The main objective of the present paper is to demonstrate, by means of a problem permitting a semi-analytical solution, the effect of the shape of pressure-dependent yield surfaces on qualitative behaviour of rigid plastic solutions in the vicinity of frictional interfaces. The yield criterion used reduces to the classical Coulomb-Mohr yield criterion at specific values of input parameters and, therefore, can be further reduced to the classical Tresca yield criterion. The solution is singular (some components of the strain rate tensor approach infinity) in the vicinity of the maximum friction surface at sliding if the system of equations is hyperbolic. The dependence of the strain rate intensity factor on input parameters of the double-slip and rotation model based on quite a general plane-strain yield criterion is found, and its consequence on some physical processes in a narrow material layer near frictional interfaces is discussed.
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