Thank you very much Mr Mohamed, your answer was so helpful and intriguing. I have never come across cosserat before as a young student. But the equation am seeking for is a precise one. Cosserat is quite compound. I have a problem and the parameters I do have to find the rotation per unit length (Torque) are representative strain, representative stress, shear stress and I guess modulus of rigidity (which was not included but am guessing it would be involved too). I had a similar problem in the past but there was a relativity equation i used in finding the torsional angle in radians: Q = (change in shear stress/modulus of rigidity) + (3*shear stress*change in representative plastic strain/representative stress). I cannot say how that relationship was derived or but that was how i solved the problem. Now I want to find the Torque and I seek to find a relativity equation using incremental theory if the stress-strain characteristics of the material are given 

To find a correlation between torque and shear stress for an specific geometry such as a tube rotating in a viscose liquid, you can extend it to parallel plate and dissolve you problem. It seems many correction will be required which depends on the tube diameter and also container.

you may find some useful information in attached link/file.

https://dspace.cc.tut.fi/dpub/bitstream/handle/123456789/.../aho.pdf?...3

Young's Modulus = Stress/ Strain = (Force/Area)/(Change in length/Length)

Force = (Young's Modulus*Poisson's Ratio)*Area

Angular Velocity = 2*pi/T;

Circular Force = Mass*(Velocity Squared)/Radius = Mass*(Angular Velocity Squared)*(radius squared)/radius

Torque = Force*Radius vector = F*r

Therefore, knowing, Young's modulus, and Poisson's ratio and radius, one can calculate the force and hence the torque...

Article Interpretation of torsional shear results for nonlinear stre...

follow this article.

In this article, interpretation methods, average shear stress and representative shear strain values are given. equation 13-17 are more useful in understanding the relationship of T and gama(shear strain).stress-strain calculation using hollow specimen is explained for logarithmic scale.

Hope it work out for you.

Ashish

Torsion equation T/J= Tou/R= G Tetha/L