Entry of tensor permeability for magnetics simulation

Before even bothering to download....Equation Settings input panel shown at
https://www.featool.com/doc/physics#phys_ms
doesn't give me a real clue as to how it could handle non scalar permeability entry.
For instance, when trying to model one or more inherently anisotropic and non-linear permeability, laminated 'electrical steel' structures, oriented arbitrarily wrt some incident B field source(s).

Could someone familiar with that kind of problem point me to if possible a worked example, or failing that the hopefully readily enterable general form for a permeability tensor array expressions incorporating said non-uniformities.
A concrete example of something roughly analogous, say permittivity tensor entries for anisotropic & nonlinear dielectric media in an electrostatics situation, or likewise for non-isotropic & non-linear elastic media stress/strain simulation, would probably give sufficient to be able to adapt to the magnetics case accordingly.

Hi,

Anisotropic materials would currently have to be introduced manually be editing the PDE equations, as described in the linked example for below (specifically step 15 in the tutorial instructions):

https://featool.com/model-showcase/02_Heat_Transfer_04_orthotropic_heat_conduction1

https://featool.com/doc/Heat_Transfer_04_orthotropic_heat_conduction1

Although this example is for heat transfer, other physics such as electrostatics would be handled similary.

Hi Precise Simulation,
Thanks for that response which is a great start. However the step-by-step heat flow example in 2nd linked article, refers to fixed anisotropy coefficients. For magnetic materials especially like transformer steel, permeability anisotropy is also is a highly nonlinear function of incident B (or H if one prefers) field.

So, can FEATool Multiphysics handle the added complexity of replacing those fixed coefficients in PDEs with ones that are nonlinear functions of applied B (or whatever else in some other physical situation)?

I would have to do some serious digging to find relevant manufacturers data and maybe use curve fitting apps to arrive at analytic expressions, presumably as a power series in B. Which effort would be worthwhile provided I know it can be successfully incorporated by FEATool software!

PS - I wrote 'applied B field' last post, but actually the correct term is 'resultant i.e. net B field'.
This may be a bit too tricky as it implies rather compicated recursive feedback?

Yes, nonlinear coefficients and equations are handled automatically. However, if your problem is very nonlinear it might be difficult to get it to converge unless you have a starting guess close to the solution.

Tabulated data is also supported if you write your own coefficient function (from where you can load/process your data), see for example:

https://featool.com/doc/physics#phys_coef_user

Again thanks Precise Simulation. Suppose one uses some functional form for mu(x,y,B) like
mu0[(axB + bxB^2 +...)x, (ayB + byB^2 +....)y] (not worrying about exact syntax here),
where ax, bx,... ay, by,... are the respective x, y, coefficients for permeability mu as a function of NET locally acting B.
All very well in the case of a known applied uniform H field as will be the case for available manufacturers data. The perhaps sticky problem is locally B(x,y) (thus also mu(x,y,B)) will have unknown initial values generally very different to the externally generated source B field.

Not wanting to be a pest but what I'm trying to get at is the software must I think automatically recursively rewrite the B(x,y) values in the initially given PDEs until self-consistent convergence is achieved. Presumably it would start out by using the source B field and work from there. That is the actual case?

Coefficients with nonlinearities, will be solved with fixed point iterations, so evaluated from the solution at the previous iteration (or given initial values for the first iteration). For using the Newton method, you can use the FEniCS solver, or provide an analytical form for the Jacobian if you prefer. I'm not quite sure if it answers your question, but there is no particular clever analysis or processing done for the coefficients.

OK thanks that should be all I need to take the plunge and purchase - once I get to setting up my new machine that is.

Thank you for the interest. I would recommend you download and try to see if it works for your use case, before you purchase. You can download the toolbox from https://www.featool.com/download