Abstract
Using the Boundary Element Method, we numerically study the indentation of prismatic and tapered indenters with polygonal cross-sections. The contact stiffness of punches with flat bases in the form of a triangle and a square as well as a number of higher-order polygons is determined. In particular, the classical results of King (1987) for indenters with triangle and square base shapes are revised and more precise numerical results are provided. For tapered indenters, the equivalent transformed profile used in the Method of Dimensionality Reduction (MDR) is determined. It is shown that the MDR-transformed profile of polygon-based indenters with power function side is given by the power function with the same power; it differs from the 3D profile only by a constant coefficient. These coefficients are listed in the paper for various types of indenters, in particular for pyramidal and paraboloid ones. The determined MDR-transformed profiles can be used for study of other contact problems such as tangential contact, normal contact with elastomers, and, in an approximate way, to adhesive contacts.
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