Mass Scaling in LS-Dyna

Objective: To perform the simulation by reducing and stabilizing the runtime with the help of a mass-scale factor.

Mass scaling:

In an explicit method, the time step usually is tiny to maintain numerical stability. However, small step size prevents this method from being useful for routine analysis work. Mass scaling is often used to reduce the CPU cost and improve the performance to increase the time step size in each cycle. Several methods can be used with LS-DYNA to accomplish this. The simplest method is to use a large mass density for the blank. Alternatively, the user may specify the desired minimum time step size in *CONTROL_TIMESTEP.

Mass-scaling is a technique whereby nonphysical mass is added to a structure to achieve a larger explicit timestep. One can employ mass scaling manually by artificially increasing the material density of the parts. This manual form of mass scaling is done independently of the automatic mass scaling invoked by DT2MS in *CONTROL_TIMESTEP. When DT2MS is input as a negative value, mass is added (with a safety factor) only to those elements whose timestep would otherwise be less than TSSFAC * |DT2MS|. By adding mass to these elements, their timestep becomes equal to TSSFAC *|DT2MS|. The trend is that the smaller the TSSF, the greater the added mass. In return, stability may improve as TSSF is reduced (just as in non-mass-scaled solutions).
If stability is a problem with the default TSSF of 0.9, try 0.8 or 0.7. If you reduce TSSF, you can increase |DT2MS| proportionally so that their product, and hence timestep, is unchanged.

The difference between using a positive or negative number for DT2MS in*CONTROL_TIMESTEP is as follows:
Negative: Mass is added to only those elements whose timestep would otherwise be less than TSSF*abs(DT2MS). When mass scaling is appropriate, I recommend this method.
Positive: Mass is added or taken away from elements so that the timestep of every element is the same. My opinion is there is no advantage to using this method over the negative DT2MS method.

Procedure:

• Import the given keyword file in the LS-PrePost.

Fig 1: Geometry and mesh information in the keyword file.

Fig 2: Fully defined desk with all the necessary keywords.

Explicit Analysis(With Mass-scale):

Case 1: DT2MS: -3.5E-5 & TSSFAC: 0.9:

• Open the TIMESTEP card in the control deck.
• Since DTMS and TSSFAC are the essential parameters in the *CONTROL_TIMESTEP card that transforms the simulation's timestep and runtime.
• To do that, we could change these values in each iteration to obtain an optimized runtime with a stable solution and to make sure mass scaling accomplishes 8%.

DTINIT - Initial time step size (Default)
TSSFAC - Scale factor for computed time step
DT2MS - Time step size for mass scaled solution

• For the first case, the values are left as it is.

Fig 3: Timestep card and its values.

• Open the Start LS-Dyna analysis, browse the keyword file, and hit run to run this keyword file.

Fig 4: LS-Dyna analysis browser.

Fig 5: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is 21 hrs 19 mins. As a result, there is no mass added with a given DT2MS of -3.5E-05; this can be varied by changing the values of DT2MS and TSSFAC.

Case 2: DT2MS: -3.5E-5 & TSSFAC: 0.7:

• The value of the TSSFAC is changed to 0.7, and the analysis is run.

Fig 6: Timestep card and its values.

Fig 7: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is increased to 27 hrs 51 mins, as a change in TSSFAC=0.7 leads to a rise in timing. However, we can see that the mass-scale factor still pertains to zero.

Case 3: DT2MS: -6.5E-5 & TSSFAC: 0.9:

• The values of the DT2MS and TSSFAC are changed to -6.5E-5 and 0.9, respectively, and the analysis is run.

Fig 8: Timestep card and its values.

Fig 9: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is decreased rapidly to 12 hrs 10 mins.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.5E-05 with a percentage of mass increase in 5.7852E-02.
• Since the added mass exceeds the limit, the energy values also vary considerably. Values need to be increased.

Case 4: DT2MS: -6.5E-4 & TSSFAC: 0.9:

• The value of the DT2MS is changed to -6.5E-4, and the analysis is run.

Fig 10: Timestep card and its values.

Fig 11: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is decreased rapidly from 12 hrs 10 mins to 1 hrs 13 mins.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.5E-04 with a percentage of mass increase in 3.7311E+03.
• Since the added mass exceeds the limit, the energy values also vary considerably. Values need to be reduced.

Case 5: DT2MS: -1.5E-4 & TSSFAC: 0.9:

• The value of the DT2MS is changed to -1.5E-4, and the analysis is run.

