Rate of stress versus velocity gradient

AI Thread Summary
The equation ∫dot{s}_{ij}∂v_{j}/∂x_{i} dV represents the rate of change of stress in relation to the velocity gradient within a volume of material. Here, dot{s} denotes the stress rate, v_{j} is the velocity of the stressed element, and V signifies the volume of the body. The discussion clarifies that this equation serves as a criterion of uniqueness in material behavior. For further details, reference to specific journal articles is suggested. Understanding this equation is crucial for analyzing stress and velocity interactions in materials.
maros522
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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.
 
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I don't remember that equation. vj is the velocity of the element under stress? What's V (on dV)?
 
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.
 

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