On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractWe 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.
CitationOn the Construction and Properties of Weak Solutions Describing Dynamic Cavitation 2014, 118 (2):141 Journal of Elasticity
JournalJournal of Elasticity