-core model,
which allows for the core-width to vary with acceleration. A variable core width model
is also presented for a static dislocation in order to estimate the Peierls lattice friction
stress.