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# What is mandel stress?

Fri, 2014-05-30 23:10 - YangTan

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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## Clarification

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

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.

## Re: Mandel stress

You can begin with http://en.wikipedia.org/wiki/Flow_plasticity_theory#Elastic_regime

-- Biswajit

## hello, Biswajit From the

hello, Biswajit

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

Thanks for your help.

## Mandel Stress

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

hi, Mohsen

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