CAVITATING PENETRATION OF A PLASTIC MEDIUM BY BODIES OF MINIMUM RESISTANCE

An approximate approach to the description of the deep penetration of a plastic medium by elongated bodies [1] is developed. The results obt ained in [2-5] are generalized to another geometry and to a wider rang e of velocities, which is subdivided into intervals. An attempt is mad e to provide an averaged description of the motion in each of the inte rvals assuming quasistationarity, and the formula for the depth of pen etration is analysed. Lavrent'yev's idea on the closeness of the veloc ity and stress fields during the high-velocity motions of bodies in a solid medium and in a liquid, which has been translated into the langu age of asymptotic representations [5], has been further developed in a n hypothesis on the closeness of the configurations of bodies of minim um resistance in a plastic medium and a liquid subject to the conditio n of the smallness of the ratio of the strength (resistance) force to the hydrodynamic drag force. The advantage of tubular bodies compared with solid bodies with respect to mass and depth of penetration is ind icated. The bounds of the limiting penetration depths are estimated.