The qualitative difference in solution behavior in the vicinity of maximum friction surfaces is demonstrated for two distinct models of pressure-dependent plasticity (the double-shearing and coaxial models) using closed-form solutions for planar flow through an infinite wedge-shaped channel and plane-strain compression of an infinite block between parallel plates. Singular velocity fields (some components of the strain rate tensor approach infinity at the friction surface) occur in the solutions based on the double-shearing model. This is similar to behavior in the vicinity of maximum friction surfaces in classical plasticity of pressure-independent materials. A singular velocity field is also obtained in the solution based on the coaxial model for the problem of channel flow; but, in contrast to the double-shearing model and classical plasticity, sticking must occur at this friction surface. For the problem of compression of a material obeying the coaxial model, no solution based on conventional assumptions exists with the maximum friction law. This is quite different from both the corresponding solution based on the double-shearing model and the channel flow solution based on the coaxial model.
Comparison of Double-Shearing and Coaxial Models for Pressure-Dependent Plastic Flow at Frictional Boundaries
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, November 30, 1999; final revision, August 19, 2002. Associate Editor: B. M. Moran. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Alexandrov, S. (March 27, 2003). "Comparison of Double-Shearing and Coaxial Models for Pressure-Dependent Plastic Flow at Frictional Boundaries ." ASME. J. Appl. Mech. March 2003; 70(2): 212–219. https://doi.org/10.1115/1.1532319
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