Rate of stress versus velocity gradient

[maros522]

Hello,
I don't understand the meaning of equation
$$\int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}}$$ dV
where $$\dot{s}$$ is rate of change of stress, $$v_{j}$$ is velocity.

Can anybody describe the meaning of this equation? Thank you.

 

[vargasjc]

I don't remember that equation. vj is the velocity of the element under stress? What's V (on dV)?

 

[maros522]

Hello, thanks fo posting. vj is the velocity of the element under stress and V is volume of the body. If you have access to journal you can check it

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TXB-46G508Y-H8&_user=10&_coverDate=06%2F30%2F1959&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1226210839&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=62860f8f06fe35bfce725cc38553669a

It is in the equation 4 and 5. And the main meaning is that it is criterion of uniqueness.