# Time Step Scale Factor

The theoretical stable time step for both elements and nodes is an approximation and may change during the following time increment.

To maintain simulation stability and prevent divergence, the calculated theoretical stable time step is multiplied by a time step scale factor $\text{Δ}{T}_{sca}$ . If no time step control options are being used, then the minimum nodal or element time step of a model that is printed in the Starter output is multiplied by the time step scale factor with the result shown as TIME-STEP in the Engine output file.

Minimum time step listed in the Starter output:
      SOLID ELEMENTS TIME STEP
------------------------
TIME STEP       ELEMENT NUMBER
2.6322377948203E-04      11021
Default element time step activated in the Engine file:
/DT
0.9 0
Engine time step is then
TIME-STEP = 0.9 * 2.6322377948203E-04 = 0.2369E-03
Which matches the Engine output file cycle zero:
CYCLE    TIME      TIME-STEP  ELEMENT
0          0.000        0.2369E-03     SOLID

When using any of the time step control methods, such as /DT/NODA/CST or /DT/BRICK/CST, the time step control is activated when the minimum time step of the mesh multiplied by the time the time step scale factor is less than the entered minimum time step, $\text{Δ}{T}_{sca}*\mathrm{min}\left(\text{Δ}{t}_{\mathrm{m}esh}\right)\le \text{Δ}{T}_{\mathrm{min}}$ .

The minimum time step listed in the Starter output is:
       NODAL TIME STEP (estimation)
---------------
TIME STEP         NODE NUMBER
6.9475433E-07          10009
If the contant nodal time step option is used in the Engine file:
/DT/NODA/CST
0.9 7.0E-07
The initial Engine time step is:(1)
Since this initial time step is less than $\text{Δ}{T}_{\mathrm{min}}=7.0E-7$ , mass is added to increase the theoretical minimum time step of the mesh. Enough mass must be added to increase the minimum mesh time step so that $\text{Δ}{T}_{sca}*\mathrm{min}\left(\text{Δ}{t}_{\mathrm{m}esh}\right)\le \text{Δ}{T}_{\mathrm{min}}$ , which means:(2)
$\mathrm{min}\left(\text{Δ}{t}_{\mathrm{m}esh}\right)=\frac{\text{Δ}{T}_{\mathrm{min}}}{\text{Δ}{T}_{sca}}=\frac{7.0E-07}{0.9}=0.7778E-06$
The Engine output shows the time step is the same as entered and there is a mass error (MAS.ERR), due to mass added to increase the time step.
CYCLE    TIME      TIME-STEP        ELEMENT          …  MAS.ERR
0      0.000    0.7000E-06     NODE     10009         0.2887E-01
1   0.7000E-06  0.7000E-06     NODE     10009         0.2887E-01
2   0.1400E-06  0.7000E-06     NODE     10009         0.2887E-01
If $\text{Δ}{T}_{sca}=0.67$ , then more mass must be added to make the theoretical time step of the mesh is higher.(3)
$\mathrm{min}\left(\text{Δ}{t}_{\mathrm{m}esh}\right)=\frac{\text{Δ}{T}_{\mathrm{min}}}{\text{Δ}{T}_{sca}}=\frac{7.0E-07}{0.67}=1.0448E-06$
The default time step scale factor of 0.9 works well in most situations; however, in some cases, other values are recommended. One example would be models with foam materials, where there can be a sudden increase in stiffness, as shown in Figure 1.
This increase in stiffness causes a decrease in the model’s critical time step and can cause divergence, if the simulation time step is larger than the model’s critical time step. Some common situations where a time step other than 0.9 should be used are:
1. Models that use advanced mass scaling, /DT/AMS to increase the time step: $\text{Δ}{T}_{sca}=\text{0.67}$
2. Models with foam materials: $\text{Δ}{T}_{sca}=\text{0.66}$
3. Model with one element: $\text{Δ}{T}_{sca}=\text{0.1}$
4. Model with two finite elements: $\text{Δ}{T}_{sca}=\text{0.2}$
5. Model with more than three finite elements: $\text{Δ}{T}_{sca}=\text{0.9}$
6. Never use a scale factor greater than 1.0