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.
feynman1
Messages
435
Reaction score
29
What's the derivative of deformation gradient F w.r.t cauchy green tensor C, where C=F'F and ' denotes the transpose?
 
Engineering news on Phys.org
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
 

Thread 'Bubble formation in 4 mm gap vessel'

How did you find PF?: Via Google search Hi, I have a vessel I 3D printed to investigate single bubble rise. The vessel has a 4 mm gap separated by acrylic panels. This is essentially my viewing chamber where I can record the bubble motion. The vessel is open to atmosphere. The bubble generation mechanism is composed of a syringe pump and glass capillary tube (Internal Diameter of 0.45 mm). I connect a 1/4” air line hose from the syringe to the capillary The bubble is formed at the tip...
View full post »
Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'

Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'

Scenario 1 (figure 1) A continuous loop of elastic material is stretched around two metal bars. The top bar is attached to a load cell that reads force. The lower bar can be moved downwards to stretch the elastic material. The lower bar is moved downwards until the two bars are 1190mm apart, stretching the elastic material. The bars are 5mm thick, so the total internal loop length is 1200mm (1190mm + 5mm + 5mm). At this level of stretch, the load cell reads 45N tensile force. Key numbers...
View full post »

Thread 'Find 3D Printer & Software Resources for Prototype Creation'

I'd like to create a thread with links to 3-D Printer resources, including printers and software package suggestions. My motivations are selfish, as I have a 3-D printed project that I'm working on, and I'd like to buy a simple printer and use low cost software to make the first prototype. There are some previous threads about 3-D printing like this: https://www.physicsforums.com/threads/are-3d-printers-easy-to-use-yet.917489/ but none that address the overall topic (unless I've missed...
View full post »

Similar threads

A Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor
Replies
3
Views
2K
Understanding the Cauchy Stress Tensor: Clearing Up My Confusion
Replies
7
Views
2K
I Confusion about Cauchy surfaces
Replies
8
Views
1K
Cauchy Stress Components from Surface Force
Replies
12
Views
2K
Showing that the gradient of a scalar field is a covariant vector
Replies
5
Views
4K
A Gradient of deformation tensor-rigid body
Replies
1
Views
1K
I How to apply tensor transformation rule
Replies
9
Views
2K
Nature of displacement and the deformation tensor
Replies
1
Views
2K
Lagrange multipliers understanding
Replies
8
Views
2K
I Component derivative of a tensor
Replies
10
Views
3K

Hot Threads

Recent Insights

Back
Top