Singular strain rate and stress fields are examined at the tip of a rigid conical indentor penetrating an incompressible viscous solid. Attention is focused on friction effects induced by wall roughness. The problem is formulated within the usual framework of eigenvalue analysis of locally singular fields. Some special cases are investigated further with emphasis on a boundary layer expansion for the rigid/perfectly plastic solid sliding along the perfectly rough wall. It has been found that the level of singularity increases as the cone becomes sharper and the wall friction decreases. Numerical results, presented for a variety of cases, suggest a boundary layer build up for sharp cones with rough walls.

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