The semi-Implicit method is a solution scheme in which the analysis starts out using an implicit solution approach but transitions to a semi-implicit solution approach when the implicit solution fails to converge. This is a hybrid method with some features from both the traditional implicit finite element method and the traditional explicit finite element method.
Similar to the explicit method, the semi-implicit approach relies on central difference time integration. This guarantees a solution for every substep of the semi-implicit solution phase. (A guaranteed solution is not possible with the implicit method since it requires Newton-Raphson iterations.)
Similar to the implicit finite element method:
The semi-implicit method has fully coupled nodal acceleration and, hence, involves solving a set of coupled equations at every substep (unlike the explicit method).
Lagrange multiplier-based constraints and mixed element formulations (mixed u-P based solid elements) are supported.
The semi-implicit method uses a bisection scheme.
The semi-implicit method is recommended for problems that, due to extreme nonlinearities, experience a brief period during which they cannot converge in the implicit solution. For example, snap-through problems, models with local buckling, analyses in which temporary rigid body modes are activated, and models with sudden changes in material constitutive behavior can all benefit from the semi-implicit method. For the brief period of extreme nonlinear behavior, the solution uses the semi-implicit solution scheme. The analysis may or may not transition back to the implicit method, depending on a user-specified criterion for time spent in the semi-implicit phase.
The following semi-implicit topics are available: