Analysis of frictionless contact between a spherical indenter and a poroviscoelastic medium with a constant contact radius

The research aims to understand the force relaxation that occurs when a spherical indenter is pressed into poroviscoelastic materials, which exhibit viscoelastic properties of solid network and drainage behavior of infiltrated fluid. To achieve this, an analytical approach is proposed to model spherical indentation on a poroviscoelastic medium under the condition of a constant contact radius. This analysis is conducted in the Laplace-transformed domain, and provides closed-form expressions in the transformed domain for both the normal approach and the contact force of the indenter while maintaining a fixed contact radius. These expressions are then numerically inverse-transformed to the time domain for practical analysis. To account for different scenarios, we consider various combinations of drainage conditions at the top and smoothness conditions at the bottom of the medium. We examine three categories of viscoelastic solid behavior, as understanding how they respond under indentation is crucial for characterizing their mechanical behavior. Additionally, we conduct finite element simulations of spherical indentation on poroviscoelastic media, serving as a comparison to the semi-analytic results obtained. Notably, the thickness of the medium relative to the contact radius and the Poisson's ratio play significant roles in the evolution of both the normal approach and contact force of the spherical indenter over time.