The paper briefly analyzes a number of published works devoted to cumulative explosion under conditions of the possible development of surface instability of the collapsing liner of a shaped charge. Most studies stated that surface instability was initially initiated by harmonic surface disturbances or disturbances in the parameters of a given load simulating an explosive one. The instability manifested itself in the form of the development of surface disturbances over time; the absence or limited growth was considered as the preservation of the stability of the deformable shell. In addition to the influence of instability on cumulative processes, related jet flows were also investigated. This is the so-called explosive dispersion (dusting), which occurs both under the influence of the interference of shock waves and unloading waves, and in the presence of initial disturbances of the surface shape. The analysis is built within the framework of the phenomenological approach — both the main results of the experiments and their mathematical descriptions were considered, which in most cases were carried out from the positions established in the mechanics of continuous media, as well as with the help of numerical modeling. Based on the results, conclusions were formulated about the reasons and forms of manifestation of surface instability of collapsing metal liners of shaped charges, the nature of the development and parameters of functioning of such charges, as well as about the features and laws of this process.

The paper presents research of the collapse of the elastic-plastic shell under external surface forces simulating explosive loading by mathematical simulation using numerical methods. The problem was solved in two-dimensional curved geometries as a non-stationary problem of continuum mechanics. We applied the Wilkins Lagrangian method. The instability of the shell was initiated by harmonic surface perturbations on the outer or inner surfaces. The characteristics of the explosive loading were also changed: the maximum pressure, pressure fall time constant, and the time of application of the explosive load. The size of instability was determined by the deviation of the disturbed surface or the boundary of the jet-forming layer from the cylindrical one. We have established the parameters of the shell and the impulse loading on the shell, which affect most strongly the growth of instability during collapse.

The mathematical model for the subsequent numerical study of the shaped charge liner collapse affected by external surface forces simulating an explosive load is presented. The basic liner was considered as an originally cylindrical compressible elastoplastic shell within the framework of a two-dimensional flat nonstationary problem of continuum mechanics. To ensure the rationality of the modeling and numerical calculation at the initial time the design fragment was discriminated in the liner by central beams. Deformation of the fragment being a part of the shell was taken into account by the boundary conditions of cyclic repeatability in the tangential direction. For numerical solving the well-known Wilkins Lagrangian method was used, which was refined in terms of the relations describing the mechanical behavior of an elastoplastic medium. Additionally, a self-developed grid adjustment procedure was used, excluding the appearance of highly elongated cells in the calculation. The instability of the shell deformation was initiated by harmonic surface perturbations, initially assigned on the outer or inner surfaces. The degree of instability was assessed by the deviation of the disturbed surface (or the boundary of the so-called stream-forming layer) from the cylindrical one. The used finite-difference algorithms are implemented in the form of appropriate calculation programs. A number of computational verification measures was performed proving the viability of the developed mathematical model and the possibility of its further use