Combined implicit/explicit algorithms for crashworthiness analysis

In order to simulate an industrial process, an explicit method, which is conditionally stable, is the most adapted while the non-linearities evolve rapidly (impact phase, stamping process, etc.). But when the dynamics becomes quasi-linear (post-impact analysis, springback simulation, etc.), an implicit method, which is iterative, presents the advantage of unconditional stability. The optimal solution is then to have both implicit and explicit methods readily available in the same code and to be able to switch automatically from one to the other. Criteria that decide to switch from one method to another, depending on the current dynamics, have been developed. Implicit restarting conditions are also proposed that annihilate numerical oscillations resulting from an explicit calculation.