"Plane Remains Plane" boundary condition in Abaqus

Equation constrain is quite limited, and can only consider the dofs of participating nodes. However, since it considers linear relationship among constrained nodes, therefore, it could be erroneous when large rotation is involved. 

 For the constraint type Plane remains Plane, you first would need to orientation three orthogonal axes for the plane. One axis is simply the surface normal to the plane. The other two can be arbit but in plane with your plane. Now you would need to constrain all motions that would subject nodes on the plane to move out of plane. 

With equation constrain, it could be quite messy to do so. On the other hand, if you have your surface normal aligned with any of the global axes, then you could use kinematic coupling (in other cases you may need to erect your own system using *orientation keyword).

For example, let say you've n nodes (1, 2, ..., n), and you chose node 1 as master (reference node), and added remaining nodes (2,..., n) in set SLAVE. All your nodes lie in YZ plane (where XYZ are any axes you created or could be global axis). So, for YZ plane to remain plane at any deformation you would need following things to be satisfied>

1) If it is pure translation along X (out of plane), all nodes should move equally.

2) If it is pure rotation about any axes other than X (i.e., rotation about Y or Z), the nodes should move such that they remain in plane.

Using kinematic coupling you can do it very easily as:

*Kinematic Coupling, Ref Node = Referene node

 SLAVE, 1, 1

 SLAVE, 5, 6

This will be valid even in case of large rotation. 

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The world started with 0, is progressing with 0, but doesn't want 0.