Axisymmetric Frictionless Indentation of a Transversely Isotropic Elastic Half-Space

  • Ivan ArgatovEmail author
  • Gennady Mishuris
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 91)


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.


Transversely Isotropic Indentation Elastic Modulus Indenter Shape Function Indentation Stiffness Axisymmetric Frictionless Contact Problem 
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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MechanicsTechnical University of BerlinBerlinGermany
  2. 2.Department of Mathematics, IMPACSAberystwyth UniversityAberystwythUK

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