Engineering Rock Mechanics

Strain analysis 41 3

that P and P' remain coincident

and Q moves to Q. Hence

du = - sin a-dy

The total change in u (i.e. du) is given by the sum of these components:

du = (change in u as x changes) + (change in u as y changes)

hence

similarly

av av

ax ay

dv = -dx + - dy.

We can put these equations into matrix form:

This shows how the displacements (du, dv) are functions of the original
separation of P and Q (dx, dy). The problem is, we need the displacement
independent of this separation: i.e. we need strain.

Strain in terms of displacement functions

In general, when a body deforms, the following components of defor-
mation take place:

Rigid body Rigid body x-direction y-direction Shear
translation rotation normal strain normal strain strain
We can ignore rigid body rotation-we are only interested in the
displacement of points relative to each other. Now all we have to do is
analyse each component individually, and then combine them.