Solution verification for explicit transient dynamics problems in the presence of hourglass and contact forces

This paper presents solution verification studies applicable to a class of problems involving wave propagation, frictional contact, geometrical complexity, and localized incompressibility. The studies are in support of a validation exercise of a phenomenological screw failure model. The numerical simulations are performed using a fully explicit transient dynamics finite element code, employing both standard four-node tetrahedral and eight-node mean quadrature hexahedral elements. It is demonstrated that verifying the accuracy of the simulation involves not only consideration of the mesh discretization error, but also the effect of the hourglass control and the contact enforcement. In particular, the proper amount of hourglass control and the behavior of the contact search and enforcement algorithms depend greatly on the mesh resolution. We carry out the solution verification exercise using mesh refinement studies and describe our systematic approach to handling the complicating issues. It is shown that hourglassing and contact must both be carefully monitored as the mesh is refined, and it is often necessary to make adjustments to the hourglass and contact user input parameters to accommodate finer meshes. We introduce in this paper the hourglass energy, which is used as an “error indicator” for the hourglass control. If the hourglass energy does not tend to zero with mesh refinement, then an hourglass control parameter is changed and the calculation is repeated.