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.