Generalization of the Prandtl problem for a creep model

S. E. Aleksandrov^a, E. A. Lyamina^a, N. M. Tuan<sup>b

a</sup> Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
^b Institute of Mechanics, 264, Hanoi, Vietnam

Abstract: An approximate solution to the problem of compression of an infinite layer of material between rough parallel plates is constructed with the creep equations being fulfilled. Constitutive relations in accordance with which the equivalent stress tends to a finite value as the equivalent strain rate tends to infinity are used. The behavior of the solution in the neighborhood of the maximum friction surface is studied. It is shown that the existence of the solution depends on one of the parameters included in the constitutive equations. If the solution exists, the equivalent strain rate tends to infinity in the neighborhood of the maximum friction surface, and the asymptotic behavior of the solution depends on the same parameter. It is established that there is a range of this parameter in which the nature of the change in the equivalent strain rate near the maximum friction surface is the same as in the solutions for rigid plastic materials.

Keywords: creep, Prandtl problem, infinite layer of material, friction surface.

UDC: 539.374

Received: 30.05.2013

 English version: Journal of Applied Mechanics and Technical Physics, 2014, 55:4, 682–688

Bibliographic databases:

•