Numerical investigation of indentation tests on a transversely isotropic elastic material by power-law shaped axisymmetric indenters

Nowadays, there exist many well-known classical models of frictionless adhesive contact including the Johnson–Kendall–Roberts (JKR) model, the Derjaguin–Muller–Toporov (DMT) model, and the Maugis solution for the JKR-type-to-DMT-type transition regimes. These models are very helpful for studying molecular adhesion between two contacting linearly elastic isotropic spherical bodies. However, in experimental studies, such as nanoindentation tests, the shapes of the indenters are often more general than the spherical or flat ones. Moreover, very often, the materials to be tested are anisotropic. A special case of anisotropy is transverse isotropy, which contains a plane of isotropy, implying that the material can be rotated with respect to the loading direction about one axis without measurable effect on the material's response. In this paper, numerical studies on JKR-type frictionless adhesive contact between power-law shaped indenters and transversely isotropic materials are presented. It shows that the formulae for numerical simulations of JKR-type frictionless adhesive contact for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials, except that the effective elastic contact modulus has different expression for different materials. The DMT-type and JKR-type-to-DMT-type transition regimes have been explored by conducting the simulations using smaller values of Tabor parameters. The good agreement between numerical simulation results and existing analytical solutions shows that this numerical simulation method can be extended to simulate indentation tests using indenters of arbitrary shapes.