What are the Hashin-Shtrikman bounds?

[handsomecat]

Is anyone familiar with the Hashin-Shtrikman bounds and the principles behind them? Will you be so kind as to post a simple explanation?

So far, what I have grasped is that they came up with a functional and the bounds are obtained when a certain tensor is chosen to be positive definite/negative definite.

 

[jitender]

hi
I am working on the same problem Hashin-Shtrikman formula for permittivity of a homogeneous uniaxially anisotropic material.I have the formula of permittivity of the same material.

But I don't know to derive it . Please help me If you have got any idea in this topic.

 

[jitender]

Is anyone familiar with the Hashin-Shtrikman bounds and the principles behind them? Will you be so kind as to post a simple explanation?

So far, what I have grasped is that they came up with a functional and the bounds are obtained when a certain tensor is chosen to be positive definite/negative definite.

hi
I am working on the same problem Hashin-Shtrikman formula for permittivity of a homogeneous uniaxially anisotropic material.I have the formula of permittivity of the same material.

But I don't know to derive it . Please help me If you have got any idea in this topic.