COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 169

shape factors of the numerical P − curve of these candidate materials
can be compared with that of the measured P − curve: only the true
solution can have the minimum error. This iteration process involves no
additional FEM simulation, and it is based on the fact that a deep
spherical indentation may lead to unique solution of reverse analysis.
As an illustrative example, in Fig. 6-8 we show that using spherical
indentation, the pair mystical materials given in Fig. 6-7a can be
effectively distinguished using deep spherical indentation (right). The
reverse analysis result (symbols in the figure on left) agree very well
with the input material properties (true solution) and properties of this
pair of mystical materials can be measured separately.

6. Indentation on Thin Films and Composites

In the indentation analyses discussed above, the specimen is assumed to
be a bulk with infinite thickness. This is perhaps the simplest model for a
solid and the proposed computational modeling of indentation can be
readily applied to homogeneous, isotropic, time-independent biological
materials. However, when the specimen thickness is finite (as in many
cases for small material structures) and bonded to a substrate or a testing
platform, the so-called substrate effect strongly affects the indentation
measurement and it usually should be avoided. Note that such effect is
very common in biological materials, such as indentation on cell
membrane where the effect of cytoskeleton also comes into play
significantly. Various techniques have been proposed to subtract off
the substrate effect from indentation analysis in order to measure the
intrinsic film properties. 1,11,84 In addition, film-coating is just one of the
simplest form of a composite material, and composite materials are very
common in biological materials. The orientation of the reinforce phase
(inclusion) can be random or ordered, and the inclusion can be fiber-like
or particle-like. Moreover, other microstructural features, such as
porosity, often come into play. All these underlying material structures
need to be effectively accounted for during the indentation analysis, and
the computational modeling must be adapted to the new changes.
We first use the simplest film indentation as an example. Many
researchers 1,3,11 propose that the indentation depth must be sufficiently