Numerical–analytical model of penetration of long elastically deformable projectiles into semi-infinite targets

A new numerical–analytical model of penetration of long axisymmetric elastically deformable projectiles in semi-infinite targets is presented. A background of this model is the integral–differential equation of ballistics for non-deformable projectile. This equation is obtained on the basis of the Lagrange–Cauchy integral for non-stationary irrotational motion of an incompressible fluid, as well as the solutions for the quasi-static spherical cavity expansion problem in an infinite medium. The velocity field in a target is defined by actual projectile shape. The functional dependence of penetration velocity is determined for both elastic and rigid projectiles. The effect of forced elastic longitudinal oscillations on penetration velocity is estimated. An estimate is made for the critical impact velocity at which point the projectile plastically deforms causing irreversible changes in its shape, and also leads to instability of its trajectory in the target. This velocity depends on both elastic and strength characteristics of the projectile and target, their densities and projectile shape. Results from our penetration modeling are compared with existing experimental and calculated data.