Pure deformation and rigid body motion (Contd...)

We can introduce following notations:

(1.12)

are called the components of strain.

Furthermore we can introduce the notations:

(1.13)

Hence we can divide the tensor in following symmetric and anti-symmetric parts:

(1.14)

Using these definitions of in equation 1.8, we have:

(1.15)

So the original affine transformation can be divided into two parts: Symmetric and Anti-Symmetric.

(1.16)