Slow Penetration of a Plane Punch into a Plastic Medium

Vitali Babakov


Mathematical Modelling, Plasticity , Velocity, Upper bound theorem


The problem of the penetration a rigid body into a plastic medium is a classical problem of the mechanics of solids. The study of the penetration process is a difficult mathematical problem that requires complicated computer simulations. The article contains a relatively simple mathematical solution for the penetration of a plane punch into a plastic medium. Key point of the investigation is application of upper bound theorem for ideal plastic medium. It can be considered as a first approach of a strict theoretical solution. The comparison of the new solution, shown here, and classical results obtained by L.Prandtl and V. Sokolovskii confirms the acceptance of such approach to solution of the penetration problem. The solution can be used in engineering practice and for teaching purposes.

Important Links:

Go Back