One way coupling of hydrostatic stress and effective plastic strain on a kernel

[shredderbvek]

I want to implement the kernel for the weak form given below,
$-\int_\Omega \nabla \phi . \left( \frac{D \bar{V_H}}{R T} C_L \nabla \sigma_H \right) d\Omega$
with material model for calculating $N_T$ as given below,
$N_T = 10^{(23.6 - 2.33 \exp{(- 5.5 \epsilon^P)})}$
Where, $\nabla \sigma_H$ (Gradient of Hydrostatic stress) and $\epsilon^P$ (Effective plastic strain) are to be passed using one way coupling from solid mechanics. Also $C_L$ is the degree of freedom.
Can somebody help me to find information about how to compute gradient of hydrostatic stress as a coupled variable?

[GiudGiud]

Hello

Can somebody help me to find information about how to compute gradient of hydrostatic stress

Hydrostatic stress, coming from solid mechanics? If so it's likely a material property (not a coupled variable, displacements are the variables), likely a tensor.
Did you identify how to output that stress in a regular simulation?

with material model for calculating NT as given below,

That's for postprocessing right?

I want to implement the kernel for the weak form given below,

That kernel being fairly complicated, I think the way forward is to examine the related kernels in solid mechanics

[shredderbvek]

Hydrogen.Embrittlement.2.pdf
The attached pdf is a log to keep track of my current work, where I have the complete governing equation. I am trying to replicate the work done by Paneda ( reference: https://doi.org/10.1016/j.actamat.2020.08.030) where he used UMAT and UMATHT subroutines for the coupling of hydrogen transport and solid mechanics. $N_T$ is actually a variable term in the govering equation which is influenced by the effective plastic strain.

To output hydrostatic stress, I guess we can maybe use the stress tensor, compute its trace and divide it by 3. I am having trouble computing the gradient of hydrostatic stress for the kernel.

[GiudGiud]

I guess we can maybe use the stress tensor, compute its trace and divide it by 3. I am having trouble computing the gradient of hydrostatic stress for the kernel.

you can retrieve material properties in kernels using getMaterialProperty<RealTensorValue>("name of property")
see MatDiffusion for an example.

I think you might want to look at the StressDivergenceTensors kernels though