62
3 Mechanical Aspects of Biosystems
before rupture. Thus, the compliance value decreases toward zero as the lung is
forced to unusually large volumes. This behavior is similar to stretching a material
beyond its linear region. The relation between the force and the stretch may become
inelastic and possibly hysteretic, a property described below.
An elastic membrane of compliance C and surrounding a volume will store
energy in the amount
pδV giving
E = (C/(2)(p
2
− p
2
0 )
(3.26)
when expanded by an increase of the internal pressure from p 0 to p.
3.8 Limits of Stress
As we know, we can take only a certain amount of stress(!). There are several
possible reactions as stress is increased on a material. Table 3.3 shows the various
material responses to stress.
If the stress on a material is relaxed and that material returns the energy it stored
by distortion back into mechanical work with no heat generated, then the material
is acting elastically and the process is called ‘adiabatic’. 38 On an atomic level, an
‘adiabatic stress’ causes atoms to undergo a relative shift in position, but not to
change their quantum states. Most solid materials will distort adiabatically if the
Table 3.3 Behavior of materials under stress
Behavior
Description
Linear elastic region
Strain is proportional to stress
Non-linear elastic region
Strain non-linearly related to stress
Inelastic region
Mechanical energy is lost during strain of the
material
Material creep
Individual atoms within the material have relative
movement in relief of long-duration stress
Material yield
Whole layers of atoms or molecules displace in
relative position
Microfracturing
Microscopic two-dimensional regions of separation
occur
Macroscopic fracture
One or more large two-dimensional regions separate
but by a relatively small amount
Material failure
Fracture separation across the whole material occurs
Material burst
Some energy that is stored because of stress is
released by material ejection
38 Adiabatic is from the Greek adiábatos for ‘not passable’, in this case referring to insulating walls
stopping heat flow.
3 Mechanical Aspects of Biosystems
before rupture. Thus, the compliance value decreases toward zero as the lung is
forced to unusually large volumes. This behavior is similar to stretching a material
beyond its linear region. The relation between the force and the stretch may become
inelastic and possibly hysteretic, a property described below.
An elastic membrane of compliance C and surrounding a volume will store
energy in the amount
pδV giving
E = (C/(2)(p
2
− p
2
0 )
(3.26)
when expanded by an increase of the internal pressure from p 0 to p.
3.8 Limits of Stress
As we know, we can take only a certain amount of stress(!). There are several
possible reactions as stress is increased on a material. Table 3.3 shows the various
material responses to stress.
If the stress on a material is relaxed and that material returns the energy it stored
by distortion back into mechanical work with no heat generated, then the material
is acting elastically and the process is called ‘adiabatic’. 38 On an atomic level, an
‘adiabatic stress’ causes atoms to undergo a relative shift in position, but not to
change their quantum states. Most solid materials will distort adiabatically if the
Table 3.3 Behavior of materials under stress
Behavior
Description
Linear elastic region
Strain is proportional to stress
Non-linear elastic region
Strain non-linearly related to stress
Inelastic region
Mechanical energy is lost during strain of the
material
Material creep
Individual atoms within the material have relative
movement in relief of long-duration stress
Material yield
Whole layers of atoms or molecules displace in
relative position
Microfracturing
Microscopic two-dimensional regions of separation
occur
Macroscopic fracture
One or more large two-dimensional regions separate
but by a relatively small amount
Material failure
Fracture separation across the whole material occurs
Material burst
Some energy that is stored because of stress is
released by material ejection
38 Adiabatic is from the Greek adiábatos for ‘not passable’, in this case referring to insulating walls
stopping heat flow.