  Hypervelocity ejection of material by impact spallation is considered a
plausible mechanism for material exchange between two planetary bodies. We have
modeled the spallation process during vertical impacts over a range of impact
velocities from 6 to 21 km/s using both grid- and particle-based hydrocode
models. The Tillotson equations of state, which are able to treat the nonlinear
dependence of density on pressure and thermal pressure in the strongly shocked
matter, were used to study the hydrodynamic and thermodynamic response after
impacts. The effects of material strength and gravitational acceleration were
not considered. A two-dimensional time-dependent pressure field within a
1.5-fold projectile radius from the impact point was investigated in
cylindrical coordinates to address the generation of spalled material. A
resolution test was also performed to reject ejected materials with peak
pressures that were too low due to artificial viscosity. The relationship
between ejection velocity veject and peak pressure Ppeak was also derived. Our
approach shows that late stage acceleration in an ejecta curtain occurs due to
the compressible nature of the ejecta, resulting in an ejection velocity that
can be higher than the ideal maximum of the resultant particle velocity after
passage of a shock wave. We also calculate the ejecta mass that can escape from
a planet like Mars (i.e., veject higher than 5 km/s) that matches the
petrographic constraints from Martian meteorites, and which occurs when Ppeak
from 30-50 GPa. Although the mass of such ejecta is limited to from 0.1-1
percent of the projectile mass in vertical impacts, this is sufficient for
spallation to have been a plausible mechanism for the ejection of Martian
meteorites. Finally, we propose that impact spallation is a plausible mechanism
for the generation of tektites.
