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Is there a way to couple nodes using periodic boundary conditions?

I am working on a project where we are trying to homogenize a honeycomb material using unit cells.


The displacement of the nodes at the first boundary of the unit cell should be the same as at the opposing boundary.

From a textbook:


In each of the first three load cases a uniform compression deformation of 0.01 mm is applied. All nodes on the two boundary surfaces which limit solid in x-dimension are connected with couplings in their y-displacement (y(0,y,z) = y(ux,y,z)). Amount and direction of their y-displacements are thus equal. The same nodes have to be connected by constrain equations in their x-displacement (x(0,y,z)+x(ux,y,z) = 0), resulting in an equal amount of displacement in the opposite direction.
All nodes on the boundary surfaces in which limit the solid in y-dimension are coupled in x-displacement and connected by constrain equations in y-displacement.
Furthermore, the nodes are coupled in z-displacement, but the nodes at the upper and lower surfaces of the unit cell are not coupled.
These periodic boundary conditions according to the homogenisation theory ensured that the deformed surfaces would still fit perfectly together. The homogenisation theory assumes that the unit cell is imbedded within an infinite array of identical unit cells and displacements or forces are imposed at infinity, then every unit cell will deform identically.




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I am working on a project where we are trying to homogenize a material using unit cells like you.

I used two kinds of BC: they are Kinematic uniform and periodicity BC.

I use Zebulon, not HyperWork.

I think first you should begin with KU and after that with PBC because As far as I know PBC = KU + v, where v is a periodic fluctuation. 

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You can consider Mat LAw 28 for modelling honeycomb material in RADIOSS.
Concerning the question about periodic boundary conditions:
We have multi-point constraints for nodes but I think it would be a lot of work to define all the MPC for a large number of elements. 
Please go through Multi-Point Constraints (/MPC) in the Help Menu for more.

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