MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 135

approach involves the sampling of a large number of individual
indentation responses across the material surface and using the obtained
range of responses to bound the inferred microstructure in terms of phase
length-scale 18 and mechanical properties. 19 Substantially more effort is
required to develop a robust method for the mechanical characterization
of composite materials by indentation without the need for finite element
analysis. 20
Figure 5-8. Schematic illustration of indentation of a composite material, in which the
observed response depends on the placement of the indenter relative to microstructural
features and the relative indentation and microstructural length-scales ( a vs r ).
5.3. Layered systems
The analyses presented thus far have been oriented towards bulk
materials. However, in the majority of soft tissue indentation tests, the
soft tissue layer of interest ( e.g . cartilage) is supported by a much stiffer
substrate (frequently bone). Just as in the case of composite materials,
the indentation of a layered structure introduces a length-scale into the
indentation problem, where the indentation contact depth or contact
radius ( h c or a , respectively) are considered relative to the layer thickness
( t f ) as shown in Fig. 5-9 . The most commonly employed analysis for soft
tissue indentation testing relies on the finite thickness of the tissue layer,
considering the underlying bone as a rigid substrate. 21 The elastic
expression employed for analysis is thus a modification of the bulk flat-
punch elastic solution ( Eq. 5-7 ) and is written: