second invariant of rate-of-strain tensor

Chun Min Chew

The shear, or strain, rate is often calculated based on the square root of the second invariant of rate-of-strain tensor. The tensor itself is made up of all the possible deformation of a fluid element, which includes volumetric and shear deformation. I would like to invite comments from everyone concerning:

1) if this second invariant, in its general definition, includes both the volumetric-rate of deformation and shear-rate of deformation? Or simply shear-rate of deformation alone?

2) the physical meaning of the 'second invariant' of the strain rate tensor. I take it as a way to 'average' all the strain components in the tensor, thus an 'effective' strain rate.

I look forward for your comments.

Cheers.