Force relaxation of a flat indenter on a poroviscoelastic half-space

Abstract

The indentation method is widely used for characterizing the mechanical properties of materials because of its simplicity. However, the interpretation of the force relaxation of a flat indenter at a fixed displacement to obtain the properties of polymeric gels is challenging, especially when the viscoelasticity of the solid network and the drainage of the infiltrated fluid both contribute to the relaxation. This paper formulates flat indentation on a poroviscoelastic half-space analytically using displacement functions in a Laplace-transformed domain. The dual integral equations formed by the mixed boundary conditions are solved and the force of the indenter at a fixed displacement is expressed in closed form in the transformed domain and later numerically inverse-transformed to the time domain. The force relaxation is analyzed for three drainage conditions prescribed on the surface of the half-space, namely a completely pervious condition, a completely impervious condition, and a mixed condition that combines an impervious surface underneath the indenter and a pervious surface elsewhere. The closed-form solution can be reduced to that of a flat indentation on a poroelastic half-space. Moreover, finite element simulations of a flat indentation on a poroviscoelastic half-space are carried out and their results are compared with the semi-analytic results. Three categories of viscoelastic solid behavior are considered and the results for a wide variety of polymeric gels are provided.