I have tried with the following enhanced interpolation matrix (9+3):

This gives indentical results with SOLID185, (KEYO(2)=2 and KEYO(6)=0) when the hexahedral is perfect cube and traditional 2x2x2 Gaussian quadrature rule is used and same 6×6 transformation matrix T_0 is used than in Andelfinger and Ramm([321]  paper.

However when the hexahedral element is initially parallelepiped or arbitrarily distorted there is difference between the results so this enhanced interpolation matrix M_xi is not correct one.

I also tried this 9+4 version of the enhanced interpolation matrix, but it gives almost identical results with the above one:

I have read many PhD theses and scientific publications about these EAS methods, but I haven’t yet found the 9+4 version for the enhanced interpolation matrix which is mentioned in the Ansys Theory manual.

Could someone explain or show what is the correct form for the matrix and are there other aspects to consider ? This isn’t explained in the Ansys Theory Manual clearly.

Best regards,