Influence of surface energy on the nanoindentation response of elastically-layered viscoelastic materials

In the context of integrated nonlinear viscoelastic contact mechanics, a nonlinear finite element model is developed to predict and analyze the quasistatic response of nanoindentation problems of an elastically-layered viscoelastic materials considering the surface elasticity effects. Effects of surface energy are accounted for by employing the Gurtin–Murdoch continuum model for surface elasticity. The linear viscoelastic response is modeled by the Schapery’s creep model with a Prony’s series to express the transient component in the creep compliance. The viscoelastic constitutive equations are cast into a recursive form that needs only the previous time increment rather than the entire strain history. To satisfy the contact constraints exactly, the Lagrange multiplier method is adopted to enforce the contact conditions into the system. The equilibrium indentation configuration is obtained through the Newton–Raphson iterative procedure. The developed model is verified then applied to investigate the quasistatic nanoindentation response of two different indentation problems with different geometry and loading conditions. Results show the significant effects of surface energy and viscoelasticity on the quasistatic nanoindentation response.