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What is mandel stress?

 Dear all,

 Sometimes, we can see the conception of Mandel Stress, I wonder

What is mandel stress? How to use it?

Thanks. 

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nicoguaro's picture

Can you clarify the question please?

If you refers to the notation of Mandel for tensors (instead of Voigt's), you can read in Wikipedia:

http://en.wikipedia.org/wiki/Voigt_notation

Hello, nicoguaro 

Thanks for your reply. I have read the content in the link you posted, I think it has no relationship with the Mandel Stress.

In some place, the Mandel stress tensor is defined as follow:

M=2*Ce*∂ Ψe/Ce

where Ce is the elastic right Cauchy-Green tensor,  Ψe is the elastic part of free energy. I know the Cauchy stress, second Piola–Kirchhoff stress, and so on, different stress measure uses in different application.

But what is the Mandel Stress? where will we use it?

Thanks. 

 

 

hello, Biswajit

From the link you have provided,  I have learned that where the mandel stress will be used. 

Thanks for your help. 

The answer to your question lies in work conjugacy. In plastic regime we usually want to decompose the stress power in two parts: elastic and plastic parts. Consider the following relation:

1/rho_0 S : (dE/dt) = 1/rho_0 [S_e : (dE_e/dt) + P : L_p]

in this expression, S_e is work conjugate to E_e and P (Mandel stress) is work conjugate to L_p, where:

S_e = F_p S F_p^T,

P = C_e S_e and

L_p = (dF_p / dt) F_p^-1

The stress P was first introduced by Mandel. Other decompositions are of course possible.

Mohsen 

hi, Mohsen

Thank you for the valuable information. The most important thing is the work conjugacy.

 

 

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