NANOINDENTATION OF SOFT TISSUES AND OTHER BIOLOGICAL MATERIALS - Nanoindentation with Biological Applications - page 309

there is significant tip-sample adhesion. 83,84 This is because one of the
assumptions of the compliance method is negligible adhesion. 6 In the
presence of significant adhesion, an appropriate adhesion model must be
used to determine the modulus. While numerous models exist, contact
mechanics methods based on the Johnson-Kendall-Roberts (JKR) 86
adhesion model (which applies for compliant samples, large surface
energies) have been most frequently applied to the characterization of
compliant polymers using spherical tips. 72,83,84,87,88
Applications of the JKR model vary from applying JKR equations
to the analysis of quasi-static load-displacement curves 83,84,87 to using a
full force curve method. 72 In the force curve method, the indent process
is started out of contact so that a full force curve is captured as the
tip approaches, indents, and retracts from the sample. 72,88,89 A typical
force curve against a polydimethylsiloxane (PDMS) sample is shown in
Fig. 9-6 along with a quasi-static indent in the same material, illustrating
the error in displacement measurement (and hence contact area
calculation) that occurs when adhesion is not taken into consideration.
Analyzing compliant polymer indentation data using force curves and
JKR models has been shown to provide a more accurate measurement of
sample modulus than using the compliance method. 72,83,84 More complex
nanoindentation adhesion models have also been developed that combine
JKR and viscoelastic analyses using a force curve approach. 72,88-90 While
adhesion methods have not yet been applied to many nanoindentation
studies of biological materials, force curve methods are widely used in
the AFM community for characterization of cells and other biological
materials. 91,92 For soft tissue studies, where fluid-mediated adhesion
is likely playing a role in complicating data analysis, continued
development and application of adhesion models will probably be
essential for measuring accurate quantitative mechanical properties.
4.3.3 . Anisotropy
In addition to elastic behavior and negligible adhesion, the contact
mechanics theory upon which the compliance method is based also
assumes isotropic, homogeneous sample materials. Indentation is a
complex loading condition, with compressive load near the center of the