M.Sc Thesis

M.Sc StudentMasri Rami
SubjectDynamic Spherical Cavitation in a Porous Elastoplastic
DepartmentDepartment of Aerospace Engineering
Supervisor PROFESSOR EMERITUS David Durban


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.