General Purpose Contact (TYPE5)

This interface is used to simulate the impact between a main surface and a list of secondary nodes., as shown in Figure 1.

The penetration is reduced by the penalty method.

Another method is possible: Lagrange multipliers. But spatial distribution force is not smooth and induces hourglass deformation.

This interface is mainly used for:

Simulation of impact between beam, truss and spring nodes on a surface.
Simulation of impact between a complex fine mesh and a simple convex surface.
A replacement for a rigid wall.

Limitations

The main limitations of TYPE5 interface are:

The main segment normals must be oriented from the main surface towards the secondary nodes.
The main side segments must be connected to solid or shell elements.
The same node is not allowed to exist on both the main and secondary surfaces.
In certain situations, the search algorithm does not identify the correct node to surface impacts.

It is recommended that the main surface mesh be regular, with a good aspect ratio and that a small or zero gap be used to detect penetration.

Figure 1. Surface 1 (Nodes) and Surface 2 (Segments)

Computation Algorithm

The computation and search algorithms used for TYPE5 are the same as for TYPE3. Refer to Computation Algorithm.

Interface Stiffness

When two surfaces contact, a massless stiffness is introduced to reduce the penetration's nodes of the other surface into the surface.

The nature of the stiffness depends on the type of interface and the elements involved.

The introduction of this stiffness may have consequences on the time step, depending on the interface type used.

For a TYPE5 interface, the spring stiffness $K$ is determined by main and secondary sides. The stiffness scaling factor default value (and recommended value) is 0.2.

For a soft main surface material and stiff secondary surface, the stiffness scaling factor should be increased by the elastic modulus ratio of the two materials.

The calculation of the spring stiffness' is the same as in a TYPE3 interface.

If a segment is a shell as well as the face of brick element, the shell stiffness is used.

The overall interface spring stiffness is determined by considering two springs acting in series.

The equation for the overall interface spring stiffness is:

K = s \frac{K_{1} K_{2}}{K_{1} + K_{2}}

Where,

$s$: Stiffness scaling factor. Default is 0.2.
$K_{1}$: Surface 1 Stiffness
$K_{2}$: Surface 2 Stiffness
$K$: Overall interface spring stiffness

The scale factor, $s$ , may have to be increased if:

$K_{1} < < K_{2}$ or $K_{2} < < K_{1}$

The calculation of the spring stiffness for each surface is determined by the type of elements.

For example:

$K_{1} = \frac{1}{10} K_{2}$ implies $K = \frac{s}{11} K_{2}$ or $K = \frac{10 s}{11} K_{1}$ .

Shell Elements

For more information, refer to Shell Element.

Brick Elements

For more information, refer to Brick Element.

Combined Elements

For more information, refer to Combined Elements.

Interface Friction

TYPE5 interface allows sliding between contact surfaces.

Coulomb friction between the surfaces is modeled. The input card requires a friction coefficient. No value (default) defines zero friction between the surfaces.

The friction computation on a surface is the same as for TYPE3 interface. Refer to Interface Friction.

Darmstad and Renard models for friction are also available:

Darmstad Law:: $μ = C_{1} \cdot e^{(C_{2} V)} \cdot p^{2} + C_{3} \cdot e^{(C_{4} V)} \cdot p + C_{5} \cdot e^{(C_{6} V)}$
Renard Law:: $\begin{array}{l} μ = C_{1} + (C_{3} - C_{1}) \cdot \frac{V}{C_{5}} \cdot (2 - \frac{V}{C_{5}}) i f V \in [0, C_{5}] \\ μ = C_{3} - ((C_{3} - C_{4}) \cdot {(\frac{V - C_{5}}{C_{6} - C_{5}})}^{2} \cdot (3 - 2 \cdot \frac{V - C_{5}}{C_{6} - C_{5}})) i f V \in [C_{5}, C_{6}] \\ μ = C_{2} - \frac{1}{\frac{1}{C_{2} - C_{4}} + (V - C_{6})} i f V \geq C_{6} \end{array}$

Where,

$C_{1} = μ_{s}, C_{2} = μ_{d}$
$C_{3} = μ_{\max}, C_{4} = μ_{m:min}$
$C_{5} = V_{c r 1}, C_{6} = V_{c r 2}$

Possibility of smoothing the tangent forces via a filter:

4 F_{Τ} = α \cdot F_{Τ}^{t} + (1 - α) \cdot F_{Τ}^{t - 1}

Where, the coefficient $a$ depends on the I_filtr flag value.

Interface Gap

Refer to Interface Gap for TYPE3 interface.

