COMSOL 6.4 - Introduction to Explicit Dynamics

The time stepping for a structural dynamics analysis, that is a Time-Domain Analysis that includes inertial forces, can be made using either implicit or explicit methods. The fundamental difference between the two is that implicit methods require global equilibrium of forces to be established before advancing the solution in time, while explicit methods do not. Not requiring equilibrium greatly simplifies the computations of each time step for explicit methods, however, it comes with a distinct caveat, the stability of the method is conditional on the size of the time step. The stable time step is determined by factors such as the mesh and material properties. As a consequence, solving a time history using an explicit method typically amounts to taking many cheap but small increments in time, which can be costly for long duration events. This limitation is not shared by implicit methods where, in theory, the size of the time step is only limited by the required accuracy in time. In practice, other factors, such as the convergence of the nonlinear solver used to establish the global equilibrium, limit the step size also for implicit methods.

For many structural problems, implicit methods are the most efficient, robust, and widely used approach, so also in COMSOL Multiphysics. However, for certain conditions implicit methods struggle, for example:

The above conditions typically results in more nonlinear iterations and smaller time steps, increasing the overall cost of implicit solution. Often, it may also be difficult to establish equilibrium at all causing a premature termination of the solution. Here is where explicit methods has a clear advantage and can be the preferred choice.

Problems suitable to solve using explicit time stepping generally involves short duration events, but explicit dynamics can also be used to solve nonlinear quasistatic problems. A summary of typically situations that may warrant the use of explicit dynamics is given below

Many models will include a combination of the above. For example, a postbuckling analysis by definition involves geometric nonlinearity, but the large deformations often also leads to severe plastic deformations, and contact is typically required to handle self-intersections.