Scientific seminar on the differential and functional differential equation on topic “Inertial effects during rapid compression of thin plastic layers”
14 February at 12.00 (Moscow time)
Speaker: Georgievsky Dmitry Vladimirovich, Doctor of Physical and Mathematical Sciences, Professor of the Russian Academy of Sciences, Head of the Department of the Theory of Elasticity, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University.
Topic: Inertial effects during rapid compression of thin plastic layers
In the mechanics of a deformable solid body and in the theory of plastic flow, the classical Prandtl problem is known about the inertialess compression of a thin flat layer of ideally plastic material by absolutely rigid plates, possibly coated with lubricant. The fields of stresses, pressures and velocities inside the layer, as well as the law of motion of Lagrangian particles at any moment of compression, are well known and are included in the training courses. The classical solution presented by L. Prandtl, W. Prager and H. Geiringer in the 1930s has limits of applicability. It is true only in the quasi-static approximation, i.e. when the accelerations of the particles are so small that they can be neglected in comparison with the stress gradients included in the equations of motion (and then these equations of motion actually become equations of equilibrium). However, no matter how slowly the plates approach each other, in the time range just before the collapse of the layer, it is already illegal to use quasi-statics; a complete dynamic, or inertial, analysis of the problem is necessary. The dynamic Prandtl problem and qualitatively new effects arising in its solution will be discussed in the report.