Serving the Numerical Simulation community since 1989 
Helpful Hints and Tips: Newton-Raphson Integration Technique for Geometric Nonlinear Analysis
The Newton-Raphson integration technique is recommended when there is strong coupling between membrane and bending effects when analyzing thin domains, and should be used if the Direct Integration technique diverges and/or becomes unstable. The Newton-Raphson integration technique is illustrated for a thin diaphragm with elastic-perfectly-plastic materials under uniform pressure.
Additional example where the Newton-Raphson integration technique is recommended:
StressCheck Tutorial: Linear vs Nonlinear Results for a Single Lap Joint
