Hi,

I observed that with
periodic boundary conditions on unit concrete unit cell, when uniaxial load is applied structure
behaves as if it is constrained to move in lateral direction, when
shear or other traction laoding is applied it has displacement
compatible behavior i.e, parallel edges has periodic deformation
behavior. With these above behavior can I conclude that for uniaxial
loading I need not apply periodic BCs and simply applying roller is
sufficient on lateral edges or there is no need to apply and periodic
BCs for uniaxial loading.

In the attached paper (accepted for publication), we present enriched FE formulations to impose Bloch-periodic boundary conditions. Bloch-periodic BCs arise in the description of wave-like phenomena in periodic media: periodic composites, Schrodinger equation in quantum mechanics, photonic band-gap materials, etc. For a perspective, see the J-Club on elastodynamic bandgaps and metamaterials that was organized by Biswajit Banerjee