Advanced Averaging
Advanced averaging means that tensor (or vector) results are transformed into a consistent system and then each component is averaged separately to obtain an average tensor (or vector).
Where, are tensors transformed to the reference system for corners A2, B1, C3, and D4, respectively.
The components are extracted and the invariants are computed from this averaged tensor or vector .
Element Type  Reference System  Projection Rule  Description 

Solid  Global  N/A  All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector as explained above. 
Userdefined  N/A  Variation ON All corresponding tensors and vectors are transformed to the userdefined coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the userdefined system for components extraction and invariants calculation. 

Shell  Global  ON  The global coordinate system is projected to the Nodal Projection plane
(described in the Projection rule) to obtain the Nodal Projection system. All
corresponding tensors/vectors are then transformed to the Nodal projection system
and an average tensor/vector is calculated. The components and invariants are
obtained from this tensor/vector. As a result, even if the reference system is the same, the projected systems in participating elements can be different. Simple averaging for components ignores variations in systems. 
OFF  All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector.  
Userdefined  ON  The userdefined coordinate system is projected to the Nodal Projection
plane (described in the Projection rule) to obtain the Nodal Projection system.
Variation ON All corresponding tensors/vectors are then transformed to the Nodal projection system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the Nodal projection system for components extraction and invariants calculation. 

OFF  Variation ON All corresponding tensors and vectors are transformed to the userdefined coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the userdefined system for components extraction and invariants calculation. 
Valid reference coordinate system: Global and Userdefined.