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An indentation experiment involves five variables: indenter shape, materialbehavior of the substrate, contact size, applied load and indentation depth.Only three variable are known afterwards, namely, indenter shape, plus load anddepth as function of time. As the contact size is not measured and thedetermination of the material properties is the very aim of the test; twoequations are needed to obtain a mathematically solvable system.  For elastic materials, the contact size can always be eliminated once and forall in favor of the depth; a single relation between load, depth and materialproperties remains with the latter variable as unknown.  For viscoelastic materials where hereditary integrals model the constitutivebehavior, the relation between depth and contact size usually depends also onthe (time-dependent) properties of the material. Solving the inverse problem,i.e., determining the material properties from the experimental data, thereforeneeds both equations. Extending Sneddon's analysis of the indentation problemfor elastic materials to include viscoelastic materials, the two equationsmentioned above are derived. To find the time dependence of the materialproperties the feasibility of Golden and Graham's method of decomposinghereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems inlinear viscoelasticity, Springer, 1988) is investigated and applied to a singleload-unload process and to sinusoidally driven stationary state indentationprocesses.

Load-depth sensing of isotropic, linear viscoelastic materials using rigid axisymmetric indenters