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Non-linear fitting with a forward problem that is not closed-form

niels-reflektor

I have model that describes a non-linear stress-strain relation (uniaxial incompressible neo-Hookean material). This model. however, requires a solution to a non-linear equation itself. As I have read and understood it, it is only possible to input closed form models to JMP for fitting. Is this correct?

If my question is unclear, here is a simplified example of what I want to do:

I have datapoints in coloumns: x, y

I have a model that I would like to fit my data to:

y = a*Q*x + b*Q^(3/5)*x^2 + a/b (1)

where a and b are the parameters to be found with a fit. Q is an intermediate parameter that needs to be solved for any given combination af (x, a, b), as:

0 = sqrt(Q) + a/x - x*(Q^(5/3) + b) (2)

This is the step I do not know how to perform in JMP. If could analytically solve for Q and insert in the equation (1), I would know how to use JMP for the rest of the way – but with som models (like this one), it is not possible.