Subcycling: Treatment of Submodel Interface Nodes cont.

To try to understand the algorithm implemented in LS Dyna, we have also analysed the energy transfer throughout the system in Figure 4. Once the half sine velocity pulse has been fully applied to system (after 0.01ms), a nominal change in energy is observed.

However, once again if we look to compare the simulation with the CONTROL_SUBCYCLE_2 keyword, one observes an increase in total energy when the pulse interacts with the interface (around 0.03ms). From Figure 5, it is evident that there is a transfer of energy at the time of arrival of the pulse at the interface, leading to an increase followed by decrease in internal energy, simultaneously an increase and decrease in kinetic energy. This oscillation is not seen when the CONTROL_SUBCYCLE keyword is removed.

The .k can be provided upon request of the benchmark for your reference, and potential testing on other LS-Dyna solvers. The current solvers I have tried/have access to are:

*ANSYS 2020R2 LS-DYNA Student 12.0.0\LS-DYNA\lsdyna.exe*

*LSDYNA\program\ls-dyna_smp_d_R11_0_winx64_ifort131.exe*

Both solvers show this increase in velocity at the interface nodes. It should also be noted that we have observed similar erroneous results for benchmarks with:

- Larger K Values for CONTROL_SUBCYCLE_K_L
- Compressive Loading – Increased velocity magnitude (-ve) at the interface nodes
- Loading from “Coarse” Domain – Erroneous decrease at the interface nodes

As a result, would it be possible to have the following questions answered in this enquiry:

- Does the algorithm introduce corrective internal forces or is it solely the prescription of velocities?
- Is there any special treatment mass for those nodes on the interface?
- Is there any literature aside from [1-4] that are utilised in the development of the algorithm inside Dyna that may help explain these erroneous interface values?

Thank you for taking the time to read our enquiry, we look forward to your reply.

Kin

[1] Borrvall, T., Bhalsod, D., Hallquist, J. O., & Wainscott, B. (2014). Current Status of Sub-cycling and Multi scale Simulations in LS-DYNA. In 13th International LS-DYNA Users Conference.

[2] T. Belytschko and R. Mullen, Explicit integration of structural problems, in P. Bergen et.al. (eds.), Finite Elements in Nonlinear Mechanics, Vol. 2, (1977), pp. 697-720.

[3] T. Belytschko and Y.Y. Lu, Explicit multi-time step integration for first and second order finite element semidiscretizations, Computational Methods of Appl. Mech. and Engrg., 108 (1993), pp. 353-383.

[4] P. Smolinski, S. Sleith and T. Belytschko, Stability of an explicit multi-time step integration algorithm for linear structural dynamics equation, Computational Mechanics, 18 (1996), pp. 236-244.