TAM Seminar Presents:
Xanthippi Markenscoff
Distinguished Professor Emerita
Dept. of Mechanical and Aerospace Engineeering
University of California, San Diego
“Volume Collapse” Instabilities in Deep-Focus Earthquakes: a Shear Source Nucleated and Driven by Pressure
Abstract
Symmetry-breaking instabilities in high- pressure phase transformation produce the counterintuitive phenomenon of “volume collapse” producing only shear radiation, with little, or no, volumetric component, even under conditions of full isotropy, and explain the mystery of the long-standing observations in deep-focus earthquakes (400-700 km). Due to instability, at a critical “nucleation pressure”, an arbitrarily small densified region, in the shape of a “pancake-like” flattened ellipsoidal Eshelby inclusion, grows self-similarly as a “lacuna” (zero particle velocity) with the phase transformation occurring under conditions of equilibrium in uniform strain/stress and at constant potential energy (at the vanishing of the M integral, when the radius-expanding driving force overcomes the radius-shrinking self-force). The symmetry-breaking flattened shape favors minimization of the energy needed for the boundary to grow large, while for the accommodation of the large collapsing volume in the very thin inclusion deviatoric stresses are developed to avoid openings and overlaps. It is shown that, if an arbitrarily small flattened densified region is generated planarly, and the pressure exceeds the critical nucleation value, then it will necessarily produce a shear seismic source, with little or no, volumetric component, nucleated and driven to propagate by the pressure. The obtained stress/deformation fields of a densified 2D flattened elliptical inclusion constitute a new defect that models the “anticrack” in geophysics and densified shear bands. The instability analysis can be extended to the nucleation and growth of the phase transition from water to a solid ice phase under high pressure, with the discovered instabilities providing insight to other phenomena of dynamic phase transformations, such as failure waves, amorphization, planetary impacts, etc.
Biography
Xanthippi Markenscoff is Distinguished Professor Emerita and Recalled Professor in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego. She obtained a Diploma in Civil Engineering from the National Technical University of Athens, Greece, and a Ph.D. from Princeton University. She has been a Visiting Miller Professor at UC Berkeley and a Springer Professor in Mech. Eng. at UC Berkeley, and also held visiting appointments at Brown University, Oxford University, and Ecole Polytechnique in Paris, France. Her expertise is in the elastodynamics of defects, dislocations and inclusions (Eshelby), conservation laws and configurational mechanics, singular defect interactions, and asymptotic homogenization.
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