Defining perioidc BC for 1 element elastic model for Biaxial pull in ABAQUS

For simplicity in understanding Perioidic BC in ABAQUS, I am trying to implement in a single element elastic model.

Material is elastic. There are two reference points defined Refpoint 1 for x-direction pull and Refpoint 2 for y-direction pull. Please find the attached picture for clarity in the model.

I have defined the equations for PBC in ABAQUS as below:

x1-x2+Refpoint1=0

y1-y2+Refpoint1=0

x3-x4+Refpoint1=0

y3-y4+Refpoint1=0

x2-x3+Refpoint2=0

y2-y3+Refpoint2=0

x4-x1+Refpoint2=0

y4-y1+Refpoint2=0

I get the following error:

2 nodes are missing degree of freedoms. The MPC/Equation/kinematic coupling constraints can not be formed. The nodes have been identified in node set ErrNodeMissingDofConstrDef.

This happens because of defining constraint for the same node repeatedly. But in my case I have not done still I get error.

In this model for defining the perioidic boundary conditions, can  anyone please help in writing the 8 equations ?

AttachmentSize Single element elastic model with 2 ref points modelled in ABAQUS7.48 KB

Hi

Hi

If you check the constraint equation , you can see for example you relate the x1 to x2, then x2 to x3, x3 to x4 and then x4 to x1!! I think this kind of constraint equations leads to the mentioned erorr! I suggest use the method propsed by Kouznetsova, V.G in following refrence : Kouznetsova, V.G. 2002 Computational homogenization for the multi-scale analysis of multi-phase materials.

This method is easy to implement in finite elemnt software like ABAQUS. 