Wierzbicki on projectile physics and mechanics

See last paragraph in particular for ways in which projectiles into and solid objects or thin sheets are different from planes into buildings. :


In the language of mechanics the above observation can be expressed via the statement of energy balance given by Eq.(1) where all the components entering Eq.(1) are listed below.

E_kinetic is the kinetic energy of the airplane;

E_plane is the energy dissipated by the crushing and breakup of the aircraft;

E_{external _ column} is the energy required to cut through the exterior columns;

E_floor is the energy dissipated by the floors;

E_core is the energy absorbed by the core column destruction. In subsequent sections we will estimate all five different terms entering Eq.(1).

This is not an easy task because the relative contribution of various terms will depend on the activated failure modes and contact forces developed between different components of the airplane and the Towers. Both the airplane and the WTC Towers are built as closed or open, thin-walled, three-dimensional structures, which deform plastically, crush and crumble, fracture and break up into small pieces. Thus, whatever evidence remained has been burned in the 10-story high pile of debris.

What tools did the present team have at its disposal for accomplishing the stated objectives? To answer this question, one must place the local aircraft impact damage in the context of existing knowledge. A distinguishing feature of the attack on the Twin Towers was the high impact velocity that the airplanes had relative to the ground vehicle collisions extensively studied in the literature. A review of recent methods and results in the area of crashworthiness engineering can be found, for example, in references [7-9]. This class of problems is dominated by membrane and bending deformation of thin, shell-like structures accompanied by large displacement, rotation, and strain of material elements, as well as internal contact. Global inertia of structural members is important, but the effect of local inertia is negligible. Fracture is seldom a problem in crashworthiness engineering.

On the other end of the spectrum are projectile impacts into solid objects and/or thin sheets causing penetration and perforation. Here, fracture and local inertia play a major role, but projectiles are treated as rigid bodies when impacting thin-walled targets. Projectile impact velocities may exceed, by an order of magnitude, those that were encountered in the WTC Towers impact. For a review of the mechanics and physics of projectile impact, the reader is referred to excellent articles by Corbett et al [10] and Goldsmith [11].