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

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SUMMARY

The derivative of the deformation gradient tensor F with respect to the Cauchy Green tensor C, defined as C = F'F, is the primary focus of this discussion. Participants clarify that the inquiry is specifically about the relationship between F and C, rather than time derivatives. The discussion emphasizes the mathematical relationship inherent in continuum mechanics, particularly in the context of finite deformation theory.

PREREQUISITES
  • Understanding of continuum mechanics principles
  • Familiarity with the deformation gradient tensor F
  • Knowledge of the Cauchy Green tensor C
  • Basic calculus, particularly differentiation of tensor functions
NEXT STEPS
  • Study the mathematical properties of the deformation gradient tensor F
  • Explore the derivation of the Cauchy Green tensor C from F
  • Learn about tensor calculus in the context of continuum mechanics
  • Investigate applications of the Cauchy Green tensor in material science
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Researchers, engineers, and students in the fields of mechanical engineering, materials science, and applied mathematics who are focused on the mathematical modeling of material deformation and behavior under stress.

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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