Extrapolation of results from Integration points to nodes.

In Abaqus the direct solution variables like displacement, temperature etc. are calculated directly at nodes. But the quantities like stress etc are calculated at so called material integration points. These points do not lie on the nodes but rather at an offset inside the element from the nodes.

In Abaqus Viewer you can request such results at integration points or at the nodes. When requested at nodes, the Viewer follows the following steps to extrapolate the results to nodes.

1. The tensor components are extrapolated from the integration points to the nodes.
2. For each element surrounding a node, the invariants are independently calculated using the corresponding unaveraged, extrapolated values.
3. The independent values of the invariant are then averaged to get a single value at the node.
   

As an example, lets consider the Stress tensor output. The above steps will then become:

1. S11, S22, S12, etc. are extrapolated from integration point to nodes.
2. For each element sorrounding the node, the invariants of stres tensor, MISES, TRESC, PRESS, INV3, are calculated seperately.
3. Then these independent values are averaged based on the threshold value set.