On the time discretization of equilibrium
Advanced numerical simulation of tubes and plates hydroforming

The discrete system (equation (23)) is non-linear, given the forming process and the thermo-viscoplastic behavior coupled with damage. After assembly, the problem is solved using implicit quasistatic analysis (inertial effects are negligible) or explicit dynamic analysis (damping effects are negligible). The Newton-Raphson scheme uses an incremental technique, which consists in discretizing the total loading into several increments and searching for a succession of configurations corresponding to the different loading steps.

Determining the current configuration C_n+1 from the previous configuration C_n...