Engineering Rock Mechanics

Strain analysis 41 5

Hence

or

Note that the tensorial shear strain is half the engineering shear strain.
(d) Combined strain and rotation. We can now add together cases (a), (b)
and (c) to form a single set of equations. It is useful to keep strain and
rotation separate though:
This is because only the strain matrix represents distortion. The rotation

strain matrix rotation matrix

matrix is just that: a rotation of the rigid body.

However, in the analysis of displacement we found that

so

Writing these equations in full gives:

From which we find

and