Biomedical Engineering Reference
In-Depth Information
the bone does not always proceed along the theoretic perpendicular plane of maxi-
mum stress, but rather once a crack is initiated, it may propagate obliquely across
the thickness following the line of the maximum shear stress. The tearing strength
of the aorta is higher in the longitudinal direction than in the transverse direction.
A thorough knowledge of the complex biomechanical function of the body
structures and joints is essential to make accurate clinical diagnoses and decisions
regarding injury treatments. Techniques such as a universal force-moment sensor,
which can mimic different loading conditions, have been developed for a few joints.
However, evaluating the material properties and predicting failure under combined
loading for various components are difficult due to problems associated with the
repeatability of results. Computational techniques such as the finite element analy-
sis (FEA) are used in conjunction with experiments for a better understanding of
the stress and deformation characteristics. For detailed description of the FEA,
refer to [5].
5.4.2 Viscoelastic Characteristics
The behavior of metals such as steel or aluminum and quartz do not deviate much
from the linear elasticity at room temperature within a small strain range. However,
all other materials deviate from Hooke's law (5.14) in various ways, for example,
by exhibiting viscous-like and elastic characteristics. A perfectly elastic material
stores all the energy created by the deformation forces so that on the removal of
the forces, material can return to its original dimensions independent of time. In
contrast to elastic materials, a Newtonian viscous fluid under shear stress obeys
d
d
ε
(5.39)
σμ
=
with
as the viscosity, and this fluid dissipates energy as heat or in the drag of the
fluid that is exuded and absorbed during loading and unloading. There are materi-
als whose response to a deforming load combines both viscous and elastic qualities;
that property is called
viscoelasticity
. The relationship between stress and strain
depends on time. Anelastic solids represent a subset of viscoelastic materials that
possess a unique equilibrium configuration and ultimately recover fully after the
removal of a transient load. Synthetic polymers, wood, and all human tissues (cells,
cartilage, bone, muscle, tendon, and ligament) as well as metals at high temperature
display significant viscoelastic effects. As an example, consider the behavior of a
soft tissue such as cartilage or ligament subjected to a constant compressive strain
(Figure 5.15)
.
When the tissue is subjected to a constant deformation [point B in
Figure 5.15(b)] and is maintained at that state,
its stress varies over time. Initially,
stress increases with the efflux of water, followed by a time-dependent reducing
stress phase where the fluid within the cartilage redistributes. Immediately after
loading occurs, the small permeability of the extracellular network impedes an in-
stantaneous fluid flow through the matrix. With time, the load causes the fluid to
be driven away from the loaded site, through pores in the matrix. This fluid flow
also explains another feature of viscoelasticity (i.e., that the biomechanical behavior
μ
