Semi‐analytical solution of axisymmetric indentation of poroelastic multi‐layer coating on a substrate

We propose a novel semi‐analytical solution of the indentation problem for a poroelastic multi‐layer system. This study addresses the time‐dependent behavior of materials, such as biological tissues, where mechanical properties vary within the structures. The axisymmetric indentation of a poroelastic multicoating bonded to a poroelastic substrate indented by a rigid, flat‐ended cylindrical indenter are investigated. Poroelastic solutions are expressed through two displacement functions, and the transfer matrix method is employed to formulate the effect of a multi‐layer composite. In addition, we adopt an analytical method that uses the Laplace–Hankel transform and expresses the normal contact stress at the surface layer as an appropriate series in terms of Chebyshev orthogonal polynomials to reduce the dual integral equations to an infinite system of simultaneous equations in the Laplace transform domain. Subsequently, a numerical inverse Laplace transform is applied to obtain numerical results for the time‐dependent consolidation of the rigid cylindrical indenter. Results of consolidation for a single layer bonded to a rigid impervious substrate are consistent with those reported in previous studies. This study examined various combinations of the material properties of a poroelastic multi‐layer system. We focus on the effects of the shear modulus, drained and undrained Poisson's ratios, permeability of the surface layer and substrate, and poroelastic layers on the consolidation of the rigid indenter. It is confirmed from the numerical results that consolidation varies with various parameters. These results can be applied to a simplified evaluation of the mechanical properties for multi‐layer poroelastic materials by indentation tests.