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SUMMARY:Self-similarly expanding regions of phase change yield cavitationa
 l  instabilities and model deep earthquakes  - Prof Xanthippi Markenscoff\
 , Department of Mechanical &amp\; Aerospace Engineering\, University of Ca
 lifornia\, San Diego
DTSTART:20190503T130000Z
DTEND:20190503T140000Z
UID:TALK119524@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:The dynamical fields that emanate from self-similarly expandin
 g ellipsoidal regions undergoing phase change (change in density\, i.e.\, 
 volume collapse\, and change in moduli) under pre-stress\, constitute the 
 dynamic generalization of the seminal Eshelby inhomogeneity problem (as an
  equivalent inclusion problem)\, and they consist of pressure\, shear\, an
 d M waves emitted by the surface of the expanding ellipsoid and yielding R
 ayleigh waves in the crack limit. They may constitute the model of Deep Fo
 cus Earthquakes (DFEs) occurring under very high pressures and due to phas
 e change. Two fundamental theorems of physics govern the phenomenon\, the 
 Cauchy-Kowalewskaya theorem\, which based on dimensional analysis and anal
 ytic properties alone\, dictates that there is zero particle velocity in t
 he interior\, and Noether’s theorem that extremizes  \n(minimizes for st
 ability) the energy spent to move the boundary so that it does not become 
 a sink (or source) of energy\, and determines the self-similar shape (axes
  expansion speeds). The expression from Noether’s theorem indicates that
  the expanding region can be planar\, thus breaking the symmetry of the in
 put and the phenomenon manifests itself as a newly discovered one of a “
 dynamic collapse/ cavitation instability”\, where very large strain ener
 gy condensed in the very thin region can escape out.  In the presence of s
 hear\, the flattened very thin ellipsoid (or band) will be oriented in spa
 ce so that the energy due to phase change under pre-stress is able to esca
 pe out at minimum loss condensed in the core of dislocations gliding out o
 n the planes where the maximum configurational force (Peach-Koehler) is ap
 plied on them. Phase change occurring planarly produces in a flattened exp
 anding ellipdoid a new defect present in the DFEs. The radiation patterns 
 are obtained in terms of the equivalent to the phase change six eigenstrai
 n components\, which also contain effects due to planarity through the Dyn
 amic Eshelby Tensor for the flattened ellipsoid. Some models in the litera
 ture of DFEs are evaluated and excluded on the basis of not having the ene
 rgy to move the boundary of phase discontinuity. Noether’s theorem is va
 lid in anisotropy and nonlinear elasticity\, and the phenomenon is indepen
 dent of scales\, valid from the nano to the very large ones\, and applicab
 le in general to other dynamic phenomena of stress induced martensitic tra
 nsformations\, shear banding\, and amorphization. 
LOCATION:Department of Engineering - LR4
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