Breakdown of continuum models for spherical probe adhesion tests on micropatterned surfaces

The adhesion of fibrillar dry adhesives, mimicking nature's principles of contact splitting, is commonly characterized by using axisymmetric probes having either a flat punch or spherical geometry. When using spherical probes, the adhesive pull-off force measured depends strongly on the compressive preload applied when making contact and on the geometry of the probe. Together, these effects complicate comparisons of the adhesive performance of micropatterned surfaces measured in different experiments. In this work we explore these issues, extending previous theoretical treatments of this problem by considering a fully compliant backing layer with an array of discrete elastic fibrils on its surface. We compare the results of the semi-analytical model presented to existing continuum theories, particularly with respect to determining a measurement system- and procedure-independent metric for the local adhesive strength of the fibrils from the global pull-off force. It is found that the discrete nature of the interface plays a dominant role across a broad range of relevant system parameters. Accordingly, a convenient tool for simulation of a discrete array is provided. An experimental procedure is recommended for use in conjunction with this tool in order to extract a value for the local adhesive strength of the fibrils, which is independent of the other system properties (probe radius, backing layer thickness, and preload) and thus is suitable for comparison across experimental studies.