Unit_Error while solving equations using solve_block.

You are NOT working with the same values when you omit the units!!

Without units you use values like 288.7, but with units you use 288,7 MPa which is internally represented by Prime  in its base unit Pa.

So the numeric algorithm used by the solve block now uses the number 288700000.
On the other hand you use for example the number 50 for d but in the other sheet you use 50 mm, which is represented by the number 0.05 internally (base unit meter). Even worse when it comes to the areas. Unit-less value 942.5 versus 0.0009425 (m^2).

So the numbers in use when you use units cover a rather large range from very small to very large which may make a big difference concerning convergence behaviour within a limited tolerance.

So I think that's the reason why your solve block is so sensible concerning the guess values.

In the attached (unit-less) file I changed all values to the same numeric values which are used in the sheets with units.

As you can see, the calculations fail now!

You would have to set the system variable CTOL (convergence tolerance) to a rather large value like 10^-1 (default is 10^-3) to make the solve block work again and this at the cost of precision.

OR you let CTOL at its default value and provide other/better guess values.

I found that a guess value of 60*10^-3 makes for both sets the calculation work OK

Using other guesses was already the 'solution' in the sheet with the units.

In the new sheet here I found that 60*10^-3 and also 80*10^-3 are good guesses, but the second calculation (strain_500) fails with a guess of 70*10^-3. So there is a high sensibility concerning the guesses...

BTW, the "root" function, as shown by Luc, is usually much less sensible concerning the guess value and could also be use in a second way without having to provide a guess.