Force relaxation of contact between a flat-ended cylindrical indenter and a poroviscoelastic layer

Abstract

Interpreting the contact force relaxation between an indenter and a poroviscoelastic material at a fixed displacement to obtain the materials properties is a challenging task, because both fluid drainage and solid viscoelasticity contribute to the relaxation. In this research, the indentation of a poroviscoelastic layer caused by a flat-ended cylindrical indenter is formulated analytically by the displacement functions in the Laplace-transformed domain. The contact force of the indenter at a fixed displacement was expressed by a closed-form in the transformed domain and numerically inverse-transformed to the time domain. The force relaxation is analyzed for combinations of three drainage conditions prescribed on the layer top and two boundary conditions prescribed on the layer bottom. The closed-form solution can approach that of the flat-indentation on a poroviscoelastic half-space, when the layer is very thick compared to the indenter radius. In addition, finite element simulations of the flat-indentation on poroviscoelastic layers were carried out as a comparison for the semi-analytical results. The relaxation ratios at the limits of the drained-nonviscoelastic state, the nondrained-viscoelastic state and the drained-viscoelastic state are shown for different ratios of the layer thickness to the indenter radius, and verified with the corresponding elastic solutions. The effects of the viscoelastic characteristic time on the force relaxations are also presented for different viscoelastic properties and boundary conditions.