Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 88

material, such as a metal, energy is dissipated once the plastic region is
entered. Elastic deformation occurs at low strains, whereas larger strains
are required to produce plastic deformation. Thus, there is some mini-
mum stress, associated with the onset of plastic deformation, required
before either unrecoverable strain or energy dissipation occurs. However,
in a viscoelastic material, energy is always dissipated if a viscous element
(either a Newton or St. Venant body) is required to model the stress-strain
behavior. Since this is true for all viscoelastic bodies, then all viscoelas-
tic bodies dissipate energy during deformation, irrespective of either the
magnitude of the strain or the degree of recoverability, so long as internal
creep or stress relaxation has taken place. Therefore, hysteresis consti-
tutes a considerable problem in the testing of viscoelastic materials, since
the intrinsic properties of the materials are temperature dependent. In
vivo , this effect contributes to muscle heating during exertion, in addition
to the heat produced as a by-product of cellular metabolic effort.

Complex materials

Models as discussed here lead to fairly simple stress-strain relationships.
However, the relationships in real materials, especially in real structures
made of various materials, are far more complex. This complexity in
behavior requires much more complex and detailed models.
Repetitive tensile tests of a ligament, performed at increasing strain
rates with sufficient intervals in between for “full” recovery, produce
a family of stress-strain curves as shown in the left portion of Figure
4.12. These have several features of interest. There is an initial, unrecov-
erable deformation, called “preconditioning,” which occurs during the
first cycle (see Chapter 5 for a complete discussion of preconditioning).
Each successive cycle shows full recovery, with steeper curves and less
hysteresis, as strain rate increases.

Increasing

ε

σ

56
3 4

12

ε

FIGUre 4.12 a model for ligaments.