Contact and Global Timestep

You may have seen this popular message that is printed out by LS-DYNA for every simulation.

The LS-DYNA time step size should not exceed 0.456E-06
to avoid contact instabilities. If the step size is
bigger then scale the penalty of the offending surface

Lets review this to understand a little more. As we know, Explicit time integration scheme is conditionally stable and the global computing timestep must be less than (LS-DYNA uses a 10% reduction factor) models highest natural frequency. It is difficult to compute the highest natural frequency and so it is approximated using the well known ratio of characteristic length and the sound speed. Contacts in LS-DYNA are treated using the penalty stiffness method (default contact-impact treatment) which uses invisible linear springs between the slave node (or segment for pinball) and the master segment. The stiffness and the mass of the contact springs are computed based on the parent element and its material properties. The computed contact spring stiffness and the mass as used to compute a “contact timestep” much like we do for the traditional spring elements

LS-DYNA loops through all the slave and master surfaces of each contact definition (penalty only) and stores the minimum contact timestep encountered. The contact linear springs are not used in determining the stability timestep but a check is simply made to ensure that they are not too much apart from the global stability timestep. It is common to see the contact timestep an order of magnitude lower or higher than the global timestep without affecting the stability of the solution. However, if the contact timestep is vastly different than the global stability timestep, then contact breakdowns or contact “pushing” will occur that destroys the stability and the accuracy of the model

Recently, I found that it is extremely important to have the contact timestep very close (within 10%) of the global computing timestep when using TIEBREAK contacts (see here and here ) which is a penalty based contact as well in which the tensile and the compressive forces are transmitted until failure. To ensure that the contact timestep is close to the global timestep, it is first important to use default penalty scale factors and use realistic material properties. In case the contact timestep is much lower than the global timestep, it may be necessary to reduce the scale factor only for those surfaces. The offending surfaces can be identified by reviewing the D3HSP file which lists all the slave and master surfaces for each contact definitions. Once the offending surface is found, you can scale the penalties for the parent component using *PART_CONTACT or in *CONTACT keywords.

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