Singular plastic flow fields near surfaces of maximum friction stress

Assuming a rigid/perfectly plastic material model with arbitrary isotropic smooth yield criterion, it is shown that the velocity fields adjacent to su rfaces of maximum friction, except for some special planar flows, must be d escribable by non-differentiable functions where the maximum shear strain r ate and the effective strain rate approach infinity. This is consistent wit h experimental results that show very large gradients of velocity near such surfaces and with computational results that indicate difficulty in descri bing such behavior with finite elements using simple interpolation function s. Moreover, this result leads naturally to the definition of a strain rate intensity factor which has similar meaning to the stress intensity factor in linear elastic fracture mechanics. As an example of the application of t he singular velocity field, simple compression of a plastic layer between p arallel, rough plates is considered. An upper bound solution is found by as suming the singular field in the layer. As expected, it lies between the up per bound obtained by assuming simple compression in the layer and a slip l ine solution. (C) 2000 Elsevier Science Ltd. All rights reserved.