INSTRUMENTATION AND EXPERIMENTATION - Nanoindentation with Biological Applications - page 40

voltages. In most commercial instrumented indenters, transducer devices
are chosen such that there is a linear relationship between the signal
voltage and output value (load or displacement).

2.1.1. Resolution and range required for testing biological materials

As commercial instrumented indenters were originally designed to
enable mechanical characterization of metal and ceramic films that were
typically of submicrometer-scale surface roughness in the as-deposited
state, it is worthwhile to consider whether the resolution and range of
force and displacement required of biological material characterization
may differ from the original instrument requirements. Indeed, some
mineralized biological materials ( e.g ., trabecular bone) contain a
significant volume fraction of mechanically stiff hard mineral, and can
exhibit volume-averaged stiffness and mean contact pressures on the
order of 1-10 GPa. 1-3 In such mineralized biomaterials, the load and
depth resolution and range of standard commercial instrumentation is
typically sufficient to extract repeatable data. However, in such
structurally heterogeneous samples, the volume of the deformed material
volume as compared to the size of the composite constituents ( e.g ., the
diameter and aspect ratio of mineralized phase) requires particular
attention if accurate calculation of phase and macroscale mechanical
properties is desired.
In more compliant biological materials, ranging from muscle and
brain tissue to extracellular matrices to individual cells, the load and
depth resolution and range of commercial instrumentation is tested
severely. First, let us consider the load resolution required to deform a
model extracellular matrix, a polymeric hydrogel exhibiting macroscale
elastic modulus E on the order of 10 kPa. Let us assume that this
hydrogel remains fully hydrated and structurally stable at room
temperature, exhibits minimal adhesion to the probe material, and
deforms within the linear elastic regime under the applied stresses and
strain rates imposed by a spherical probe of radius R = 1 mm. Let us also
simplify the effects of finite thickness to assume that we can neglect
mechanical contributions of the underlying substrate for indentation
depths h as large as 1 μ m, which is approximately the maximum