Subcycled hourglass control for explicit time integration of finite elements

Explicit methods, such as the central difference operator, rely on the economical evaluation of internal forces at each time step. One-point quadrature provides the greatest efficiency, but hourglass control is required to eliminate spurious zero energy modes. To be computationally practical, hourglass control involves considerable approximation in the spatial integration of the element. Consequently, the precision of the temporal integration of the hourglass force may be relaxed without seriously affecting the accuracy of the analysis. The central difference method requires a minimum time step to ensure stability, and hence the possibility of evaluating the hourglass terms on a larger time interval could provide significant efficiencies. This is basically a subcycling approach applied to the hourglass portion of the problem, rather than to a spatial subdivision of the problem based on element size. The proposed approach is examined in detail with the use of one and two degree of freedom mass-spring analogies. The implementation into an explicit finite element program is demonstrated on a three-dimensional example, and the merits are discussed.