Derivative of the deformation gradient w.r.t Cauchy green tensor

AI Thread Summary
The discussion centers on finding the derivative of the deformation gradient tensor F with respect to the Cauchy Green tensor C, defined as C = F'F. Participants clarify that the inquiry is not about the time derivative of the Cauchy Green tensor but specifically about the relationship between F and C. There is a focus on the mathematical implications and the need for precise definitions in the context of continuum mechanics. The conversation highlights the complexity of deriving such relationships and the importance of understanding tensor calculus. The topic remains unresolved, emphasizing the need for further exploration of the derivative in question.
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What's the derivative of deformation gradient F w.r.t cauchy green tensor C, where C=F'F and ' denotes the transpose?
 
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fresh_42 said:
Open https://de.wikipedia.org/wiki/Verzerrungstensor with Chrome and let Google translate it into a language of your choice.
very helpful but it doesn't answer my question directly
 
Are you trying to find the derivative of the CG tensor with respect to time in terms of the time derivatives of the deformation gradient tensor and its transpose?
 
Chestermiller said:
Are you trying to find the derivative of the CG tensor with respect to time in terms of the time derivatives of the deformation gradient tensor and its transpose?
no, but of F w.r.t C
 

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