Body couples

Hello Ramdas,

There have been theoretical attempts covering what you seek.

For starters, see a chapter appearing near the end of the book "Elasticity" by M. H. Saad. (Pub: Elsevier. Low cost edition republished by their own Delhi office is readily available in India.) The chapter gives quite a few further references too. Some of them refer to Eringen's work.

So, I searched a little on the Web, and found this: A. C. Eringen, "Linear Theory of Micropolar Elasticity," J. Math. Mech., Vol. 15, No. 6 (1966), available here:

http://www.iumj.indiana.edu/Help/simplesearch.php?query=Eringen&type=lastname&firstName=A.&lastName=Eringen 

Hope this helps.