340
10 Mechanical Properties of Biological Materials
called Young's modulus, after another English scientist, Thomas Young (17731829). The modulus of elasticity, E, has relatively large values for structural
metals, for example, 200 GPa for steel, 70 GPa for aluminium, and from 0.7 to
14 GPa for plastics (Gere and Timoshenko, 1991). However, it is much smaller
for biological materials.
When the loading on the material is much higher, the material follows line
EB on the stress-strain diagram (see Fig. 1O.1c). When unloading occurs, the
material follows line BC and even with the load entirely removed, some residual
strain, OC, remains in the material. In Fig. 1O.1b we have an elastic region
followed by a region in which loading causes large deformation in the material.
This property of the material is known as plasticity. Within the elastic range,
the material can be loaded, unloaded and loaded again, without significantly
changing it's behaviour. However, when loading reaches the plastic range, the
structure of the material changes.
When the bar in Fig. 1O.1a is compressed or stretched, its cross-sectional
area tends to increase or decrease, respectively. Assuming that the material is
homogeneous, we can create a ratio, /J, of the strain in the lateral direction to
the strain in the axial direction:
Ey
/J = -,
Ex
(10.3)
where Ex is the axial strain of the bar, and Ey is the strain in the direction
normal to the axis. The ratio, /J, is known as Poisson's ratio, named after the
French mathematician Simeon Poisson (1781-1840).
Because the dimensions of the bar change when subjected to compression or
tension, the volume of the bar also changes. This volume change is usually
expressed in the form of the non-dimensional quantity e, known as dilatation,
z.e.:
llV
(J
e = - = E(l - 2/J) = -(1 - 2/J).
Vo
E
(10.4)
From Eq. (10.4) it follows that the maximum possible value of /J for ordinary
materials is 1/2; any larger value of /J yields the volume decreasing when the
material is stretched, which is an unlikely event. Most materials are characterized by Poisson's ratio, /J, of about 1/4 or 1/3. In the perfectly plastic region,
no volume change (dilatation) occurs, when Poisson's ratio is taken as /J = 1/2.
10.2.2 Shear-Stress and Strain
The shearing stresses, T, acting parallel to the surface of the material are defined
as force per unit area:
F
T = A'
(10.5)
10 Mechanical Properties of Biological Materials
called Young's modulus, after another English scientist, Thomas Young (17731829). The modulus of elasticity, E, has relatively large values for structural
metals, for example, 200 GPa for steel, 70 GPa for aluminium, and from 0.7 to
14 GPa for plastics (Gere and Timoshenko, 1991). However, it is much smaller
for biological materials.
When the loading on the material is much higher, the material follows line
EB on the stress-strain diagram (see Fig. 1O.1c). When unloading occurs, the
material follows line BC and even with the load entirely removed, some residual
strain, OC, remains in the material. In Fig. 1O.1b we have an elastic region
followed by a region in which loading causes large deformation in the material.
This property of the material is known as plasticity. Within the elastic range,
the material can be loaded, unloaded and loaded again, without significantly
changing it's behaviour. However, when loading reaches the plastic range, the
structure of the material changes.
When the bar in Fig. 1O.1a is compressed or stretched, its cross-sectional
area tends to increase or decrease, respectively. Assuming that the material is
homogeneous, we can create a ratio, /J, of the strain in the lateral direction to
the strain in the axial direction:
Ey
/J = -,
Ex
(10.3)
where Ex is the axial strain of the bar, and Ey is the strain in the direction
normal to the axis. The ratio, /J, is known as Poisson's ratio, named after the
French mathematician Simeon Poisson (1781-1840).
Because the dimensions of the bar change when subjected to compression or
tension, the volume of the bar also changes. This volume change is usually
expressed in the form of the non-dimensional quantity e, known as dilatation,
z.e.:
llV
(J
e = - = E(l - 2/J) = -(1 - 2/J).
Vo
E
(10.4)
From Eq. (10.4) it follows that the maximum possible value of /J for ordinary
materials is 1/2; any larger value of /J yields the volume decreasing when the
material is stretched, which is an unlikely event. Most materials are characterized by Poisson's ratio, /J, of about 1/4 or 1/3. In the perfectly plastic region,
no volume change (dilatation) occurs, when Poisson's ratio is taken as /J = 1/2.
10.2.2 Shear-Stress and Strain
The shearing stresses, T, acting parallel to the surface of the material are defined
as force per unit area:
F
T = A'
(10.5)