Axisymmetric frictionless indentation of a transversely isotropic elastic half-space

This chapter is devoted to the main modeling concepts of the indentation method (including indentation modulus, unilateral contact, Galin–Sneddon solution, depth-sensing indentation, BASh formula). For the sake of simplicity we assume that the deformation response of tested biological samples can be modeled as that of a transversely isotropic elastic material, as described in the framework of the classical infinitesimal theory of elasticity. Moreover, the characteristic size of the contact area produced by a rigid indenter is supposed to be small in comparison to the characteristic sizes of the tested sample, so that its contact deformations can be evaluated as those of an elastic half-space, and is therefore abstracted from any size effect. Again, for simplicity’s sake, we neglect any friction at the contact interface and confine our analysis to the axisymmetric geometry, assuming that the area of contact beneath the indenter remains circular during normal (vertical) indentation.