# /IMPL/DT/3

Engine Keyword Implicit automatic time step control with Riks method.

## Format

/IMPL/DT/3

It_w L_arc L_dtn $\text{Δ}{T}_{sca_d}$ $\text{Δ}{T}_{sca_\mathrm{max}}$ C_type W_scal

## Definitions

Field Contents SI Unit Example
lt_w If the solution of a time step converges within It_w iterations, the next time step will be increased by a factor controlled by $\text{Δ}{T}_{sca_\mathrm{max}}$ .
= 0
Set to 12

L_arc Input arc-length.
= 0
Will be calculated automatically.

L_dtn Maximum number of iterations before resetting and decreasing the time step by a factor of $\text{Δ}{T}_{sca_d}$ .
= 0
Set to 25

$\text{Δ}{T}_{sca_d}$ Scale factor for decreasing the time step when L_dtn is reached.
= 0
Set to 0.67

$\text{Δ}{T}_{sca_\mathrm{max}}$ Maximum scale factor for increasing the time step.
= 0
Set to 1.2

C_type
= 0
Set to 2
= 1
Crisfield constraint equation.
= 2
Modified Forde & Steimer equation.

W_scal Scale factor for controlling the loading contribution in the constraint equation.

Default = 0.0

1. The Riks type arc-length method is suitable for nonlinear static analysis of unstable problems like buckling, snap-through. It solves at the same time for the displacement vector and for a loading scale factor by adding a constraint equation.

This method can only be used for static analysis and the loading should be proportional in each restart run.

2. A constant arc length can be defined by giving $\text{Δ}{T}_{sca_d}=\text{Δ}{T}_{sca_\mathrm{max}}=1$ or directly defining L_arc. Otherwise, an adaptive arc length based on the convergence rate will be used. The adjustment is:(1)
$L_new=L_old\cdot {\left(\frac{It_w}{It_old}\right)}^{0.5}$

Where, It_old is the number of convergence iterations of previous load increment.

3. The time step adjustment uses the same factor than arc length but bound by $\text{Δ}{T}_{sca_d}$ and $\text{Δ}{T}_{sca_\mathrm{max}}$ . Each new time step is only the predictor value as Riks method will give the final time step at the end of each load increment. Therefore, a negative time step can be obtained for some loading increments.
4. Riks method can only be used with Modified Newton (only in the sense of reforming the stiffness matrix) and line search methods, but a small number (L_A ≤ 3) is recommended for the reforming frequency of the stiffness matrix.
5. A maximum cycle number (see /IMPL/NCYCLE/STOP) can be used to stop the run in case the solution never reaches the specified load.
6. If /IMPL/DT/1, /IMPL/DT/2, or /IMPL/DT/3 are not present, the only time step controls are /IMPL/NCYCLE/STOP and /IMPL/DT/STOP. In the case of divergence, the time step will be reduced by half and repeated.
7. For the post-buckling simulations involving contact, the Riks method may not work, especially if contact has not occurred at beginning or contact is lost during the simulation. In this case, it is better to use implicit dynamic analysis.
8. If the Riks analysis includes irreversible deformation such as plasticity and a restart, using another Riks step is attempted while the magnitude of load on the structure is decreasing, the solver will find the elastic unloading solution. Therefore, restart should occur at a point in the analysis where the load magnitude is increasing, if plasticity is present.