Biomedical Engineering Reference
In-Depth Information
5.3 Ideal Stress-Strain Characteristics
The forces (or load) transferred across each joint are calculated assuming that each
segment is a rigid body. In reality, each segment is not a rigid body and there is elas-
tic storage and recovery. For example, tensile loading produces an elongation and
a narrowing of a structure (Figure 5.6), whereas compressive forces on a structure
tend to shorten and widen. In this section, we will discuss the stress-strain behavior
in relevance to biomedical applications.
5.3.1 Structural Parameters and Material Parameters
To understand the load-bearing capacities of materials, and compare material char-
acteristics, two terminologies are used: stress and strain. If
F
is the applied force on
a cross-sectional area of
A
, then stress,
σ
, is given by
(5.13)
σ =
FA
The deformation of a material to an applied force can be expressed either as an
absolute change in length (
Δ
L
) or as strain that is defined as the change in length
per unit initial length (
L
/
L
i
). Strain is a dimensionless unit and is expressed as a
percentage, while shear strain is expressed in radians. Strength of a material is de-
fined as the ultimate stress (
Δ
σ
u
) at which failure occurs.
In the body, tissues come in different geometric dimensions as well as differ-
ent densities. For example, cortical (compact) bone has very high density relative
to cancellous (trabecular or spongy) bone. When a force is applied on two tissues
of different cross sections, stresses developed in a tissue of small cross section are
significantly higher than in a tissue with a larger cross section. Hence, when com-
paring two elements, geometric parameters play a significant role. Strength defined
structurally is the ultimate load (or force) at which failure of the system occurs.
Consider the lower leg bone tibia and its corresponding fibula that support the
