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Figure 1.3 Hookean solid under compression [1]
P
VtrbV
The isotropic compression due to the pressure acting on all sides of the cube shown in
Figure 1.3 is given by the engineering compression ratio K
where AV is the reduction of volume of a body with the original volume V0 due to
deformation.
1.1.1 Hooke'sLaw
The linear relationships between stress and strain of a Hookean solid are given by [I].
P
(1.8)
(1.9)
(1.10)
(1.11)
Where E is the modulus of elasticity, G is the shear modulus, and K is the bulk modulus.
These moduli are constant for a Hookean solid. In addition, the relationship existing
between £, G and K is expressed as [ 1 ]
For an incompressible solid this leads (K —», jl —> 0.5) to [1]
E = 3G
1.2 Newtonian Fluids
(1.12)
(1.13)
There is a linear relationship between stress and strain in the case of Newtonian fluids
similar to the one for ideal elastic solids.
The fluid between the upper plate in Figure 1.4 is moving at a constant velocity Ux and
the lower stationary plate experiences a shear stress T (see also Figure 1.2).