Periodic Boundary Conditions vs Homogenous Boundary Conditions in 2D RVE

Hello all,

I want to simulate loading of 2D RVE of dual phase steels, by giving individual phases properties, to get homogenised mechanical properties like yield strength,  % elongation etc, using micromechanics based approach. Litterature shows people have used two kinds of boundary condition viz. Periodic boundary condition and homogenous boundary condition for this case. My doubt is two folds:

1) What is the theoretical difference between these two kinds of boundary conditions? 

2)  how to apply these boundary conditions in a finite element framework, along with loading?. Specifically, I am interested to know what are the boundary condition on the 4 corner nodes of RVE, and how to apply loading?

Thnks in advnce,

Danish.