Why is a force distributed over an area? Why couldn't the stress be directly equal to the force? So, my question might seem silly. I know in real life when we apply a force with our hand and push on lets say a cylinder , we know the force will be distributed over the cross section of the area, so if we had a wider area, we need more force, and if we had smaller area, then we need less force to push the cylinder a certain distance.
So its intuitive. The stress will be the force divided by the given area.
But why? like what happens at the micro-scale, and what makes the force be divided?
Thanks.
 A: You have a misunderstanding: the force is only on the area your hand touches, if you do it with your fingertip only the area of the fingertip counts, not the area of the cylinder. Thats why you can get a nail with very small area in wood, but not  your finger.If you push wit your fingertip you need more force than with your  flat hand.
A: Actually as @trula said the external force you apply acts only at the contact point but since all atoms are connected to each other via "interatomic forces" , your external force gets distributed all along the surface and so we need to define force per unit area viz. Stress.
The spring model of atomic structure is quite self explanatory about the interatomic force distribution.

A: The answer comes from the fact that every part of an object must be in force equilibrium regardless of the location or shape considered. Additionally, the internal deformation due to these internal forces must be smooth and continuous inside a homogeneous material.
So you cannot have a single line of molecules loaded under the contact all the way to the support because the internal deformation will not be continuous. Depending on the material properties this spreading out of the applied force happens more or less on all materials.
There is a concept of load path, where the most stressed internal molecules lie in the path between the applied load and the support, but this is just a tool for explaining the observed effects, and not a mathematical description of what is going on.
