The explicit solution method is a true dynamic procedure originally developed to model high-speed impact events in which inertia plays a dominant role in the solution. Out-of-balance forces are propagated as stress waves between neighboring elements while solving for a state of dynamic equilibrium. Since the minimum stable time increment is usually quite small, most problems require a large number of increments.

The explicit solution method has proven valuable in solving quasi-static problems as well—ABAQUS/Explicit solves certain types of static problems more readily than ABAQUS/Standard does. One advantage of the explicit procedure over the implicit procedure is the greater ease with which it resolves complicated contact problems. In addition, as models become very large, the explicit procedure requires fewer system resources than the implicit procedure. Refer to “Comparison of implicit and explicit procedures,” Section 2.4, for a detailed comparison of the implicit and explicit procedures.

Applying the explicit dynamic procedure to quasi-static problems requires some special considerations. Since a static solution is, by definition, a long-time solution, it is often computationally impractical to analyze the simulation in its natural time scale, which would require an excessive number of small time increments. To obtain an economical solution, the event must be accelerated in some way. The problem is that as the event is accelerated, the state of static equilibrium evolves into a state of dynamic equilibrium in which inertial forces become more dominant. The goal is to model the process in the shortest time period in which inertial forces remain insignificant.

Quasi-static analyses can also be conducted in ABAQUS/Standard. Quasi-static stress analysis in ABAQUS/Standard is used to analyze linear or nonlinear problems with time-dependent material response (creep, swelling, viscoelasticity, and two-layer viscoplasticity) when inertia effects can be neglected. For more information on quasi-static analysis in ABAQUS/Standard, see “Quasi-static analysis,” Section 6.2.5 of the ABAQUS Analysis User's Manual.