Return-mapping algorithm for J2 flow theory

[Prof. S. Govindjee]

Simo's article in the Handbook of Numerical Analysis has the algorithm you want to follow; it is better than earlier versions.  You can also use the article to follow the implementation in FEAP which is nearly identical.

[Sun]

Many thanks to Prof. Taylor and Prof. Govindjee for your advice.
I took a closer look to the publications and could find a few bugs in my source code. Before I tried to describe the plasticity with Cauchy stresses, because these are true stresses. In doing so I made a few mistakes with the determinant of deformation gradient (det(F) and det(Fe)). After reading the books I tried to implement plasticity with Kirchhoff stresses. With this implementation I could obtain convergent solutions.

Best regards and many thanks

Sun