Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 95

ANSWER:
Y, N, Y, Y, N. Cases A and B show the results of constrained constant
strain rate experiments on a single material for which t 1 < t min < t 2 . Case
A is a stress relaxation experiment, which yields data equivalent to those
of a creep experiment. For strains applied in times less than t min , the
material will behave elastically; thus, ε = 0.025 leads to σ = 40 MPa,
irrespective of strain rate.
PROBLEM 4.7
For the material represented in Figure 4.16, find E U , E R , and σ y .
ANSWER:
E U may be calculated from the end point of unrelaxed deformation
(cur ves A ): E U = 40/0.025 = 1600 MPa = 1.6 GPa . E R is calculated
from the fully relaxed (horizontal) parts of curves A: E R = 30/0.025 =
1.2 GPa . Curves A and B display viscoelastic behavior; thus, there is no
definable yield stress.
PROBLEM 4.8
How much energy is lost in the hysteresis loop shown in curve B dis-
played in the left graph of Figure 4.16?
ANSWER:
Since strain is linear in time (constant strain rate), the left curves are
equivalent to stress-strain curves (relabeling the time axis as a strain
axis). Therefore, the left curves display hysteresis, and the energy loss
per strain cycle (estimated by ruling squares under the upper and lower
portions of stress vs. time in curve B ) is approximately 45%.
PROBLEM 4.9
A viscoelastic material (select best answer)
A. Behaves like a spring when stressed
B. Is never found in vivo
C. Degrades mechanically with time
D. Exhibits deformation that depends on both the load applied and
the rate of load application
E. None of the above
ANSWER:
The best answer is D , which is a good definition of viscoelasticity.
Viscoelastic materials only behave elastically (as springs) for stress and
strains observed in times less than the minimum relaxation time ( t min ).
Virtually all soft and hard tissues are viscoelastic. Despite their viscous