Title: Mechanical
properties of
biological tissues
Mechanical properties
of biological tissues
Kyagova Alla
D.M.Sc., Professor of Biophysics
Department of Physics and Mathematics
Pirogov Russian National Research Medical University
Why study?
Injury occurs when an imposed load exceeds the
tolerance (load-carrying ability) of a tissue
– Training effects
– Drug effects
– Equipment Design effects
1
Strength of Biological Materials
The strength of biological materials is defined
by the ability of the material to withstand stress
without failure
The strength of a
material is affected by:
– Microstructure, Age, Fluid
content
– Type, direction and
velocity of loading
Terminology
Load – the sum of all the external forces and
moments acting on the body or system
Deformation – local changes in shape (size
and geometry) within a body
2
Types of Loads
The way in which the body deforms depends upon
the type of the load (external force applied to it)
Uniaxial Loads:
(Forces applied along a single line,
typically along a primary axis)
Axial
–
–
Multiaxial Loads:
Bending
Torsion
Compression
Tension
Shear
F
o
r
Types of Loads
(application of direct forces)
c
e
a
p
p
li
c
a
t
i
o
n
3
Normal (Axial) Stress (s )
A force F on a solid acts on an
F
area A
For compression or
tension, the normal stress
A
s
is the ratio of the force to the
cross sectional area (the force
per unit area upon which it acts)
– Measures pressure and
quantifies the internal forces
acting on the object as a
reaction to the external
applied forces
– SI unit is Pascal (Pa)
– Pa = N / m2 = kg / m s2
s
Strain (e )
For compression or tension
L0
F
A
L= L - L0
Deformation is relative to the
size of an object
The displacement (change
in length) compared to the
length is the strain e
e
L
L0
– Measures a fractional change
(% change in deformation of the
object)
– Unit less quantity
4
How are Stress (s) and Strain
(e) related?
Stress is what is done to an object; strain is how
the object responds
Stress and Strain are proportional to each other
(up to a certain point)
Modulus of elasticity = stress/strain:
is constant for a specific substance (up to a certain point)
Elasticity (Young’s) Modulus
stiff material
Stress
s
Higher E  higher “stiffness”
elastic material
Strain
e
A graph of stress versus
strain is linear for small
stresses
The slope of stress versus
strain is a modulus that
depends on the type of
material
For normal stress this is
Young’s modulus E
s F/A
FL
E 

e L / L A  L
same units as s, N/m2 or Pa
– Connects to Hooke’s law:
F (
EA
)  L  k  L
L
stiffness coefficient
5
Stress-Strain Behavior (for Tension)
Elastic Plastic
Elastic and Plastic
deformation
Elastic deformation
Reversible:
( For small strains only)
Stress
Stress removed  material
returns to original size
Plastic deformation
Irreversible:
Strain
Stress removed  material
does not
return to original
dimensions
ULTIMATE TENSILE STRESS:
•If a material is stretched until it breaks, the tensile stress has reached the
absolute limit and this stress level is called the ultimate tensile stress
STRESS STRAIN DIAGRAM
Stress-Strain Diagram
6
STRESS STRAIN DIAGRAM
Elastic behavior
Proportional limit,
Elastic limit
The curve is straight line trough
out most of the region
Stress and strain are directly
proportional to each other
Material to be linearly elastic
Proportional limit (●A)
•The upper stress limit to linear line
is called proportional limit
•The material still respond
elastically
•The curve tends to bend and
flatten out
Elastic limit (●B)
• Upon reaching this point, if load is removed, the specimen
still return to original shape
STRESS STRAIN DIAGRAM
Y
i
e
l
d
s
t
r
e
s
s
Yielding
A slight increase in stress above
the elastic limit will result in
breakdown of the material and
cause it to deform permanently
This behavior is called yielding
The stress that causes yielding
is called the yield stress or
yield point
Plastic deformation
Once yield point is reached, the
specimen will elongate (strain)
without any increase in load
Material in this state is perfectly
plastic
7
Strain hardening
STRESS STRAIN DIAGRAM
STRAIN HARDENING
– When yielding has ended,
further load applied, resulting
in a curve that rises
continuously
– Becomes flat when reached
ULTIMATE STRESS
– The rise in the curve =
STRAIN HARDENING
– While specimen is elongating,
its cross sectional will
decrease
– The decrease is fairly uniform
N
e
c
k
i
n
g
STRESS STRAIN DIAGRAM
NECKING
– At the ultimate stress, the cross
sectional area begins its
localized region of specimen
– it is caused by slip planes
formed within material
– Actual strain produced by shear
strain
– As a result, “neck” tend to form
– Smaller area can only carry
lesser load, hence curve
downward
– Specimen break at FRACTURE
STRESS
8
Shear
Shear
Shear stress:   F / Ao
F is applied parallel to upper and
lower faces each having area A0.
Shear strain:   tan ( 100 %)
 is strain angle
Torsion
Torsion: like shear
Load: applied torque, T
Strain: angle of twist, 
Shear
Torsion
9
Measuring Young’s Modulus
F  mg
b – width of the bar
a – thickness of the bar
L – length of the bar
• Determine Elastic modulus according to:
E
F
L3
 4bd3

rect.
cross
section
F
L3
 12R 4
circ.
cross
section
Thank
you for
attentio
n!
Thank you for
attention!
10