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Dynamically expanding self-similar Inclusions:self-similar Motion

Xanthippi Markenscoff (University of California, San ), Luqun Ni (UCSD)

Symposium in honor of Rod Clifton on the occasion of his 75th Birthday

Mon 9:00 - 10:30

Salomon 101

The dynamically expanding ellipsoidal Eshelby inclusion (with general eigenstrain) in self-similar motion is analyzed following the method of Burridge and Willis [1]. The solution is shown to preserve the Eshelby property of constant stress field in the interior domain. As applied to the case of a spherical inclusion, the solution agrees with the one obtained by solving the elastodynamic equation in spherical coordinates for scale invariance, as well to the one obtained from the general motion [2]. The driving force is also obtained. [1] Burridge, R. and Willis, J.R. “The self-similar problem of the expanding elliptical crack in an anisotropic solid” , Proc. Camb. Phil. Soc.,66, pp 443-468 (1969) [2]. Markenscoff , X. and Ni, Luqun “ The energy-release rate and self-force of dynamically expanding spherical and plane inclusion boundaries with dilatational eigenstrain, J. Mech. Phys. Sol. 58, pp1-11, (2010).