
Department of Physical Mechanics, Faculty of Mathematics and Mechanics,
Saint
Petersburg State University,
Saint Petersburg, 198904, Bibliotechnaya2, RUSSIA
khan@math.spbu.ru
A new hydrodynamic theory based on nonequilibrium statistical mechanics is developed to describe the structure formation in dynamically deformed materials [12]. Selfconsistent nonlocal formulation of the boundaryvalue problem for a highstrainrate process is reduced to a nonlinear operator set similar to some resonance problems [3]. The branching of solutions to the problem determines both scales and types of the formed internal structure. A penetration problem for a long flat rigid plate into a viscous elastic medium is considered accounting for the dynamic structure formation following the highrate straining in the framework of the nonlocal selfconsistent approach. The obtained approximate analytical solution has shown to describe three regimes: initial, transient and quasistationary. It has been demonstrated that the mesoscopic structure formation had been initiated by relative accelerations in a medium localized near the plate surface moving at high velocity. The mesoscopic structures formed during the initial stage of penetration can effect on the steadystate stage. It is very important that the proposed selfconsistent theory allow taking into account the feedback influence of the mesoscopic effects on macroscopic movement of the plate. 
full paper (pdf, 200 Kb)