ABSTRACT
From Chapter 7, at a point within a three-dimensional material, there are usually six independent stresses as shown in Figure 8.1, that is:
• Three normal stresses: x , y and z • Three shear stresses: xy , xz and yz
At the same point, due to the action of these stresses, there exist six independent strains, that is:
• Three normal strains: x , y and z • Three shear strains: xy , xz and yz
For linearly elastic and isotropic materials, the six stresses and the six strains satisfy Hooke’s law as follows:
x = x E
− y E
− z E
= 1 E
[ x − y +z
]
E − x
E − z
E
= 1 E
[ y − x +z
] z =
z E
− x E
− y E
= 1 E
[ z − x +y
] (8.1a)
G
xz = xz G
G
(8.1b)
where E, G and are, respectively, Young’s modulus, shear modulus and Poisson’s ratio of the material.
