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CATEGORIES:Engineering Department Mechanics Colloquia Researc
h Seminars
SUMMARY:Self-similarly expanding regions of phase change y
ield cavitational instabilities and model deep ea
rthquakes - Prof Xanthippi Markenscoff\, Departme
nt of Mechanical &\; Aerospace Engineering\, Un
iversity of California\, San Diego
DTSTART;TZID=Europe/London:20190503T140000
DTEND;TZID=Europe/London:20190503T150000
UID:TALK119524AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/119524
DESCRIPTION:The dynamical fields that emanate from self-simila
rly expanding ellipsoidal regions undergoing phase
change (change in density\, i.e.\, volume collaps
e\, and change in moduli) under pre-stress\, const
itute the dynamic generalization of the seminal Es
helby inhomogeneity problem (as an equivalent incl
usion problem)\, and they consist of pressure\, sh
ear\, and M waves emitted by the surface of the ex
panding ellipsoid and yielding Rayleigh waves in t
he crack limit. They may constitute the model of D
eep Focus Earthquakes (DFEs) occurring under very
high pressures and due to phase change. Two fundam
ental theorems of physics govern the phenomenon\,
the Cauchy-Kowalewskaya theorem\, which based on d
imensional analysis and analytic properties alone\
, dictates that there is zero particle velocity in
the interior\, and Noether’s theorem that extremi
zes \n(minimizes for stability) the energy spent
to move the boundary so that it does not become a
sink (or source) of energy\, and determines the se
lf-similar shape (axes expansion speeds). The expr
ession from Noether’s theorem indicates that the e
xpanding region can be planar\, thus breaking the
symmetry of the input and the phenomenon manifests
itself as a newly discovered one of a “dynamic co
llapse/ cavitation instability”\, where very large
strain energy condensed in the very thin region c
an escape out. In the presence of shear\, the fla
ttened very thin ellipsoid (or band) will be orien
ted in space so that the energy due to phase chang
e under pre-stress is able to escape out at minimu
m loss condensed in the core of dislocations glidi
ng out on the planes where the maximum configurati
onal force (Peach-Koehler) is applied on them. Pha
se change occurring planarly produces in a flatten
ed expanding ellipdoid a new defect present in the
DFEs. The radiation patterns are obtained in term
s of the equivalent to the phase change six eigens
train components\, which also contain effects due
to planarity through the Dynamic Eshelby Tensor fo
r the flattened ellipsoid. Some models in the lite
rature of DFEs are evaluated and excluded on the b
asis of not having the energy to move the boundary
of phase discontinuity. Noether’s theorem is vali
d in anisotropy and nonlinear elasticity\, and the
phenomenon is independent of scales\, valid from
the nano to the very large ones\, and applicable i
n general to other dynamic phenomena of stress ind
uced martensitic transformations\, shear banding\,
and amorphization.
LOCATION:Department of Engineering - LR4
CONTACT:Hilde Hambro
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