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How to use non-dimensional form in open source codes instead of Units

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

nu = 0.35;                   // Poisson's Ratio Unitless

cohesion = 20000.0;          // N/m^2 or Pa

dilatancy_angle = 25.0;      // Degrees

hardening_parameter = 0.1;   // Unitless

friction_angle = 25.0;       // Degrees

double rho = 1750.0;         // Mass density in kg/m^3

The mesh is a (1 x 1) square mesh. So when I see the displacement caused by wave propagating on this mesh using the above parameters, in Paraview, is it meaningful to assume that the output shall be in metres (m). Also, in such platforms, how does one compare the mesh to a realistic scenario? For example, can I assume that my mesh is a 1km x 1km square ground surface and the displacement I am viewing is in metre? What if I take a (10 x 10) mesh? Can anyone please explain how this non-dimensional logic works?

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