Page 340 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIOPOLYMERS 317

Polymers can exhibit both viscous and solid mechanical behavior; this phenomenon is called vis-
coelasticity. For a given polymer, the degree of viscous behavior depends on temperature. Below T ,
g
polymers will behave more or less as elastic solids with very little viscous behavior. Above T , polymers
g
exhibit viscoelastic behavior until they reach their melting temperature, where they behave as liquids.
When designing with polymers it is important to keep in mind that many polymers deform over
time when they are under a continuous load. This deformation with time of loading is called creep.
Ideal elastic solids do not creep since strain (deformation) is proportional to stress and there is no
time dependence. Viscous materials (liquids) deform at a constant rate with a constant applied stress.
Equation (13.6) describes the strain in a viscous material under constant load or stress σ.
d ε
σ = η (13.4)
dt
ε σ t
∫ 0 dε = η ∫ 0 dt (13.5)
σ
ε = t (13.6)
η

Figure 13.10 shows the strain with time of constant stress for a viscous and elastic material. The
stress is applied at t and removed at t . The elastic model shows an instantaneous deformation when
i f

Stress

Strain = σ

E

A

Strain = σ t
η

B
t i t f
Time
FIGURE 13.10 Response of elastic model (a) and viscous model
(b) to a constant stress applied from t to t . [Reproduced from Ency-
f
i
clopedia of Materials Science and Engineering, M. B. Bever (ed.).
Cambridge, MA: MIT Press, 1986, p. 2919.]