The
research originally aimed at the study of dynamic penetration into concrete and
rock targets, employing the Durban-Fleck formulation for dynamic expansion of a
spherical cavity in a porous elastoplastic medium (the Drucker-Prager solid).
In fact, the research has focused on an analytical and numerical investigation
of the spherical cavity expansion model (Durban-Fleck model) with particular
emphasis on some special cases including - the small strain linear elastic
field, the deep plastic field, the Mises solid, the incompressible
Drucker-Prager material and the associated solid. The analytical treatment is
for arbitrary hardening characteristics with special reference to an
elastic/perfectly-plastic solid and to the Ramberg-Osgood relation. The work
has exposed the analytical richness of the Durban-Fleck model, has improved
understanding of dynamic cavitation in a porous elastoplastic medium and has
provided useful analytical results for further research and applications. An
exact relation for cavitation pressure in a hardening incompressible Mises
solid is given for any cavitation velocity. We have defined the useful concept
of an incompressible Drucker-Prager material along with a few solutions, exact
and approximate, for the cavitation pressure. These analytical solutions show,
for the first time, the influence of the material porosity parameter. Also
given are perturbation solutions for the compressible Mises solid, accounting
for strain-hardening , and an analysis of the influence of Poisson’s ratio, as
well as strain-hardening, on the cavitation pressure. For the first time we
see, in a relatively simple analytical way, how those parameters influence the
dynamic part of cavitation pressure. The research concludes with an updated
formulation for a dynamic spherical cavitation model in a porous elastoplastic
medium incorporating our previous observations. A few numerical solutions
illustrate and support the validity of the analytical results while for the
associated solid we have only a numerical solution.
