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Singular plastic flow fields near surfaces of maximum friction stress

2001; Elsevier BV; Volume: 36; Issue: 1 Linguagem: Inglês

10.1016/s0020-7462(99)00075-x

1878-5638

Sergei Alexandrov, Oliver P. Richmond,

Granular flow and fluidized beds

Assuming a rigid/perfectly plastic material model with arbitrary isotropic smooth yield criterion, it is shown that the velocity fields adjacent to surfaces of maximum friction, except for some special planar flows, must be describable by non-differentiable functions where the maximum shear strain rate and the effective strain rate approach infinity. This is consistent with experimental results that show very large gradients of velocity near such surfaces and with computational results that indicate difficulty in describing such behavior with finite elements using simple interpolation functions. 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 the singular velocity field, simple compression of a plastic layer between parallel, rough plates is considered. An upper bound solution is found by assuming the singular field in the layer. As expected, it lies between the upper bound obtained by assuming simple compression in the layer and a slip line solution.