For hemispherical cumulative liners of degressive (decreasing from the top to the base) thickness, an increase in the velocity of the head of the forming cumulative jet is observed with an increase in the difference in thickness at the top and at the base of the liner, which is ensured by the fact that the process of its explosive compression becomes closer to spherically symmetrical. Based on the numerical solution of a model problem of inertial centrally symmetric collapse of a shell in the form of a spherical segment with a model of a material that does not resist all-round stretching, it is shown that the maximum velocity of cumulative jets from hemispherical liners of degressive thickness that do not undergo volumetric destruction should be higher in comparison with jets from conical liners: at least 12 km/s in the case of liners made of copper. The production of a coherent copper cumulative jet with a head velocity at the specified level was recorded in a numerical simulation of the explosion of a charge with a liner of degressive thickness, having a hemispherical outer surface and a semisuperellipsoidal inner surface with an exponent of 2.05 in the semisuperellipsoid equation.
С.В. Федоров (Sun,) studied this question.