Моделирование процессов динамического внедрения пространственных тел в сжимаемую упругопластическую среду

The paper considers the problem of the normal impact and penetration of rigid spatial bodies into the half-space of the elastoplastic medium. For the medium, a model of a linearly compressible elastoplastic medium is adopted with a linear dependence of the yield stress on the pressure (the Mises-Schleicher-Botkin plasticity condition). The solution of the problem is carried out numerically in a three-dimensional formulation using the software package LS-Dyna. The elastic-plastic penetration medium is considered using a fixed Euler grid with the allocation of empty cells into which the material flows during deformation. The strikers are modeled by a rigid undeformed body in the Lagrangian coordinate system. For comparison, the parameters of the penetration process, i.e. the resistance forces to penetration and the penetration depth of the strikers, were also obtained within the framework of the local interaction model on the basis of the analytical solution of the problem of expanding the spherical cavity. Earlier the applicability of the local interaction model to the determination of the force and kinematic characteristics of sharp conical bodies is shown based on the data of the inverted experiments and numerical calculations in an axisymmetric formulation. Verification of the model applicability aimed at describing the motion of three-dimensional bodies in the full three-dimensional formulation has not been carried out before. The investigated bodies, i.e. a circular cone, three- and tetrahedral pyramids, and a body with a star-shaped cross-section, have the same area of the base, the normal to the lateral surface of the bodies makes up a constant angle of 60 0 with the direction of motion. The peculiarity of constructing the shape of the three-dimensional bodies in question is the fact that within the framework of the local interaction model these bodies should have the same resistance to the introduction, which coincides with the resistance to the introduction of the circular cone. All these bodies have a height less than the height of the cone. The results of the three-dimensional numerical calculations of the bodies’ penetration along the normal into an elastoplastic medium with subsonic and supersonic velocities are presented, which demonstrate an increase in resistance to penetration proportional to a decrease in body height. For the bodies of the same height, the changes in the form of the cross section do not lead to significant differences in the strength of the resistance and penetration depth.