How to pass the order parameter c to SplineFunction for phase-field simulation?

[ZER0-auto]

I need to use a cubic spline to handle the relationship between the order parameter c and the free energy for my subsequent phase-field simulations. I referred to the solution discussed in #30528 and plan to use SplineFunction, but I do not know how to pass the variable c to the SplineFunction. Below is the relevant part of my code:
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[]

[Kernels]
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F_total
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[]

[AuxVariables]
[./total_free_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]

[Functions]
[./f_spline_func]
type = SplineFunction
x = ' 0.0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 '
y =' 0.0 0.04672677137932725 0.07675234493686434 0.09016926411234366 0.09181444021690517 0.09166386769340495 0.09344652096236047 0.08672581153256216 0.0685767761163886 0.0410397730427269 -0.000746771414836811 '
yp1 = 0.1
ypn = 1
[../]
[]

[AuxKernels]
[./total_free_energy]
type = TotalFreeEnergy
variable = total_free_energy
f_name = F_total
kappa_names = kappa_c
interfacial_vars = c
execute_on = 'initial TIMESTEP_END'
[../]
[./func_val_aux]
type = FunctionAux
variable = c
function = f_spline_func
[../]
[]

[Materials]
[./total_free_energy]
type = DerivativeParsedMaterial
expression = 'func_val_aux'
material_property_names = 'func_val_aux'
coupled_variables = 'c'
property_name = F_total
enable_jit = true
derivative_order = 2
[../]
[]

Clearly, the current code cannot be executed because c is a Variables rather than an AuxVariables.

[GiudGiud]

Hello

Functions are only meant to be functions of time and space (and postprocessors, but that's a little bit anecdotic).

So to use a function (here a spline) to compute a property, you don't go through the Functions system.
If it's a simple function you can use the ParsedMaterial.
Else you have to code an object. You can call a Function from that object, with the x,y,z,t arguments that you wish to use, for example "f(c.,0,0,0)" to use the variable c as an argument to the function

We do this in this object: if computing an auxiliary variable you can use this to feed functor (=variable) values into the x,y,z,t arguments of a Function.
https://mooseframework.inl.gov/source/auxkernels/FunctorCoordinatesFunctionAux.html
If there is an equivalent Material you could try to use that

[ZER0-auto]

Hi GiudGiud,

Thank you for your helpful explanation and suggestion. Following your advice, I created a custom Material type by combining the implementations of SplineFunction and DerivativeParsedMaterial. This allowed me to properly pass the variable c to the spline function and compute the free energy and its derivatives for my phase-field simulations. The solution now works perfectly. Thanks again for your guidance!