Fig 12: Timestep card and its values.

Fig 13: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time increased from the previous case to 7 hrs 4 mins.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.500e-04 with a percentage of mass increase in 1.1432E+02.
• Since the added mass exceeds the limit, the energy values also vary considerably. Values need to be reduced slightly.

Case 6: DT2MS: -1.1E-4 & TSSFAC: 0.9:

• The value of the DT2MS is changed to -1.1E-4, and the analysis is run.

Fig 14: Timestep card and its values.

Fig 15: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is 11 hrs 56 mins.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.1E-04 with a percentage of mass increase in 2.0393E+01.
• Since the added mass exceeds the limit, the energy values also vary considerably. Values need to be reduced slightly

Case 7: DT2MS: -1.01E-4 & TSSFAC: 0.9:

• The value of the DT2MS is changed to -1.01E-4, and the analysis is run.

Fig 16: Timestep card and its values.

Fig 17: Added mass and percentage increase is shown at the beginning of the solution.

• The above image shows a slight decrease in the computational time to 7 hrs 50 mins.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.01E-04 with a percentage of mass increase in 6.9297E+00.
• Since the added mass lessened the limit, the energy values also varied considerably. Values need to be reduced slightly.

Case 8: DT2MS: -1.029E-4 & TSSFAC: 0.9:

• The value of the DT2MS is changed to -1.01E-4, and the analysis is run.

Fig 18: Timestep card and its values.

Fig 19: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time remains almost the same as 7 hrs 41 mins.
• After many iterations, TSSFAC=0.9, DT2MS of -1.029E-4 attains the percentage of mass around 8.0050E+00.

The mass scaling can be done by changing the TSSFAC values, and The TSSFAC values will generally range between 0.5 to 0.9.

Case	DT2MS	TSSFAC	Mass added	Computational Time
1	-3.5E-5	0.9	0.00E+00	21 hrs 19 mins
2	-3.5E-5	0.7	0.00E+00	27 hrs 51 mins
3	-6.5E-5	0.9	1.6462E+04	12 hrs 10 mins
4	-6.5E-4	0.9	1.0617E+09	1 hr 13 mins
5	-1.5E-4	0.9	3.2530E+07	7 hrs 4 mins
6	-1.1E-4	0.9	5.8027E+06	11 hrs 56 mins
7	-1.01E-4	0.9	1.9718E+06	7 hrs 50 mins
8	-1.029E-4	0.9	2.2778E+06	7 hrs 41 mins

Computational time vs. DT2MS plot:

Explicit Analysis(Without Mass-scale):

• The timestep card should be deleted to perform explicit analysis without mass scaling, and the analysis is run.

Fig 20: Timestep card is removed from the control deck.

Fig 21: Added mass and percentage increase is shown at the beginning of the solution.

• From the above image, the computation time is about 21 hrs 19 mins.

Implicit Analysis:

• LS-Dyna solver utilizes an Explicit method for all the FE models. To perform an Implicit method, the solver needs the following keywords to change from Explicit to Implicit analysis.
• Add CONTROL_IMPLICIT_AUTO card with the following values.
  

IAUTO: Automatically adjusts the time step size.
ITEOPT: Optimum equilibrium iteration count per time step.
ITEWIN: Allowable iteration window. If the iteration count is within ITEWIN iterations of ITEOPT, the step size will not be adjusted.

Fig 22: Implicit_auto card is added.

• Add CONTROL_IMPLICIT_General card with the following values.

IMFLAG - Implicit/Explicit analysis type flag: 1- implicit analysis.
DT0 – Initial time step size for implicit analysis (Termination time/100).
IMFORM - Element formulation flag for seamless spring back: 2 retain original element formulation (default).

Fig 23: Implicit_general card id added.

• There is no mass added during the computational time from the above image, also attached with CONTROL_TIMESTEP.
• In this method, the computation time is about 4 seconds maximum for this setup case.

Explicit vs. Implicit:

Explicit FEM is used to calculate the state of a given system at a different time from the current time. In Implicit analysis, each time step has to converge, but we can set pretty long time steps, and it is based on iterations. On the other hand, explicit doesn't have to converge in each time step, but for the solution to be exact, time steps must be small. The running time for implicit analysis is shorter than the explicit analysis method because the timestep is defined more in implicit than explicit analysis, and we have used constant timestep formulation.

Conclusion: From the above cases, mass scaling was obtained 8% by varying the DT2MS values along with TSSFAC.