The subject of this work is the application of the Smoothed Particle Hydrodynamics
(SPH) method to modelling high-velocity impact dynamics.
The first part of this thesis proposes an extension of the original first-order Godunov
SPH scheme, for material with strength, to second-order in space using a
time-splitting approach for the hydrodynamic and deviatoric components of the
stress tensor. A non-linear slope-limiting procedure is used to extend the hydrodynamic
component to second-order while the deviatoric component is discretized
directly. Exact conservation of total energy is enforced in the new scheme using a
time-centering approach for the velocity field. The new scheme is shown to perform
well for a variety of one and two-dimensional fluid and solid-dynamics test
cases. In particular, the numerical viscosity is shown to be lower than the original first-order scheme and particle clustering is less pronounced than in the standard artificial viscosity method.
The second part of this thesis applies the newly developed SPH scheme to
modelling high-velocity impacts on a synthetic porous poly-crystalline graphite
material. In the course of investigation it was found that the applicability of
the porous P - α equation of state is questionable for this type of graphite; an
experimental investigation concluded that the assumptions required for the use
of the porous equation of state are invalid. Therefore, an empirically derived
polynomial equation of state is proposed instead. A widely used material model for
brittle materials, based on the Continuum Damage Mechanics (CDM) approach, is
used for the graphite deviatoric constitutive equation. In light of the time-splitting
procedure, an algorithm for inclusion of CDM constitutive models was developed.
Numerical simulations of high velocity impacts on the graphite material were then
performed and compared with experimental results.