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

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Discussion Overview

The discussion centers on the mathematical relationship between the deformation gradient tensor \( F \) and the Cauchy Green tensor \( C \), specifically seeking the derivative of \( F \) with respect to \( C \). The scope includes theoretical and mathematical reasoning related to continuum mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant asks for the derivative of the deformation gradient \( F \) with respect to the Cauchy Green tensor \( C \), defined as \( C = F'F \).
  • Another participant suggests that the inquiry may relate to the time derivative of the Cauchy Green tensor in terms of the time derivatives of \( F \) and its transpose.
  • A subsequent response clarifies that the original question is specifically about the derivative of \( F \) with respect to \( C \), not the time derivative of \( C \).

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there is confusion regarding the specific derivative being sought, with differing interpretations of the question.

Contextual Notes

There is ambiguity regarding the definitions and relationships between the tensors involved, as well as the specific nature of the derivatives being discussed.

feynman1
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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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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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