Evaluation of contact stresses in the surface of an elastic-plastic plate penetrated by a flat-ended rigid cylindrical punch

The finite element method is applied to the calculation of normal contact stresses arising in an elastic-plastic plate indented by a flat-ended rigid cylindrical punch, with and without regard for contact interaction. The conformity of the distribution of normal contact stresses on the plate surface is demonstrated for the both cases; it is shown that maximum stresses arise at the boundary of the punch-plate contact area and that they have close values. The ratio of normal contact stresses at the boundary of the punch-plate contact area to those in its center, with the used boundary conditions, is 1.8 in the calculation both with and without regard for contact interaction. Consequently, a simplified calculation without consideration of contact interaction provides a qualitative and quantitative evaluation of the distribution of normal contact stresses on the plate surface, and it is applicable to the evaluation of contact stresses when a flat-ended rigid cylindrical punch is indented into a plate made of an elastic-plastic material.