Computation Checks

This is a method to check the quality of simulation results. Even if the run does not fail, it needs to be verified that three fundamental conservation laws are respected. The time step variation and the qualitative evaluation of results may help to avoid modeling errors.

Energy Balance

Taking into account the external works, the total energy must remain constant or decrease slightly. The total energy can increase at the end of the computation, during the spring back or at the beginning during the first cycles.

Internal energy + Kinematic energy + Hourglass energy + Contact Energy + … = Variation of the External Work

If under-integrated elements are used, the total hourglass energy must remain lower than 10% of the total energy. If this is not the case, the mesh should be reworked or elements with physical stabilization method should be used.

The contact energy is not really physical. For each subset and for each part the following limitation is recommended:

\frac{E_{h} + E_{c}}{E_{t}} \leq 15 %

Where,

$E_{h}$: Hourglass energy
$E_{c}$: Contact energy
$E_{t}$: Total energy

The energy error is computed by Radioss as:

% E r r o r = 100 (\frac{E_{k} + E_{k}^{r} + E_{i}}{E_{k, 1} + E_{_{k, 1}}^{r} + E_{i, 1} + E_{w k} - E_{w k, 1}} - 1)

Where,

$E_{k}$: Translational kinetic energy
$E_{k}^{r}$: Rotational kinetic energy
$E_{i}$: Internal energy
$E_{w k}$: External work
$E_{k, 1}$: Initial translational kinetic energy
$E_{_{k, 1}}^{r}$: Initial rotational kinetic energy
$E_{i, 1}$: Initial internal energy
$E_{w k, 1}$: Initial external work

The error must be negative and decreasing (except for the first cycle or in spring-back stage). The error must be less than 15% at the end of computation (5% for a good model). If the error increases a little, then decreases may be normal. If the error increases, this means that a problem has occurred. Then, the error may grow to 99.9% with computation failure message.

Mass Balance

If the mass increases, its variation must remain smaller than 1% for each subset and for each part ( $\frac{d M}{M} < 1 %$ ). If the mass variation is between 1% to 3%, check if the nodes with the added mass are moving or not. If this is the case, the added mass results in an increase in kinetic energy. For more than 3% of variation, the results are probably bad.

Momentum Balance

The dynamic equilibrium of each node is satisfied by the Newton law at the end of each cycle. As Radioss resolves the equilibrium equations at each cycle, normally the momentum balance is satisfied. However in case of a problem, a cross-check between nodal accelerations and the impactor forces (interface, rigid wall, barrier, and so on) can help to better understand problems.

F_{w a l l} = \frac{M o n e n t u m \begin{matrix}  \end{matrix} v a r i a t i o n}{d t}

Time Step Evolution

If the time step decreases and then it increases quickly, this is not a problem. If it varies greatly from one cycle to another, it may be due to the interface stiffness.

If the time step remains low, a problem has occurred. In this case, find the node (or element) controlling the time step and try to understand why the decrease occurred.

Visual Inspection of Deformed Parts

After getting some animation files, the overall deformation of the structure can be compared to the physical behavior. Inspect the deformed shape to verify:

There are no flying nodes (parts)
The deformed shape is smooth
The chord angle between adjacent elements is sufficiently small
There are no intersections

Good physical behavior is obtained when:

The plastic strain is less than 30%
$\frac{E_{k} + E_{k}^{r}}{E_{t}} \leq 1 %$

Meaningless Results

Contact forces, von Mises stress, nodal velocities, and accelerations have to be checked carefully. If the values are meaningless (for example: von Mises stress = 1 GPa), the first check may be the unit system consistency. Refer to the Appendix for more information.