Nanoindentation in finite thickness viscoelastic materials

In this work, we present an analytical model to describe atomic force microscopy force curves of standard linear solid and power-law viscoelastic materials by taking indenter geometry and finite thickness effects into account. We show that conical/pyramidal cantilevers are less susceptible to finite thickness effects than other shapes, such as spherical and flat punch indenters. This is confirmed by finite element modeling of the stress field distribution within the sample. We also perform a systematic error analysis for the cases where finite thickness samples are analyzed with an infinite thickness force model. In particular, we show that for spherical indenters and indentation depth up to 20% of sample thickness, the mechanical response of viscoelastic materials will wrongly mimic a purely elastic behavior even within timescales where viscoelastic relaxation should appear.