Page 245 - Introduction to Continuum Mechanics

230 The Elastic Solid

Comparing Eq. (5.4.12) with (5.4.11), we see that the Lame's constant n is also the shear
modulus G.
A third stress state, called the hydrostatic stress, is defined by the stress tensor T = of. In
this case, Eq. (5.3.7) gives

As mentioned in Section 5.1, the bulk modulus k, is defined as the ratio of the hydrostatic
normal stress o, to the unit volume change, we have

From, Eqs. (5.4.6),(5.4.7), (5.4.9) and (5.4.14) we see that the Lame's constants, the Young's
modulus, the shear modulus, the Poisson's ratio and the bulk modulus are all interrelated.
Only two of them are independent for a linear, elastic isotropic material. Table 5.1 expresses
the various elastic constants in terms of two basic pairs. Table 5.2 gives some numerical values
for some common materials.
Table 5.1 Conversion of constants for an isotropic elastic material