Working on a crack-propagation problem when I encountered some odd behavior with a recursive variable definition.

The dependence of β on the value of a requires an iterative process to find the critical value of a. However, attempting to evaluate this formula with pi in it yields a "Result is above max. allowed positive integer" error after just 3 iterations. Replacing pi with 3.14159 solves the issue.

It seems when SMath tries to store the definition analytically as a fraction, it quickly grows too difficult to store. Is there an option/function somewhere to instruct SMath to evaluate and store the approximate numerical result in a variable instead of the typical behavior?

This is neither bug or problem. Limitation of symbolic equation.
Use eval(), it will convert symbolic calculation of a.f to numeric value.
Or convert calculation method of selected region to numeric.



Using one of these methods, increasing N to 100 won't even matter for calculation time.
Your for loop will be instantaneously calculated.

Regards