Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 79

Although a broad variety of different viscoelastic behaviors is pos-
sible, all such solid materials share these general properties of appearing
plastic (or viscous) and ductile at low strain rates and elastic and brittle
at high strain rates. Thus, the derivation of the term viscoelastic is both
obvious and mnemonic.

Models

The variety of viscoelastic behaviors that are observed in real materials
do not relate in an easy, generic way to types of materials as do the vari-
ous shapes of simple stress-strain curves for elastic-plastic materials
(see Chapter 3). Additionally, these behaviors are not related simply and
directly to the bond types present in the material but are related more
closely to details of molecular structure and arrangement and to larger-
scale aspects of material organization.
To deal with these problems, it has become the practice to analyze
the behavior of viscoelastic materials as if they were composed of arrays
of small, simple mechanical elements connected together with pins and
tie rods. This is an intellectual exercise; the model elements used in this
approach generally have no close correspondence to physical parts of
the actual material. However, when taken together, the stress-strain
behavior of these model elements mirrors that of the actual material.
In addition, when formal mathematical descriptions of stress-strain
behavior are required, it is possible to generate them very quickly from
these model elements, each of which has a very simple mathematical
description.
There are three principal model elements (also called bodies ) used to
construct viscoelastic models.

1. Spring (or Hooke body) (Figure 4.2). The simplest element pos-
sesses fully elastic behavior and is represented by a spring. The
instantaneous application of a stress, by placing a weight on it,

W

σ

L o

L

Schematic
representation

σ σ

ε

On Off

FIGUre 4.2 the spring or hooke body.