Week - 8 Mass Scaling

Aim:

• To perform the simulation by reducing and stabilizing the runtime with the help of a 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

Mass scaling

In an explicit method, the time step usually is very small to maintain numerical stability. However, the 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:

• 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%

Case 1 Explicit Analysis(With Mass-scale) 

Import

• Import the given FE model usually as a keyword parameter consists a set of keywords demanded

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

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

• From the above image, the computation time is 56 hrs 4 mins. As a result, there is no mass added with given DT2MS of -3.500e-05">3.500e−053.500e-05, this can be varied by changing the values of DT2MS and TSSFAC

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

• From the above image, the computation time is increased by 4 hrs 31 mins by 60 hrs 35 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

• From the above image, the computation time for is decreased rapidly from 60 hrs 35 mins to 27 hrs 42 mins, there is a considerable decrease in computation time
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.500e-05">−6.500e−05-6.500e-05 with a percentage of mass increase in 5.7852E-02">5.7852E−025.7852E-02
• Since the added mass exceeding the limit, the energy values also vary considerably. Values need to be increased 

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

• From the above image, the computation time for is decreased rapidly from 27 hrs 42 mins to 2 hrs 35 mins, there is a considerable decrease in computation time
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -6.500e-04">−6.500e−04-6.500e-04 with a percentage of mass increase in 3.7311E+03">3.7311E+033.7311E+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 decreased rapidly from 2 hrs 35 mins to 13 hrs 55mins, there is a considerable increase in computation time
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.500e-04">−1.500e−04-1.500e-04 with a percentage of mass increase in 1.1432E+02">1.1432E+021.1432E+02
• Since the added mass exceeding the limit, the energy values also vary considerably. Values need to be reduced slightly

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

• From the above image, the computation time for is decreased rapidly from 13 hrs 55 mins to 16 hrs 41 mins, there is a considerable increase in computation time
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.100e-04">−1.100e−04-1.100e-04 with a percentage of mass increase in 2.0393E+01">2.0393E+012.0393E+01
• Since the added mass exceeding the limit, the energy values also vary considerably. Values need to reduced slightly

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

• From the above image, the computation time for is decreased rapidly from 16 hrs 41 mins to 19 hrs 30 mins, there is a considerable increase in computation time
• However, mass added with a default value of TSSFAC=0.9, DT2MS of -1.010e-04">−1.010e−04-1.010e-04 with a percentage of mass increase in 6.9297E+00">6.9297E+006.9297E+00
• Since the added mass lessened the limit, the energy values also vary considerably. Values need to reduced slightly 

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

• From the above image, the computation time is decreased rapidly from 19 hrs 30 mins to 17 hrs 59 mins, there is a considerable increase in computation time
• After many iterations, TSSFAC=0.9, DT2MS of -1.029e-04">−1.029e−04-1.029e-04 attains the percentage of mass around 8.005E+00">8.005E+008.005E+00

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

DT2MS	MASS PERCENTAGE	COMPUTATION TIME
-3.5e-5">−3.5e−5-3.5e-5	0">00	56hrs4mins">56hrs4mins56hrs4mins
-3.5e-5">−3.5e−5-3.5e-5 0.7TSSFAC">0.7TSSFAC0.7TSSFAC	0">00	60hrs35mins">60hrs35mins60hrs35mins
-6.5e-5">−6.5e−5-6.5e-5	5.7852e-2">5.7852e−25.7852e-2	27hrs42mins">27hrs42mins27hrs42mins
-6.5e-4">−6.5e−4-6.5e-4	3.7311e3">3.7311e33.7311e3	2hrs35mins">2hrs35mins2hrs35mins
-1.5e-4">−1.5e−4-1.5e-4	1.432e2">1.432e21.432e2	13hrs55mins">13hrs55mins13hrs55mins
-1.1e-4">−1.1e−4-1.1e-4	2.0393e1">2.0393e12.0393e1	16hrs40mins">16hrs40mins16hrs40mins
-1.01e-4">−1.01e−4-1.01e-4	6.9297">6.92976.9297	19hrs30mins">19hrs30mins19hrs30mins
-1.029e-4">−1.029e−4-1.029e-4	8.005">8.0058.005	17hrs59mins">17hrs59mins17hrs59mins

Case 2 Explicit Analysis(Without Mass-scale)

• From the above image, the computation time is about 33 hrs 22 mins, there is a considerable higher computational time

Case 3 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)

• 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 

Explicit vs Implicit

As we know, 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. Explicit on the other hand doesn’t have to converge each time step, but for the solution to be accurate time steps must be small. Though the running time for implicit analysis is shorter than the explicit analysis method because the timestep is defined larger in implicit compared to explicit analysis and we have used constant timestep formulation

Conclusion:

• From the above cases, I have learned mass scaling and obtained 8% by varying the DT2MS values along with TSSFAC