Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 78

However, the need to show strain and stress, respectively, as functions of
time in reporting these behaviors alerts us to the possibility of describing
the stress in a material as a function of both strain and time. (The choice
of stress as the dependent variable is arbitrary here; viscoelasticity is char-
acterized by the involvement of time in any function linking stress and
strain.) Materials in which time is a feature of the relationship between
stress and strain are called viscoelastic . This is a compound word, com-
bining the ideas of viscous flow, such as that of maple syrup straight from
the refrigerator, and elastic deformation, such as that of a rubber band,
suggesting that both properties are present in such materials.
Similarly, in shorthand fashion, we can write

σ = f (ε, t )

or more specifically

σ = E ( t )*ε

This introduces the idea of a modulus (the ratio between stress and
strain) depending on time rather than being a constant, as is assumed in
the discussion of elastic behavior.
If we take an imaginary material with typical viscoelastic properties
and perform a set of load-deformation experiments at increasing rates of
loading (and thus at increasing strain rates), we would produce the fam-
ily of stress-strain curves seen in Figure 4.1.
These curves differ from those for elastic-plastic materials in several
ways, including the following:

1. At low strain rates, for the imaginary material selected, there is no
observable elastic region.

2. At high strain rates, the material appears elastic and brittle, with
no plastic region.

A number of materials behave very much like this imaginary exam-
ple, including fresh saltwater taffy and the silicone “rubber” used as a
hand-exercising material.

Increasing
strain rate

σ

ε

FIGUre 4.1 stress-strain curves for a viscoelastic material.