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If you use AD, it will capture that additional dependencies naturally when computeResidual is called for computing the Jacobian.

If you do not use AD, then implementing the computeOffDiagJacobian is where you need to capture all these dependencies, manually. You ll need to add the derivatives of the material properties with regards to the variables coupled in

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@NateAM
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@GiudGiud
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@lindsayad
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@NateAM
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@GiudGiud
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