I am straggling with obtaining the potential of the following weak form of the differential equation.

$\int_\Omega \omega (\bar \epsilon_{eq} - \epsilon_{eq})d \Omega + \int_\Omega \nabla \omega.C \nabla \bar \epsilon_{eq} d \Omega = 0$

According to the paper the above weak form yield the following potential energy in a form such that, $\delta P = 0$, in which P is the potential energy:

$P = 1/2 [(\bar\epsilon_{eq} - \epsilon_{eq})^2 + C \nabla \bar \epsilon_{eq}. \nabla \epsilon_{eq}]$

I tried to find the solution but unfortunately I couldnt find the procedure.

P.S. : $\omega$ is the weight function that is used to obtain the weak form of the strong PDE.



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