In a collision, what causes solids to break? example: A car crashes into a wall, breaking the wall into pieces at collision. 
Was it the transfer of of KE from the car to the wall particles that did this? Or the force exerted onto the wall by the car? Or the transfer of momentum from the car to the wall’s particles?
What actually causes the wall to break in the collision?
 A: When a car collides with the wall or a concrete retaining wall two things happen.
-The car starts to crumple and in better built cars, absorbs a lot of energy of the collision in sacrifice parts designed to collapse while absorbing a lot of the energy.
-A fast moving stress wave starts to expand rapidly in the wall and will find almost immediately the existing weak points such as grout joints, existing cracks, sudden changes in geometry, fatigue hair lines, and will blow them apart by mostly vibrating them in totally incongruent frequencies.
Many of the random appearing break patterns are but the weakest face and or the outcome of the an original hair crack hit by another ricochet shockwave echoing back from a part of the wall that has been vibrating with just the right frequency and intensity. This process continues till enough mass has been obliterated that has taken almost all the energy of the collision. 
A: The kinetic energy of the car is absorbed by the wall materials breaking molecular bonds and generating heat. 
From the work energy theorem, the net work done on the car by the wall (average force time distance) equals the change in kinetic energy of the car. Since the force exerted by the wall on the car is in the opposite direction of the movement of the car, the work done by the wall on the car is negative, meaning energy is transferred from the car to the wall. That energy is dissipated as heat in (and some sound from) the wall.
Hope this helps.
A: The other answer deals with the classical view, so as an extension, I will give you a more QM explanation.
The materials you talk about are mostly solids, like the wall, car's metal etc. These solids have certain lattice structures, where the molecules and atoms are in certain relative positions, and these relative positions can hardly change. 
The bond that bonds the atoms into the molecular structure of the lattice in the metal and the wall is called covalent bond (some residual effect of the EM force). This bond means that certain electrons, will exist around the whole molecule rather then the single atoms.
And yes, it is this effect of the EM force that keeps the atoms in the molecule, and the lattice. Now if you want to brake the lattice (brake the wall), then you need to apply enough energy to brake the covalent bond.
When the car hits the wall, the kinetic energy of the car's matal's molecules and atoms is enough to brake the wall's atoms out of the covalent bond of the wall. The metal of the car has a lattice that is even more tough, strong. The metal atoms will stay in the lattice more likely, and together they make sure that the kinetic energy is transferred onto the wall's molecules and atoms, and since this level of kinetic energy reaches the limit, where the wall's lattice's atoms will lose the covalent bond, the wall will fall apart.
So there are two effects:


*

*the kinetic energy needs to be enough to brake the atoms out of the covalent bond from the wall's lattic

*the lattice's covalent bond of the car's metal is just tougher, stronger then the wall's lattice's covalent bond
You can see this if you try to brake the wall with let's say another material, a wooden car or a plastic car or a glass car or a ceramic car. That will never brake the wall (completely), however hard you hit the wall with it.