Interface Algorithm

The algorithm used to calculate interface interaction for each secondary node is:

Determine the closest main node.
Determine the closest main segment.
Check if the secondary node has penetrated the main segment.
Calculate the contact point.
Compute the penetration.
Apply forces to reduce penetration.

For more information, refer to Auto Contacts.

Detection of Closest Main Node

The Radioss Starter and Engine use different methods to determine the closest main node to a particular secondary node.

The Starter searches for the main node with the minimum distance to the particular secondary node. The Engine carries out the following algorithm, referring to Figure 3.

Get the previous closest segment, $S_{0}$ , to node $N$ at time $t_{1}$ .
Determine the closest node, $M_{1}$ , to node $N$ which belongs to segment $S_{0}$ .
Determine the segments connected to node $M_{1}$ ( $S_{0}$ , $S_{1}$ , $S_{2}$ and $S_{3}$ ).
Determine the new closest main node, $M_{2}$ , to node $N$ at time $t_{1}$ . The new main node must belong to one of the segments $S_{0}$ , $S_{1}$ , $S_{2}$ or $S_{3}$ .
Determine the new closest main segment ( $S_{2}$ , $S_{4}$ , $S_{5}$ and $S_{6}$ ).

The Starter CPU cost is calculated with the following equation:

CPUstarter = a x Number of Secondary Nodes x Number of Main Nodes

The Engine CPU cost is calculated with the following equation:

CPUengine = b x Number of Secondary Nodes

The algorithm used in the Engine is less expensive but it does not work in some special cases. In Figure 4, if node

N

is moving from

N ​ (t_{0})

N ​ (t_{1})

and then to

N ​ (t_{2})

, the closest main nodes are

M_{0}

and

M_{1}

. When the final node movement to

N ​ (t_{2})

is taken, the impact on segment

S

will not be detected since none of the nodes on this segment are considered as the closest main node.

Detection of Closest Main Segment

The closest main segment to a secondary node

N

, shown in Figure 5, is found by determining a reference quantity,

A

Figure 5. Closest Main Segment Determination Method

The $A$ value for segment $S_{1}$ is given by:

A = (M {\vec{B}}_{2} \times M {\vec{P}}_{1}) (M {\vec{B}}_{1} \times M {\vec{P}}_{1}) < 0

Where,

$P_{1}$: Projection of $N$ on plane ( $M$ , $B_{1}$ , $B_{2}$ )
$B_{1}$ and $B_{2}$: Tangential Surface Vectors along segment $S_{1}$ edges.

The $A$ value for segment $S_{2}$ is given by:

A = (M {\vec{B}}_{3} \times M {\vec{P}}_{2}) (M {\vec{B}}_{2} \times M {\vec{P}}_{2}) > 0

Where,

$P_{2}$: Projection of $N$ on plane ( $M$ , $B_{2}$ , $B_{3}$ )

The same procedure is carried out for all main segments that node $M$ is connected to.

The closest segment is the segment for which $A$ is a minimum.

In some special cases (curved surfaces), it is possible that:

All values of $A$ are positive.
More than one value of $A$ is negative.

Detection of Penetration

Penetration is detected by calculating the volume of the tetrahedron made by secondary node $N$ and the main nodes of the corresponding main segment, as shown in Figure 6.

For a given normal

n

, the sign of the volume shows if penetration has occurred.

Figure 6. Tetrahedron used for Penetration Detection

Figure 7. Negative Volume Tetrahedron - Penetrated Node

Reduction of Penetration

The penetration,

p

, is reduced by the introduction of a massless spring between the node,

N

, and the contact point,

C

Figure 8. Forces Associated with Penetration

The force applied on node $N$ in direction $\vec{N C}$ is:

F = K p

Where, $K$ is the interface spring stiffness.

Reaction forces $F_{1}$ , $F_{2}$ , $F_{3}$ and $F_{4}$ are applied on each main node (shown in Figure 8) in the opposite direction to the penetration force, such that:

F_{1} + F_{2} + F_{3} + F_{4} = - F

Forces $F_{i}$ ( $i$ = 1, 2, 3, 4) are functions of the position of the contact point, $C$ . They are evaluated by:

F_{i} = \frac{d_{i}}{\sum_{j = 1}^{4} d_{j}} F

Where, $d_{i} = \frac{N i (S_{c}, t_{c})}{\sum_{j = 1}^{4} N_{j}^{2} (S_{c}, t_{c})} m_{i}$

or more simply:

F_{i} = N_{i} (S_{c}, t_{c}) F

Where,

$N_{i}$: Standard linear quadralateral interpolation functions
$S_{c}$ and $t_{c}$: Isoparametric coordinates contact point

The penalty method is used to reduce the penetration. This provides:

Accuracy
Generality
Efficiency
Compatibility