Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation

The normalized relaxation modulus represents a salient feature of viscoelastic materials and its determination is of great significance for various applications. From the normalized relaxation modulus, for instance, one can derive the loss factor of a viscoelastic polymer and judge whether a material is suitable for damping applications or not. By using dimensional analysis and the elastic–viscoelastic correspondence principle, the normalized relaxation function of a linear viscoelastic material obtained from indentation relaxation tests is shown to depend only on the indentation load but not on the indenter geometry and the shape of the indented solid. The result could enable circumvention of the difficulties encountered in the calibration of the indenter geometry and the preparation of indented samples. Numerical simulations are performed on a number of cases of practical interest, including the spherical indentation test of a soft layer lying on a rigid substrate, a flat punch indenter indenting into a soft layer with a rough surface bonded to a rigid substrate, a rigid indenter with irregular shape indenting into a particle, inclined contact of a cylindrical indenter with a cylinder, and indentation of porous substrates. The numerical examples demonstrate that the conclusion from the theoretical analysis is valid for all these situations.