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How to differentiate left and right cauchy deformation tensor in biomechanics modelling?
Mon, 2012-06-04 10:31 - Wei Ong
Hi, dear all,
I am facing problem on differentiating left Cauchy deformation tensor and right Cauchy deformation tensor.
thanks for notes in http://www.engin.umich.edu/class/bme456/ch3strain/bme456straindef.htm, i can derive the them in terms of mathematical equation, but i cannot differentiate them in engineering modelling filed.
From what i read is
right Cauchy deformation tensor is equal to the square of the right stretch tensor?
left Cauchy Deformation tensor is the square of the left stretch tensor ?
What is signifcance between 'left' and 'right' when using it to defining hyperelastic material properties in terms of invariant form?
Forums:
Left and right Cauchy-Green tensors
Wei,
The left and right Cauchy-Green tensors are related simply by a rotation. As such, the invariants of the two tensor are the same.
Matt Lewis
Los Alamos, New Mexico
Hi, Lewis, Thanks
Hi, Lewis,
Thanks for reply and confirmation
The right Cauchy-Green
The right Cauchy-Green tensor is in the reference configurtion, while left Cauchy-Green tensor is in the current configuration. Cauchy stress (true stress) can only be a function of the left Cauchy-Green tensor.
tensorial calculus
I have started performing tensorial calculus myself but, admittedly, I am having a hard time doing so. Are there any notes that the experts here think might be not only of theoretical but practical use as well? Also, is there a matlab/mathematica package that allows one to compute derivatives (such as the ones mentioned by the originator of the thread) out?
To me the best way to do
To me the best way to do tensorial calculus is to take derivative to components, but not a tensor.
good point
Einstein notion is always garbage, as Biot said
tensorial calculus
You may take a look this book, if have not read it already:
Mikhail Itskov, 2007, "Tensor Algebra and tensor Analysis for Engineers, with applications to continuum mechanics".
Left and Right Cauchy-Green Tensors
Wei,
You said you want to take the derivative but you did not say derivative with respect to what, for example time, coordinate variables...
Mohsen
proof of left cauchy green tensor being in current configuration
Hi
As you said that "The right Cauchy-Green tensor is in the reference configurtion, while left Cauchy-Green tensor is in the current configuration. Cauchy stress (true stress) can only be a function of the left Cauchy-Green tensor"
Please tell me how can I prove that left cauchy green tensor is for the current configuration.
Thank you