A Simple Contact Mechanics Model for Highly Strained Aqueous Surface Gels

Abstract

Soft, biological, and bio-inspired materials are often compositionally heterogeneous and structurally anisotropic, and they frequently feature graded or layered organizations. This design complexity enables exceptional ranges in properties and performance yet complicates a fundamental understanding of the contact mechanics. Recent studies of soft gel layers have relied on Hertzian or Winkler foundation (“bed-of-springs”) models to characterize the mechanics but have found neither satisfactory. The contact mechanics of soft gel layers are not yet fully understood. The aim of this work is to develop a simple contact mechanics model tailored for compositionally-graded materials with soft surface layers under high strains and deformations. Concepts from polymer physics, fluid draining, and Winkler foundation mechanics are combined to develop a simple contact mechanics model which relates the applied normal force to the probe radius of curvature, elastic modulus, and thickness of soft surface layers subjected to high strains. This simple model was evaluated with two examples of graded surface gel layers spanning multiple length-scales, including commercially available contact lenses and stratified hydrogels. The model captures the nonlinear contact mechanics of highly strained soft aqueous gel layers more closely than either Hertz or Winkler foundation theory while simultaneously enabling a prediction for the thickness of the surface gel layer. These results indicate that this simple model can adequately characterize the contact mechanics of highly strained soft aqueous gel layers.