I'm currently using a predefined stress field to represent the residual stress within a part. This requires dividing the part into discrete partitions and imparting a stress field on each partition. The result of this is a piecewise approximation of the true residual stress field that I would like to represent. I've then found it necessary to include an analysis step which allows the stress field to reach equilibrium, since my piecewise approximation doesn't quite leave it exactly in equilibrium. 

Is there a way to use an equation to represent the stress field instead of needing to do a piecewise approximation? Am I missing some other approach to defining the residual stress field?

Abaqus ​​​​​​​