Indentation of a Viscoelastic Half-Space

Abstract

In this chapter, we consider frictionless indentation problems for a viscoelastic half-space. We note that, throughout the chapter, the indenter displacement is denoted by w(t). Previous notation has been altered to avoid confusion with Dirac’s delta function $\delta (t)$, as well as with the loss angle $\delta (\omega )$. As is well known, a viscoelastic material is characterized by a number of time-dependent moduli, and a certain combination of them, called the indentation relaxation modulus and denoted by $M_3(t)$, will determine the material’s response to indentation. Depending on the type of loading protocol, different information can be gathered from the indentation test about the indentation relaxation modulus and its inverse counterpart $C_3(t)$, called the indentation creep compliance.

Problems may be solved in the study which have baffled all those who have sought a solution by the aid of their senses. To carry the art, however, to its highest pitch, it is necessary that the reasoner should be able to use all the facts which have come to his knowledge, and this in itself implies, as you will readily see, a possession of all knowledge, which, even in these days of free education and encyclopædias, is a somewhat rare accomplishment.

Arthur Conan Doyle