All About Time-Step in LS Dyna

Two classical solution methods are available in LS-DYNA to solve a given problem. The widely popular Explicit solution scheme, using the central-difference method, is applied to short-duration transient dynamic problems, while the Implicit solution scheme is used for static problems. Both methods have advantages and disadvantages, which depend entirely on the problem at hand. 

What is LS-DYNA?

One of the top explicit simulation programs in the industry, Ansys LS-DYNA, is utilised for applications like drop testing, impact and penetration, smashes and crashes, occupant safety, and more.

During each time step, LS-DYNA traverses every node in the model to determine the solution in a model. Simply put, LS-DYNA will look at the total force applied to each node in the previous time step, use it to determine that node's acceleration, and use that information to determine that node's displacement. The node is moved to that distance. The calculation then updates the strain on the connecting element. The stress is then obtained through the material’s constitutive equation and used as a force on the nearby node in the following time step.

The Explicit and Implicit Approach in LS Dyna

The Explicit approach of using small timesteps to march forward is ideal for solving short-duration transient dynamic problems and requires a relatively small amount of memory to solve even very large problems. The Implicit method is ideal for solving static or low-strain rate problems but has large memory requirements that increase exponentially with problem size.

Improvements in LS-DYNA allow seamless switching between the two solution schemes allowing the user to choose the best method for a given problem.

The IMFLAG parameter in *CONTROL_IMPLICIT_GENERAL is a single parameter with multiple options that allow the user to choose the solution method either statically or dynamically as a function of several variables. By default, IMFLAG is set to 0, which instructs LS-DYNA to use the Explicit method. Changing IMFLAG to 1, switch the solution type to Implicit with non-linear geometry and material. All necessary Implicit dependent parameters are defined using *CONTROL_IMPLICIT_{OPTION} keywords. The values 0 and 1 for IMFLAG are static values, meaning that a single solution method is used for the run duration.

For IMFLAG = 4 or 5: when the implicit analysis fails to converge, LS Dyna will switch to explicit for a short time interval and then return to implicit analysis. This can help in cases with buckling or sudden contacts as the short explicit step allows the analysis to get past these instabilities. 

For IMFLAG = -n (load curve Id) using this option the user can specify a curve to control the implicit- explicit switching. The curve is the analysis method vs time(0=explicit, 1 = implicit). This is shown in the following Figure 2

By default, LS-DYNA uses a constant implicit timestep, specified using DT0 in *CONTROL_IMPLICIT_GENERAL, for the entire duration of the simulation time. The magnitude of DT0 is usually chosen as a fraction of the total simulation time and is entirely dependent on the nonlinearity of the problem. Using a constant timestep is very conservative since, irrespective of the number of iterations each was required to converge, the timestep is unchanged. It may result in a large number of expensive iterations. 

This is a good thing for a problem whose non-linearity is unknown since smaller timesteps pose lesser nonlinearity issues and may be easier to converge. However, once the user becomes familiar with a problem, careful usage of automatic implicit time step control in LS-DYNA is a good alternative to reduce the number of iterations, thereby reducing the simulation time.

Steps involved in Automatic Time Step Control

Automatic time step control is activated using *CONTROL_IMPLICIT_AUTO by setting AUTO = 1. The built-in logic in LS-DYNA then takes over to auto-adjust the timestep and the logic is purely based on the number of iterations that were taken at the current timestep. 

The parameter ITEOPT (default is 11) allows the user to specify an optimum number of iterations which is to be used to decide where to auto-adjust the current timestep. Suppose the number of iterations to converge at the current timestep is greater than ITEOPT. LS-DYNA then reduces the current timestep (using a built-in scale factor) to reduce the non-linearity of the problem. 

However, suppose the number of iterations at the current timestep is less than ITEOPT. In that case, LS-DYNA then increases the current timestep (using a built-in scale-factor), assuming the problem is getting easier to solve. To allow some tolerance to the value of ITEOPT, the parameter ITEWIN is a very useful feature that prevents LS-DYNA from hastily auto-adjust the timestep. When ITEWIN is defined (default is 15) and the number of iterations at the current timestep falls in the range of ITEOPT +/- ITEWIN, then LS-DYNA bypasses the auto-adjust of the timestep. This is shown in the following Figure 3.

To provide a minimum allowable timestep size that LS-DYNA can auto-adjust to, the parameter DTMIN can be specified. To define the maximum allowable timestep, there are two possible ways using the parameter DTMAX. When DTMAX is greater than zero, then LS-DYNA will not auto-adjust such that the timestep is either equal to or below DTMAX. When DTMAX is less than zero, it refers to a load curve that can be used to define a variable maximum allowable timestep. This is illustrated in the following Figure 4.