Microscopic origin of plasticity I was taught there are two types of materials: elastic and plastic [majorly, excluding everything in between], where elastic means the strain created on applying stress is relieved by the body and plastic means the strain is permanent.
My question: What is the microscopic origin of plasticity? 
According to the model of atoms and molecules i use to picture, all molecules are oscillating about the equilibrium position, the equilibrium being determined the potentials (or forces) between molecules within the material. So in the very basic model, there should only be perfectly elastic materials because once the external stress is removed, the equilibrium should essentially be re-obtained from newton's laws or schrodinger equation or whatever because the situation is essentially as if there was no stress in the first place. 
Obviously, this model is far, far away from truth if it predicts there are no plastic materials at all!!!
Bonus question: What's wrong with this model of potentials and forces and equilibrium that can be obtained. 
 A: Imagine a perfect crystal lattice of a material. You are right to assume that under elastic deformations, the bonds between the atoms would strain and provide the elastic force. However, if the deformations are too strong, atoms will shift by one row, jumping to the next equilibrium positions that are there due to the crystal symmetry. This "jump" is called a dislocation.

Dislocations were the exact microscopic mechanism that was found to be responsible for the plasticity of metals. To understand why dislocations make metals yield at much lower stresses, look at another picture of a dislocation in a large crystal.

In a large perfect crystal that has $N$ atoms along one of its dimensions, you have to break $N$ atomic bonds to shift the top half of the crystal by one row. However, if a dislocation is present, you can move the dislocation one atom at a time, each time breaking (and reforming) one atomic bond, then the next one, and so on. This requires much lower stresses.
I should note that dislocations are not remotely exotic: dislocations are present in (almost) every material, and the best dislocation-free samples that researchers have created are less than a millimeter large.
Now, crystal structures of real atoms are usually more complex than a square two-dimensional crystal depicted in the diagrams. Because of this, real crystals have preferred directions of plastic deformations, called slip directions. In the slip directions, atoms are closer to each other than in the othee directions, and atomic bonds are easier broken and reformed.
A: Metals work on a lattice of mostly elemental molecules. You will have a stable array of copper or aluminum atoms arranged in a pattern. The pattern is decided by the properties of the atoms. The website linked below shows some of the unit cells they form.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch13/unitcell.php
I picture them as connected by elastic lines. In metals and ceramics we learned that iron is made stronger by placing carbon atoms in the spaces between the iron atoms, this stretches the elastic lines making the system more rigid.
As far as I understand elastic deformation, when you bend a rod and it returns to it's original shape you are just stretching the elastic lines and they pull it back into shape. Plastic deformation is when you bend it and it stays bent. What I think I remember is this breaks some of the elastic lines and moves some atoms around. Some are left squished together and others are left stretched apart. These residual stresses multiply as you bend the metal repeatedly until they break, like you can break a coat-hanger wire by bending it over and over.
Ultimately the atomic particles are seeking the lowest stable form with respect to the energy  involved. The crystal lattices are the most stable for each atomic cell, when you introduce energy through bending it this rearranges the system and it seeks another stable condition. Given the energy introduced it will seek the most stable condition it can which can be a permanent plastic deformation.
A: A short answer to your question is: the microscopic origin of plasticity is 'rupturing and reformation of atomic bonds'. 
Yes, you are right, atoms are oscillating; but during elastic deformation 'neither the oscillation' nor the stretching of the atomic bonds are large enough to rupture the bond.  
