Tech Briefs

Explicit-Implicit Integration in Dynamics with ADINA

The ADINA System has been developed to provide one computational engineering software for the simulation of solids and structures, fluids, thermal problems, and their multiphysics interactions — all capabilities in one software system, complete with a graphical pre- and post-processor and interfaces. The multiphysics interactions include fluid-structure interaction, and thermo-mechanical and thermo-fluid coupling.

Reliable element formulations and algorithms are used throughout. The same reliable element formulations are used in all analysis types whether static, implicit dynamic, explicit dynamic or harmonic. This makes the switching (through restarts or otherwise) between different analysis types direct and also very reliable.

Here we focus on the switching back and forth between implicit integration and explicit integration in dynamics, to capture the advantages of each analysis type in different parts of a simulation. This switching can be a problem using other programs because of the different element formulations, etc., typically used for implicit and explicit analyses. With the ADINA System, this switching is seamless. For more details on the coupling of implicit and explicit dynamic time integration schemes, refer to Section 9.2.5 of the Finite Element Procedures book referenced below.

A typical example from the sheet metal forming industry involves restarting from explicit to implicit integration at the end of a forming process to simulate springback.

Here we present an illustrative example of dynamics involving multiple impacts between a block and a cantilever beam. The simulation shown in the above movie uses overall implicit integration but explicit integration close to and in each impact event to accurately capture the abrupt changes during impact.

Tip displacement of cantilever

For this example, the simulation using ADINA can be performed completely with just implicit integration or just explicit integration, but the analysis is more efficient with this temporary switching during the times of impact.

The use of the ADINA explicit-implicit integration in dynamic simulations, with the parallel processing offered, can clearly lead to very effective and reliable solutions of many problems.


  1. K.J. Bathe, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ, 1996.