Generalization of the Prandtl Problem for a Creep Model
S. E. Alexandrov1, E. A. Lyamina1, N. M. Tuan2
1Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia
2Institute of Mechanics, 264 Hanoi, Vietnam
Keywords: creep, Prandtl problem, infinite layer of material, friction surface
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.
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