Page 76 - Reservoir Geomechanics

60 Reservoir geomechanics

Figure 3.3. Schematic illustration of the relationships between stress, strain and the physical
meaning of frequently used elastic moduli in different types of idealized deformation
measurements.

To describe constitutive laws more precisely, it is necessary to have a rigorous defi-
nition of deformation by considering the components of the second-order strain tensor,
ε ij defined as

1
δu i δu j
ε ij = + (3.1)
2 δx j δx i
In a homogeneous and isotropic material, principal stresses and principal strains act in
the same directions.
Several physically meaningful strain components are illustrated in Figure 3.3: axial
strain and lateral expansion in a sample compressed uniaxially (Figure 3.3a); shear
strain resulting from application of a simple shear stress (Figure 3.3b); and volumetric
strain resulting from compressing a body under isostatic mean stress (which corre-
sponds to uniform confining pressure in laboratory experiments), S 00 (Figure 3.3c)
where,

1
ε 00 = ε 11 + ε 22 + ε 33 S 00 = (S 11 + S 22 + S 33 ) (3.2)
3