Dynamic Regimes of Biaxial Stretching of a Thin Ideally Rigid-Plastic Rectangular Plate

Abstract

The stress–strain state arising during dynamic tension of a homogeneous rectangular plate of an incompressible ideally rigid–plastic material, which obeys the Mises–Hencky criterion, is considered. The upper and lower bases are stress-free; longitudinal velocities are set at the ends. The possibility of deformation of the upper and lower sides of the plate is taken into account, which simulates neck formation and further development of the neck. A small geometric parameter is introduced: the ratio of the average thickness of the plate to its length along one of the directions. At different time intervals, the order of smallness of the dimensionless functions characterizing the dynamic stretching mode may be different with respect to the geometric parameter which determines the stretching mode. Two such characteristic modes are identified: one is associated with a sufficiently high rate of removal of the ends of the plate from each other, the second with acceleration. In the second case, an analysis is carried out using the method of asymptotic integration, which allows us to approximately find the parameters of the stress–strain state.