Dynamic tension of a sheet made of rigid-plastic material

The stress-strain state arising under dynamic stretching of a homogeneous sheet of an incompressible ideally rigid–plastic material, which obeys the Mises–Hencky criterion, is studied. The lateral boundary is stress–free and the longitudinal velocities are given at the ends. The possibility of thickening or thinning of the section along the length of the sheet is taken into account, which simulates necking and further development of the neck. Two characteristic stretching regimes are revealed: one of them depends on the velocity at which the end sections move away from each other and the other one depends on their acceleration. For the second regime, the asymptotic integration-based analysis allows one to find the stress–strain state parameters approximately.