Surface effects on cylindrical indentation of a soft layer on a rigid substrate

In this paper, theoretical and numerical methods are combined to investigate the two-dimensional, cylindrical indentation of an elastic soft layer bonded on a rigid substrate. By incorporating the Gurtin–Murdoch’s theory of surface elasticity into the Kerr model, we account for surface effects on the indentation behavior of a soft layer. The governing differential relation between the surface pressure and displacement of the film–substrate system is derived. For an incompressible thin layer, the explicit solutions are derived, which are simple and easy-to-use. Finite element simulations are performed using an explicit restart algorithm to study the indentation properties of the layer–substrate system and to examine the validity and accuracy of the theoretical solutions. This work holds promise for applications in mechanical characterization of soft materials, such as biological tissues and cells.