If you want to get technical, this isn't a continuous surface but weave of strings. And something that makes this more complex is the location of the string int

If you want to get technical, this isn't a continuous surface but weave of strings. And something that makes this more complex is the location of the string intersections has a static/dynamic friction component that is difficult to model analytically. But I think we accept your approximation if you are looking for numeric results.