A History of Research and a Review of Recent Developments

142
Penetration and fragmentation
research work of that era. One of the earliest penetration theories [7.1] was
due to J.V. Poncelet (1788–1867), mentioned earlier in the Introduction, who
was a French military engineer and professor of engineering mechanics at the
military school in Metz. He had a perceptive view of the physics of the
penetrative process, in which he combined the resistance of a medium to the
static penetration by a body with a resistance linked to the speed at which the
body was moving. He considered that the dynamic resistance in a material
such as soil or sand should be analogous to resistance to fluid dynamic flow.
He therefore assumed that the force resisting penetration would be given
by the equation
F=–A(a+bV (7.1)
where
F = resisting force
A = cross sectional area of the projectile
V = impact velocity
a, b were constants to be determined by experiment.
If the mass of the projectile=m, the equation of motion is
2 ),
and by integration we get the relationship
(7.2)
(7.3)
where p=vertical penetration.
This assumes that the material has sufficient depth in the direction of
penetration to bring the projectile to rest before it ‘breaks out’ of the far side.
If this is not so, adjustments have to be made to the analysis, as we shall see
later. The difference between penetration into soil or concrete, or other frangible
materials, and into strong, ductile materials is very great, and is influenced by
the average pressures resisting penetration. These can be 15 times greater in
steel armour, for example, than for concrete. For all materials it is the kinetic
energy of an undeforming projectile that crushes and distorts the target.
The contribution of Poncelet to many problems in materials science has
been well documented in the book History of Strength of Materials (ref. [7.2]),
and it is from this that we learn that he started from poor beginnings before
winning scholarships that eventually took him to the Ecole Polytechnique.
He joined Napoleon’s army in 1812 and was taken prisoner during the retreat
from Moscow. His ideas about projective geometry were developed during
his confinement for two years in Saratov. After his subsequent career at Metz
he became commandant of the Ecole Polytechnique between 1848 and 1850.