Engineering Rock Mechanics

Stress and strain are both tensor quantities 59

e = Sa

21 independent

c:E:ts

where E = anda = and S =

It can be shown from energy considerations that the S matrix is symmet-

rical, leading to 21 independent elastic constants.

This number of constants can be reduced if we assume that some of

the strain-stress linkages are not significant. For example, omitting all

shear linkages not on the leading diagonal - which means assuming

that any contributions made by shearing stress components in a given

direction to normal or shear strain components in other directions are

negligible - causes all off-diagonal shear linkages to become zero. The

compliance matrix then reduces to one with nine material properties,

which is the case for an orthotropic material.

]/Ex -v,~/E~ -%Ez^0 0 0

. -... .-..... l/Ey -vyz/&^0 0 0

.... .....

......... ._ ...... ...... 1 /Gxz 0 0

.....

'....- -.., l/Gyz 0

'..,

'...

---......

... 1 /E,

symmetric

where E is a Young's modulus, u is a Poisson's ratio, and G is a shear

modulus.