A squircle-shaped punch design for efficient contact performance of elastic materials

Abstract

A new curvature, called the squircle, is proposed as a punch profile to provide superior contact performance for bulk elastic materials. Plane contact problems of a rigid squircle-shaped punch pressed onto an elastic half-plane are treated via an integral equation (IE) approach which is evidently substantiated by a finite element (FE) approach. Compared to the piecewise-defined curvatures, the continuous surface gradient of the squircle profile enables the IE formulations more tractable. In the presence of sliding friction, the consistency condition in the IE approach is implemented through a new iteration procedure. Subsurface stresses are demonstrated via the FE approach. The squircle punch profile is shown to induce a low-magnitude and smoother pressure distribution on an elastic surface, promising to cause less wear under the action of tangential oscillations.