Flat punch indentation in viscoelastic materials: analytical, experimental, and finite element analysis results

Viscoelastic materials exhibit both elastic and viscous behavior simultaneously. The elastic part of the deformation is typically described by springs, while the time-dependent viscous part is described by dashpots. By connecting springs and dashpots in series and parallel, various models, such as Maxwell and Kelvin-Voigt (KV) model, have been developed to describe the stress-strain behavior of viscoelastic materials. Experimentally, creep and relaxation tests can be used to determine the spring constants and viscosity values in the viscoelastic models. In this work, complete load-displacement curve for viscoelastic material was solved analytically for flat punch indentation. The analytical solution was further validated with numerical solution for various scenarios: fast-fast, fast-slow, slow-fast, and slow-slow loading and unloading rates. Furthermore, the analytical and numerical solutions were tested against data obtained from flat punch indentation measurements in polydimethylsiloxane (PDMS). The creep data obtained from flat punch indentation measurements were fit to a linear viscoelastic KV model. The elastic modulus value obtained from the fitting procedure agrees well with the instantaneous modulus obtained from fast unloading. The KV model parameters were then used in a finite element model (FEM) in ANSYS to predict indentation load-displacement curves for two different conditions: fast-fast and slow-slow loading and unloading rate. The analytical and numerical solutions agree well with the experimental data, thus validating the effectiveness of the proposed approach for measuring the viscoelastic properties of polymers.