 Pirelli93
Subscriber

Hello John,

I understand the difference between mixed u-P and pure displacement formulations when enhanced assumed strain method is used. I know how to implement/use these different formulations in Ansys Mechanical, but I want to know what is the specific theory behind the Enhanced Assumed Strain method, SOLID185 with KEYO(2)=2 and KEYO(6)=0. From which paper or book I can find this spesific theory ?

The thing is that I have calculation “code” snippet in symbolic math software and I’m able to get identical results with Ansys for the Simplified Enhanced Assumed Strain (KEYO(2)=3 and KEYO(6)=0) with the method described in Andelfinger and Ramm( paper, but I can’t get identical results for Enhanced Assumed Strain method (KEYO(2)=2 and KEYO(6)=0), because I don’t know what specific EAS- version or theory it uses.

1. When SOLID185 is used with KEYO(2)=2 and KEYO(6)=0, is the special 9-point (2x2x2 + 1) or 27-point (3x3x3) or standard 8-point (2x2x2) Gaussian quadrature used for calculating stiffness matrix  ?

2. Is the transformation matrix T_0 (6×6 matrix, used for the enhanced interpolation matrix M_xi) the same as in Simplified Assumed Strain method ?

3. What is the enhanced interpolation matrix M_xi for the Enhanced Assumed Strain ? I haven’t found M_xi matrix where is 9+4 enhanced parameters. I have only found 9+3 version and additionally Andelfinger and Ramm( paper’s possible choices for M_xi: 9 (EAS-9), 9+6 (EAS-15), 9+12 (EAS-21), 9+21 (EAS-30).

4. There are also many different versions for calculting the gradients / “B-matrices”. For example calculate gradients in the element centroid, calculate the average of the gradients, use and multiply the relation of jacobian determinants det(J(0,0,0))/det(J(xi,eta,zeta)), etc… These different versions are for the enhanced assumed strain element to pass the patch test and for example to take account effects of initially distorted elements.

Best regards,

Pirkka 