dimensionless analysis

I am using an open source FEM platform, which requires you to convert your equation system to non-dimensional form. So, there are no units specified for the parameters in the problem. If you use compatible input units, you should expect the output in matching unit - just like one would do in a normal python or C++ code for solving physical problems. I have an elasto-plastic dynamic problem to solve, and these are the parameters for the Drucker-Prager Soil Model for soft clay.

E = 5000000;                 // Young's Modulus in N/m^2 or Pa

att.

 I am just wondering if there exists a negative dimensionless quantity? It seems that all dimensionless numbers I encount in my field (fluid dynamics) are positive. what if it is negative? and if negative, what does that mean? I sense that:

the imposed negative sign for a dimensionless number is just an alternative expression for a special external boundary condition, rather than no longer a characteristics over an essential in a physical law that required for being independent of external boundary conditions.