Biomedical Engineering Reference
In-Depth Information
CHaPTer FOUr
Viscoelasticity
Loads applied to materials produce internal elastic and plastic deforma-
tions. The stress-strain diagram (see Chapter 2) describes the intrin-
sic behavior of materials in a general way, such that we speak of stress
(vertical axis) as a
function
of strain (horizontal axis). In this conven-
tional manner, strain is taken as an independent variable and a test is
performed as follows:
1. A specimen is made to standard dimensions.
2. A suitable apparatus is used to deform the specimen.
3. As the specimen is deformed, the resultant force on a load cell
within the apparatus is recorded simultaneously with values of a
parameter that measures deformation.
4. The deformation (extrinsic independent variable) and the resultant
force (extrinsic dependent variable) are combined with the spec-
imen dimensions to yield the paired values of strain and stress
(intrinsic variables) required to plot the stress-strain curve.
The test described above is a standard, repeatable process that can
be used to at least partially describe the properties of any solid material.
The resulting stress-strain relationship can be referred directly to the
nature of the chemical bonds between atoms, with some interpretations
based on the presence of structural defects (cracks, etc.).
In a shorthand fashion, we can express the relationship between stress
and strain as
σ =
f
(ε)
This is a general form of the relationship that we easily recognize in
the elastic region:
σ =
E
*ε
where the function,
f
, is given by
E
, the modulus (a constant).
Unfortunately, the processes of creep and stress relaxation are
not
explainable by reference to the stress-strain curve as obtained this way.
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