Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 82

This approach is to define a standard test sequence involving both stress
and strain and then to replace the stress-strain diagram with two dia-
grams showing the variation of stress and strain, respectively, with time.
The standard test is defined as follows.

1. At the beginning of the test, t = t 0 , an external stress is applied
instantaneously and then maintained.

2. At a later time, t = t 1 , the external stress is removed but the strain
at that time is “fixed” and not permitted to change.

One simple way to think about the standard test for viscoelasticity
is that it consists of a creep test followed immediately (without recov-
ery) by a stress relaxation test. The two subtests, when combined in this
way, are sufficient to characterize fully the time-dependent stress-strain
behavior of a viscoelastic material.
Figure 4.5 shows the result of the standard test applied to a spring or
Hooke body. At t = t 0 , the strain instantaneously rises to a value ε 0 , deter-
mined by the stress and the nature of the material. This strain remains
constant until it is “fixed” at t 1 . At that point, the internal stress must be
equal and opposite to the external load (owing to equilibrium consid-
erations). (In this discussion, stresses are set “equal” to loads; stresses
describe internal conditions, loads [forces] describe external conditions.
It is assumed that equilibrium is produced in the normal manner: the
sum of internal stresses times their respective areas must be equal and
opposite to the sum of external forces.) However, when the external load
is removed and replaced by a constraint on strain, the internal stress
remains constant at the same value. For completeness, the modulus E ( t ),
the ratio of stress to strain as a function of time, is also shown. This is
constant and it is equal to σ 0 /ε 0 .

σ 0

t = t 0

σ

σ

L 0

t = t 1

ε 0

σ

ε

L

ε 0 = ( L - L 0 )/ L 0 ε 1 = ε 0

E 0 = σ 0 /ε 0 E 1 = E 0

E ( t )

Time

t 0 t l

FIGUre 4.5 the standard test for the spring or hooke body.