Week - 8 Mass Scaling

Aim-

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

Objective-

• To understand the motive of a computing time with and without a mass-scale factor.
• By ensuring the stability of mass scaling at 8%.
• Comparing implicit vs explicit runtime.

Basic Theory-

Mass scaling

In an explicit method, the time step usually is very small to maintain numerical stability. However, small step size prevents this method from being useful for routine analysis work. To reduce the CPU cost and improve the performance, mass scaling is often used 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 refers to a technique whereby nonphysical mass is added to a structure in order to achieve a larger explicit timestep. One can employ mass scaling manually by artificially increasing the material density of the parts you want to mass-scale. This manual form of mass scaling is done independently of the automatic mass scaling invoked with DT2MS in *CONTROL_TIMESTEP. When DT2MS is input as a negative value, mass is added (with a safety factor; see note at end of this file) 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-

Case 1 Explicit Analysis(With Mass-scale)

• We have to open the given LS-Dyna keyword (.k file) file in LS-PrePost, using option File>Open>LS-Dyna Keyword File as shown in below snap.

• Since DTMS and TSSFAC are the important parameters in the *CONTROL_TIMESTEP card that transforms the timestep and the runtime of the simulation.
• In order to 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

• Now we will try to run the simulation as per above default inputed values.

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

• From the above image, the computation time is 24 hrs 4 mins. As a result, there is no mass added with given DT2MS of -3.500e^-05, this can be varied by changing the values of DT2MS and TSSFAC

Iterations-2 T2MS: -3.5E-5 & TSSFAC: 0.7

• Now we will change the value of TSSFAC to 0.7 and see what happens to solution time.

• From the above image, the computation time is increased by 5 hrs 33 mins to 29 hrs 37 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 factor.

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

• Here we will change the value of DT2MS and see if we get mass scaling factor.

• From the above image, the computation time for is decreased rapidly from 29 hrs 37 mins to 20 hrs 12 mins, there is a considerable decrease in computational time.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.500e^-05 with a percentage of mass increase in 5.7852E^-02
• Since the added mass the limit is very low, the energy values also vary considerably. Values need to be increased.

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

• Again we will change the DT2MS Value.

• From the above image, the computation time for is decreased rapidly from 20 hrs 12 mins to 1 hrs 37 mins, there is a considerable decrease in computational time.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.500e^-04 with a percentage of mass increase in 3.7311E+03.
• Since the added mass exceeding the limit, the energy values also vary considerably. Values need to be reduced.

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

• From the above image, the computation time for is increased rapidly from 1 hrs 37 mins to 7 hrs 10 mins, there is a considerable increase in computational time.
• 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 exceeding the limit, the energy values also vary considerably. Values need to be reduced.

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

• From the above image, the computation time for is increased slightly from 7 hrs 10 mins to 9 hrs 1 mins, there is a considerable increase in computational time.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.100e^-04 with a percentage of mass increase in 2.0393E+01.
• Since the added mass still exceeding the limit, the energy values also vary considerably. Values need to be reduced.

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

• From the above image, the computation time for is increased slightly from 9 hrs 1 mins to 14 hrs 10 mins, there is a considerable increase in computational time.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.010e^-04 with a percentage of mass increase in 6.9297E+00.
• Since the added mass has reached nearly the required limit, the energy values vary considerably. Values need to be reduced slightly.

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

• From the above image, the computation time for is decreased from 14 hrs 10 mins to 10 hrs 18 mins, there is a considerable decrease in computational time.
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.029e^-04 with a percentage of mass increase in 8.005E+00.
• Since the added mass has reached the required limit.

Histogram for the Above Mass Scaling Trails-

Sr. No.	DT2MS	TSSFAC	Mass Percentage	Computation Time
				Evaluated	In minutes
1	-3.5e-5	0.9	0	24 hrs 4 min	1444 min
2	-3.5e-5	0.7	0	29 hrs 37 min	1777 min
3	-6.5e-5	0.9	0.0057852	20 hrs 12 min	1212 min
4	-6.5e-4	0.9	3.7311E+3	1 hr 37 min	97 min
5	1.5e-4	0.9	114.32	7 hrs 10 min	430 min
6	1.1e-4	0.9	20.393	9 hrs 1 min	541 min
7	1.01e-4	0.9	6.9297	14 hrs 10 min	850 min
8	1.029e-4	0.9	8.005	10 hrs 18 min	618 min

Case-2 Implicit Analysis-

• Generally in LS pre-post, the solver practices an Explicit method for all the FE models. In order to perform an Implicit method, the solver requires the following keywords to switch from Explicit to Implicit analysis.

CONTROL_IMPLICIT_AUTO

IAUTO: Automatically adjust 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.

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).

• Now we will run the simulation.

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

Conclusion-

• The objective of mass scaling is achieved for the given model by varying the values of DT2MS and TSSFAC using the trial and error method.
• By considering the hard limit on mass scaling being 8%, the optimized value of DT2MS = -1.029E-4 and TSSFAC= 0.9 with the lowest possible runtime required to complete the simulation being 10 hrs. 18 mins. And the TSSFAC value should be in between 0.5 to 0.9.
• The values of DT2MS and TSSFAC does not affect the runtime required to complete the simulation for implicit analysis.
• After, that we have run the analysis using implicit control cards which gives us the result that the implicit analysis is based on iterations to acheive equillibrium and doesn't depend on mass scaling. The concept of mass scaling and its necessity is in explicit analysis only.