Time-dependent viscoelastic relation between load and penetration for an axisymmetric indenter

The time-dependent deformation and flow are examined for an axisymmetric indenter (flat-ended, spherical or conical indenter) penetrating into a viscoelastic body. The analytical solutions for elastic contact combined with the Boltzmann hereditary integral lead to the constitutive equations for linear viscoelastic indentation. Some numerical analyses for simple models of viscoelastic liquid and solid are conducted to gain further rheological insights into indentation viscoelasticity. Indentation techniques provide the most efficient microprobes and nanoprobes for examining the time-dependent viscoelastic deformation and flow; testing specimens with extremely small dimensions and thin films with no special preparation, as well as compressive loading makes the test easier at elevated temperatures and in hostile environments.