Modeling Penetration Phenomena

Penetration phenomena are of interest in numerous areas (cf. [3]). They are often associated with the problem of nuclear waste containment and with the protection of spacecraft or satellites from debris and/or meteorite impact. Formally the penetration is defined as the entrance of a projectile into the target without completing its passage through the body. The penetration phenomenon can be characterized according to the impact angle, the geometry and material characteristics of the target and the projectile and the striking velocity. In this chapter we limit our considerations to the normal incidence impact of a long rod on a semi-infinite target. This model corresponds for example to the situation in which a very thick armor is penetrated by a high kinetic energy projectile. The most efficient method for the solution of this problem is the numerical modeling by the finite element method. Many finite element computer programs are capable of handling very complex material constitutive relations. These programs are expensive and often require a substantial amount of execution time. This is the main reason why simple one-dimensional theories still have considerable value. Such theories also provide insight into the interactions between the physical parameters and their relationship to the outcome of the event. These interactions are usually difficult to ascertain from the computer analyses mentioned above. As a result, simple theories often provide the basis for the design of experiments, refining the areas in which numerical modeling by finite element methods is applied. In this spirit, we will investigate some penetration models which are treated using Maple.