MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 146

1 − 2 ν 3 p

B

σ kk

2 G ζ = α + (5-51)

1 + ν

The four parameters ( G , and B ) make a complete set of material

properties for a poroelastic solid; other sets of four parameters are
possible and it is particularly useful to use a parameter set that includes

,

) is the
parameter characterizing flow through the porous elastic skeleton in
Darcy's law relating the flux ( q i ) to the pressure gradient ( p , i ):
q i = −κ p , i (5-52)
The equations of poroelasticity are coupled: a change in applied stress
leads to a change in fluid pressure or mass, and a change in fluid pressure
or mass leads to a change in the volume of the solid. Because of this
coupling, the poroelastic problem can be solved analytically in only a
few cases, such as homogeneous uniaxial creep. Numerical solutions 42 as
well as computational approaches 43 have been particularly useful in
combining the poroelastic equations with the indentation problem.
Spherical indentation has been considered for characterizing hydrated
bone 6 and acrylamide gels, 44 in both cases resulting in estimated
hydraulic permeability values consistent with values measured using
traditional ( i.e . non-indentation) methods. The application of poroelastic
material models to the routine analysis of indentation data is an area of
active current research.

u , the undrained Poisson's ratio. Finally, the permeability (

7. Conclusions and Outlook

This chapter has focused on the analysis of indentation data, with an
emphasis on material behavior that deviates from the elastic-plastic
responses typical of engineering ceramics and metals. In cases such as
linear viscoelasticity, analysis of nanoindentation data has become
routine, while new approaches are just emerging for poroelasticity. In
general, when handling nanoindentation data for biological materials, it
is critical to identify the modes of deformation active during the
indentation test, and to analyze the data appropriately for those
deformation modes.