MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 121

be used to obtain numerical values for the elastic modulus ( E ) and
hardness ( H ) of just about any sample placed into the indenter, an elastic-
plastic analysis may be inappropriate for the material (given its
constitutive behavior, which may or may not be elastic-plastic) and the
numbers thus obtained are “garbage in, garbage out.” As most biological
materials are not well-described by an elastic-plastic response—with
perhaps the exceptions of dried plant materials and biomineral
composites with large mineral fractions—other analyses are often more
appropriate than an elastic-plastic analysis. 2
This chapter will provide a background in contact mechanics—
including elastic, plastic and time-dependent deformation—with an
emphasis on experimental applications of contact mechanics. As such,
there will be no effort to derive key equations, and the reader is referred
to other works on contact mechanics 3,4 for derivations and methods of
deriving the equations presented. The chapter starts with the practical,
experimental considerations of tip geometry and loading function
selection, and how these selections influence indentation data analysis.
Next, elastic contact mechanics is considered, including solutions
for indenting elastic half-spaces with probes of different geometries
as well as for more complicated, inhomogeneous geometries. Next,
more complicated constitutive responses are considered, including
elastic-plastic, linear and nonlinear viscoelastic, and poroelastic
contact mechanics. The chapter concludes with considerations of time-
dependent contact deformation, including viscoelastic and poroelastic
approaches that have been used for the study of hydrated biological
tissues. 5,6
2. PracticalConsiderations
In this section, two practical considerations are explored: probe tip
geometry and time-history of the loading function during contact.
Indentation data analysis is based in part on the geometry of the contact,
and as such the choice of indenter tip geometry is a crucial consideration
in designing any indentation experiment. For an elastic solid, the time-
history of the loading function is irrelevant and the choice can be made