Biomedical Engineering Reference
In-Depth Information
6.2.1.1 Statics, Dynamics and Deformation
The Newton's first law of motion is used in a branch of mechanics known as
statics
.
In mechanics, statics refers to the analysis of rigid bodies (solids) that are in a state of
equilibrium, i.e. in a state where a rigid body's acceleration is zero which also means
that both net forces (for translational movement) and net moments (for rotational
movement) are also zero. Studying systems in states of equilibrium are useful to
understand what forces are in play or should be taken into consideration. According
to Nordin and Frankel [
7
], statics is generally used in biomechanics to investigate
the unknowns in problems that involve the magnitudes of joint reaction forces and
muscle tensions.
Dynamics
, also commonly referred to as
physics
, takes the simulation one step
further in that it studies how forces and torques causes the state of motion of an object
to change, i.e. how a physical system changes over time with respect to applied loads.
When forces are exerted on an object, three things can happen, either the object
exhibits a change in linear and/or rotational motion, or in the case of equilibrium, the
object experiences a localized shape change over time, a
deformation
. Forces that
can be ascribed when an object gets deformed are:
1.
Normal
or
axial
:
•
Tensile
forces (when an object elongates)
•
Compressive
forces (when an object shrinks)
2.
Tangential
:
•
Shear
forces (which in some cases result in bending or twisting of an object)
Because deformation of an object depends also on its material properties, having
a quantity that defines the average force per unit area is helpful in approximating
solutions for the analysis of intrinsic properties of the object under load. This concept
known as
stress
is the amount of applied force divided by the area it is applied on.
Similarly, two forms of stress are used, namely the
normal
stress
.
Normal or axial stress can be calculated when the exerted force lies orthogonal to the
cross-affected area under consideration. In cases where the exerted force lies tangent
or parallel to the affected area, shear stress can be calculated. Under the assumption
that the forces are uniformly distributed along the area and therefore consist of a
simple stress pattern, the stress equation can be formally written as:
˃
and
shear
stress
˄
F
A
˄ , ˃
=
where
F
is the force and
A
the cross-sectional area.
Besides stress, there is also the concept of
strain
, denoted
, that quantifies the
normalized amount of deformation after an initial configuration, i.e. the amount of
displacement of the intrinsic properties of an object from its original length to its
current length. Similarly to stress it has also two basic forms, which are
normal
and
