| The dissertation consists of four parts. We first conduct an approximate analysis of steady state axisymmetric deformations of a viscoplastic target being penetrated by a hemispherical nosed rigid penetrator. A kinematically admissible velocity field is presumed, and the unknown parameters are determined by minimizing the error in satisfying the balance of linear momentum. The solution so obtained is found to be very close to the finite element solution of the problem. In the second part, we postulate a velocity dependent expression for the frictional force on the target/penetrator interface. The values of the two constants in the expression for the frictional force are determined by comparing the distribution of the tangential traction on the penetrator nose surface as obtained from a finite element solution of the problem with that obtained by modeling the target material as a viscous fluid. The computed results show that the frictional force affects noticeably the tangential speed and the strain-rate on the penetrator nose surface, but minimally the normal traction there. Finally, we simulate numerically the penetration of a hemispherical nosed rigid rod into a thick thermoviscoplastic target and employ the aforestated expression for the frictional force. The finite element mesh is refined adaptively whenever one of its elements has been severely distorted. The computed results reveal that depth of penetration correlates well with the test value, the consideration of thermal softening of the target material influences strongly its deformations and the frictional force at the target/penetrator interface reduces the penetration depth by about 12%. |
