Mass Scaling
Objective:
To run the simulation using mass scaling for reducing the time step by trial and error method. The mass scaling does not exceed 8%. Compare both explicit and implicit analyses.
Theory:
Mass scaling:
In the 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 a desired minimum time step size in *CONTROL_TIMESTEP. Increasing the mass too much may cause severe penetration problems and increase the dynamic effect significantly. The results may not be acceptable. Penetration and kinetic energy must be monitored closely to get good results.
Mass-scaling refers to a technique whereby nonphysical mass is added to a structure in order to achieve a larger explicit timestep.
Anytime you add nonphysical mass to increase the timestep in a dynamic analysis, you affect the results (think of F=m*a). Sometimes the effect is insignificant and in those cases adding nonphysical mass is justifiable. Examples of such cases may include the addition of mass to just a few small elements in a noncritical area or quasi-static simulations where the velocity is low and the kinetic energy is very small relative to the peak internal energy. In the end, it's up to the judgment of the analyst to gauge the effect of mass scaling. You may have to reduce or eliminate mass scaling in a second run to gauge the sensitivity of the results to the amount of mass added.
One can employ mass scaling in a selective manner 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 only to those elements whose timestep would otherwise be less than dt2ms.
By adding mass to these elements, their timestep becomes equal to |DT2MS|. An infinite number of combinations of TSSFAC and DT2MS will give the same product, i.e., timestep but the added mass will be different for each of those combinations. The trend is that the bigger |DT2MS| (and the smaller TSSFAC while TSSFAC*|DT2MS|=const), the greater the added mass. In return, stability may improve as TSSFAC is reduced (just as in non-mass-scaled solutions). If stability is a problem with the default TSSFAC of 0.9, try 0.8 or 0.7. If you reduce TSSFAC, 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 and I find it harder to rationalize.
The parameter MS1ST in *CONTROL_TIMESTEP controls whether the mass is added only once during initialization (MS1ST=1) or anytime as necessary to maintain the desired timestep specified via DT2MS (MS1ST=0).
You can use ENDMAS in *CONTROL_TERMINATION to stop the calculation after a certain amount of mass has been added (active for automatic mass scaling only).
Procedure:
At first, import the model in LS-Dyna by selecting Open>LS-Dyna keyword file. Now the model is shown on the screen. Here we need to use mass scaling for reduce the timestep. We can add mass up to 8% to reduce timestep until small. We can use mass scaling using CONTROL_TIMESTEP card in CONTROL Keyword. Here we need to increase or decrease the DT2MS value to reduce timestep and to add mass by trial and error method.
Trial:1
Here Run the simulation using default values DT2MS as -3.5e^-5 and TSSFAC as 0.9.
We have huge time to solve the simulation. So we need to reduce the DT2MS value.
Trial:2
Now the value of DT2MS is -3.0e^-5 and TSSFAC value is 0.9
Here we have increased timestep than trial 1. the added mass also zero. so that we should reduce DT2MS value and give one more trial.
Trial:3
the value of DT2MS is -2.5e^-5 and TSSFAC value is 0.9
we have increased timestep and the added mass is also zero. so that we should reduce DT2MS a little bit low.
trial:4
the value of DT2MS is -2.0e^-5 and TSSFAC value is 0.9
we have a large timestep and the added mass is also zero. go to trial 5.
Trial:5
Here the value of DT2MS is -1.5e^-5 and TSSFAC value is 0.9
Here timestep value is low compared to the previous trial but zero mass is added. so we should reduce more timestep.
Trial:6
Here the value of DT2MS is -1.0e^-5 and TSSFAC value is 0.9
The timestep is lower than previous trial but mass added is zero.
Trial:7
Now increase the DT2MS value as -4.0e^-5 and TSSFAC value to 0.9
Here we get huge time steps to complete the simulation. so that we need to increase the DT2MS value.
Trial:8
Here the DT2MS value is -5.0e^-5 and TSSFAC value to 0.9
Here timestep is increased but the mass is added up to 0.001%.
Trial:9
Here the DT2MS value is -6.0e^-5 and TSSFAC value to 0.9
The timestep is decreased than the previous trial and the mass is added up to 0.0227%.
Trial:10
the DT2MS value is -7.0e^-5 and TSSFAC value to 0.9
The timestep is decreased than the previous trial and the mass is added up to 0.142%.
Trial:11
the DT2MS value is -8.0e^-5 and TSSFAC value to 0.9
The timestep is increased and the mass is added up to 0.843%.
Trial:12
the DT2MS value is -9.0e^-5 and TSSFAC value to 0.9
The timestep is decreased than the previous trial and the mass is added up to 2.75%.
Trial:13
Here the DT2MS value is -1.0e^-4 and TSSFAC value to 0.9
The timestep is decreased than the previous trial and the mass is added up to 6.42%.
Trial:14
Here the DT2MS value is -1.01e^-4 and TSSFAC value to 0.9
The timestep is decreased a little bit and the mass is added up to 6.93%.
Trial:15
Here the DT2MS value is -1.02e^-4 and TSSFAC value to 0.9
The timestep is decreased and the mass is added up to 7.47%.
Trial:16
Here the DT2MS value is -1.03e^-4 and TSSFAC value to 0.9
The timestep is decreased but the mass is added above 8%. the added mass is 8.066%. so we need to reduce DT2MS value a little bit.
Trial:17
Here the DT2MS value is -1.029e^-4 and TSSFAC value to 0.9
Now The timestep is decreased to low and also the mass is added 8% perfectly. The time is reduced to 14hrs from 32hrs.
Changing TSSFAC values:
Here we can do a trial for changing the TSSFAC values as 0.8, 0.7, 0.6 with the same DT2MS value as -1.029e^-4.
Trial:1
DT2MS value is -1.029e^-4 and TSSFAC value to 0.8
Trial:2
DT2MS value is -1.029e^-4 and TSSFAC value to 0.7
Trial:3
DT2MS value is -1.029e^-4 and TSSFAC value to 0.6
We can see the timestep is increased gradually when decreasing the timestep scale factor.
Changing the analysis into implicit :
Here we have done all trials in explicit analysis but we need to compare the results in both explicit and implicit analysis. so that we need to add some control cards for implicit analysis.
Now run the simulation in implicit cards using LS-Run.
Here we can see the timestep is lower when compared to the explicit analysis.
Results:
Now plot the graph for DT2MS and run time using Excel. Compare the results of different trials.
Here we can see the DT2MS value plays a major role to reduce the timestep. The Maximum timestep is raised at -2.0e^-5 and the minimum timestep is raised at 1.020e^-4.
Now plot the graph using TSSFAC values like 0.8, 0.7, 0.6, and runtime.
The timestep is increased when decreasing the TSSFAC value. we can see in the graph. The minimum timestep was raised at TSSFAc=0.9.
Conclusion:
Finally, we had find the DT2MS value for exact mass scaling for 8% and we had plotted the graph and compared the results of both explicit and implicit analysis.