Abstract
In this paper, Prandtl's flat punch problem is analyzed using an elasto-plastic finite element program. Detailed studies are made on the development of both plastic zones and velocity fields for punches of different surface roughness. The finite element solution, obtained by assuming the semi-infinite body to be elastic-perfectly-plastic, is compared with the slip-line solutions of both Prandtl and Hill. It is found that, although the friction condition on the punch surface has some effect on the development of plastic zone and velocity field, the finite element results in general agree very well with Prandtl's slip-line solution in all cases studied. On the other hand, no conclusive evidence supporting Hill's solution could be found for either the smooth or the rough punch cases.
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