Friday, November 8, 2013
Dynamic Eshelby Micromechanics (with inertia effects)
Xanthippi Markenscoff, Distinguished Professor, Mechanical & Aerospace Engineering, University of California, San Diego
"Eshelby micromechanics" can be called the micromechanics based on the two celebrated Eshelby papers: The "force on an elastic singularity", or "Eshelby force" (1951), (associated with Noether's theorem and conserved integrals) and the ellipsoidal inclusion with transformation strain (1957) where the Eshelby tensor allows for the solution of inhomogeneities as well. Both of these Eshelby micromechanics building blocks are extended to dynamics with inertia. It will be presented that for self-similarly expanding ellipsoidal inclusions the constant stress Eshelby property in the interior holds, and that the dynamic Eshelby tensor (for self-similar motion) is obtained analytically (which leads to the analytical solutions of dynamically expanding inhomogeneities). The elastodynamic evolution of moving defects (dislocations, expanding inclusion and inhomogeneity boundaries) is governed by the dynamic conservation laws from Noether's theorem yielding the "kinetic relations" due to inertia.