There's 4 fundamental forces - gravitational, electromagnetic, weak and strong forces. They all act in different ways, have different strengths and have a different range. For molecules the intermolecular forces are electromagnetic in nature, but on the scale of a proton it is the strong force holding it together. Is this what you were looking for?
At the smallest levels, the strong force holds quarks together to form protons and neutrons. These protons and neutrons are bound to each other in nuclei by the nuclear force, or residual strong force (the same force carrier as the strong force, but on a larger distance scale, so the force is weaker). Electrons are held in orbit around nuclei by the electromagnetic force, forming atoms. These atoms are then bound into molecules and molecules are bound to each other also by electromagnetic forces. On a much larger scale, planets and galaxies are held together by gravity.
Well, you need a model of your material on the microscopic level. The easiest example is a crystal. You find some model for the potential energy as function of distance of the atoms, and search for the minimum (this is the approximate distance of the atoms in a crystal). This correlates with the binding energy. To split a crystal, you can calculate how many bonds you have to separate and multiply this with the binding energy, it will give you some approximation of the required energy.
It is a bit more complex (and even worse if you look at material with larger structures like paper), but I hope you get an idea.
Calculating a force needs more knowledge about the splitting process.
There is no simple formula where you just insert some numbers and get your result.
Yeah, material strength is an entire science. And a lot of that is based on condensed matter physics which is a growing field. There are some relatively simple models that give relatively good estimates for some relatively simple materials, but the moment you get to something a little more interesting it gets incredibly complex. Paper, for example, is a composite material, and the number of things you need to know about it just to have a chance to make an estimate is overwhelming.
That's a fairly persistent element in condensed matter physics. You can build a material out of some very simple elements, for each of which you can write out an exact formula, but you throw enough of these into a mix, and you end up with something that works in ways you could not guess in advance and that require a whole bunch of research to describe.
Yes this is interesting. Crystal for example shows the basic way in wich that can be done.
But how can we now(calcualte, messure) the energy of binding? Is it possible to approximated it somehow, just knowing chemical formula of commponent(s)?.
And something else what I woud like to ask in is it possible from known molecular structure calculate whyv for example paper folds, when some other materials(glass,woud) can not?(paper here is not used for example for some particicular reason, what I mean is it in general possible to show what kind of deformatin will some substance(not nessesarily material with pracitcal application) be capple of?)