Elastic, flat and rounded finite contacts: When should we use half-plane theory?

Abstract

For a flat contact with radiused edges, it is shown that when the flat portion of the contact is small compared to the radius portion of the contact, half-plane theory may confidently be used, and the amount of coupling present is extremely small. When the flat region is large a good quality solution may be used by a different route, using the solution for a square-ended punch together with a corrective solution formed from a three-quarter plane problem but with a radius at the corner. The degree of coupling is captured well. Intermediate geometries are discussed in the text. A further, important, refinement is the fitting of a third solution, developed using half-plane theory for a slightly rounded, flat semi-infinite contact, as this provides an analytical description of the near-edge tractions, and is rigorously fitted into the edge of the three-quarter plane solution.