01.02.2015 | Ausgabe 2/2015
On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation
- Zeitschrift:
- Journal of Elasticity > Ausgabe 2/2015
Wichtige Hinweise
Research partially supported by the EU FP7-REGPOT project “Archimedes Center for Modeling, Analysis and Computation”, the “Aristeia” program of the Greek Secretariat of Research, and the EU EST-project “Differential Equations and Applications in Science and Engineering”. Part of this work was completed at the Institute of Applied and Computational Mathematics, FORTH, Greece.
Abstract
We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation. For dimensions d=2,3 we show that cavity formation is necessarily associated with a unique precursor shock. We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation as a function of the cavity speed of the self-similar profiles. We show that for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents.
