Biomedical Engineering Reference
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needs to be sufficiently refined within this region. Since the indenter
would contact the surface nodes one by one, the spacing between the
nodes dictates the resolution of key indentation measurements such as
stiffness and hardness. Away from the indenter, the mesh can become
more coarse.
Once the mesh is established, the material properties can be varied in
a large range, and the indenter geometry can also be changed if necessary.
Extensive FEM simulations can be carried out such that a relationship
between the shape factors of indentation curves and material properties
can be established. Appropriate functions can be chosen to fit the
numerical results, and such functions can be mechanism-based to make it
simpler. This is referred to as the forward analysis. Next, effective
algorithms can be established to reversely solve the established functions,
such that desired material properties can be deduced from indentation
measurements. During such reverse analysis, there are two key issues,
one is the uniqueness of solution (
i.e
. whether there is one-to-one
correspondence between material properties and indentation behavior),
and the other one is error sensitivity (
i.e
. how sensitive is the determined
material parameters with respect to the error of indentation data). Often
during the numerical minimization process, special care needs to be paid
to distinguish local minimum and global minimum. The working range
of reverse analysis should be kept smaller than that used in the forward
analysis, such that the numerical problems at the boundary can be
avoided.
In the following text, we focus on measurement of constitutive
properties of bulk materials to illustrate computational modeling of
indentation. Brief introduction will be given for indentation on coatings,
multilayers, composites, and other applications.
3. Sharp Indentation Analysis
For sharp indentation tests, the classic theory
2,3,8
relates the measured
indentation hardness
H
and contact stiffness
S
with the constitutive
properties of an elastic-perfectly plastic and stress-free bulk material
(with
n
=
0
):
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