A model to predict the forces on conical-nosed penetrators for normal impact into dry rock targets is developed. The target medium is described by a linear hydrostat, a linear shear failure-pressure relation, and the material density. A cylindrical cavity expansion approximation to the target response permits one-dimensional wave propagation calculations in the radial coordinate. The equations of motion are reduced, via a similarity transformation, to a nonlinear ordinary differential equation. This equation is solved numerically by a shooting technique which employs an asymptotic expansion to the solution near the wave front. Results include stress wave profiles in the target and curves for the stress on the penetrator nose as a function of its velocity for a wide range of realistic target parameters. Finally, results from the theory are compared with the deceleration history of a penetrator in a field test and reasonable correlation is observed.
We derived equations for the target-strength term used in the modified hydrodynamic model that describes long rod penetration into ceramic targets. Since ceramics have tensile strengths that are usually an order of magnitude lower than their compressive strength, this model allows for tensile cracking. In addition, our model includes the effect of pressure-dependent shear strength.
The response of a string to a mass particle undergoing a constant horizontal acceleration from rest has been calculated. The string deflection is expressed in terms of the transverse mass motion. A delay-differential equation is solved both numerically and asymptotically for the mass velocity. String profiles are presented at subsonic and supersonic speeds. Two oppositely traveling jumps in string displacement are found to appear as the mass is accelerated through the wave speed of the string.
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