Introduction

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In RADIOSS, both implicit and explicit time-integration schemes are available to you. In an explicit scheme, velocities and displacements are obtained by direct integration of nodal accelerations. With this approach, the cycle time step is often small, due to stability considerations. Therefore, for static or slow dynamic computations where the duration of the study is long, many cycles are necessary to carry out the simulation. An alternative to explicit method in such cases is the implicit time-integration scheme. It can be shown that the implicit scheme is unconditionally stable, resulting in a larger cycle time step vis-à-vis the explicit method. However, in an implicit scheme, a global stiffness matrix should be assembled and inverted, leading to higher cost and greater memory requirements, per loading step.

An explicit approach is more appealing for fast dynamic problems with highly nonlinear geometric and material behaviors. As all quantities may be treated as vectors, low storage is needed. The number of cycles to achieve simulation may be quite large, but global efficiency is generally observed. The implicit method, on the other hand is more efficient for static applications and/or long duration simulations.

The optimal solution is to have both implicit and explicit methods readily available in the same code. In addition, implicit and explicit solvers in RADIOSS share the same routines for internal force computation; thus enabling seamless switching between the two schemes without an out-of-balance issue during the transition. Therefore, the two schemes can be coupled to run multi-stage analyses such as spring-back (implicit) after sheet metal forming (explicit), or gravity loading/initial state computations (implicit) before crash simulations (explicit).

Although implicit scheme is unconditionally stable, it is not unconditionally convergeable (nonlinear case). In fact, it is generally less robust than explicit scheme and requires more user involvement.

In this section, available implicit features for different implicit analyses are first presented; followed by a list of keywords required to activate implicit simulation. In addition, some details are given to better understand and to efficiently use the various implicit options. Finally some output messages and troubleshooting techniques are listed.