汎用接触（TYPE5）

図 1に示すように、このインターフェースを使用して、メインサーフェスと、セカンダリ節点のリストとの接触をシミュレーションします。

ペナルティ法によって貫通が減少します。

別の方法としてLagrange乗数法を使用できます。しかし、力の空間分布がスムーズではないことからアワグラス変形が誘発されます。

このインターフェースの主な用途は以下のとおりです：

サーフェス上でのビーム節点、トラス節点、スプリング節点による接触のシミュレーション。
複雑な細かいメッシュと単純な凸型サーフェスとの接触のシミュレーション。
剛壁の置き換え。

制限事項

TYPE5インターフェースの主な制限を以下に示します。

メインセグメントの法線は、メインサーフェスからセカンダリ節点の方向に向いている必要があります。
メイン側のセグメントは、ソリッド要素またはシェル要素に結合されている必要があります。
メインサーフェスとセカンダリサーフェスの両方に同じ節点を存在させることはできません。
特定の状況では、検索アルゴリズムは、サーフェス衝撃の正確な節点を特定できません。

メインのサーフェスメッシュは規則的で、アスペクト比が良く、貫通部を検出するためにギャップが小さいかゼロであることが推奨されています。

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 master and slave sides. The stiffness scaling factor default value (and recommended value) is 0.2.

For a soft master surface material and stiff slave 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:(1)

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

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)

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 slave node is:

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

For more information, refer to Auto Contacts.

Detection of Closest Master Node

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

The Starter searches for the master node with the minimum distance to the particular slave node. The Engine carries out the following algorithm, referring to 図 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 master node, $M_{2}$ , to node $N$ at time $t_{1}$ . The new master node must belong to one of the segments $S_{0}$ , $S_{1}$ , $S_{2}$ or $S_{3}$ .
Determine the new closest master 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 Slave Nodes x Number of Master Nodes

The Engine CPU cost is calculated with the following equation:

CPUengine = b x Number of Slave Nodes

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

N

is moving from

N ​ (t_{0})

N ​ (t_{1})

and then to

N ​ (t_{2})

, the closest master 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 master node.

Detection of Closest Master Segment

The closest master segment to a slave node

N

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

A

The

A

value for segment

S_{1}

is given by:(5)

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:(6)

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 master 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 slave node $N$ and the master nodes of the corresponding master segment, as shown in 図 6.

For a given normal

n

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

Reduction of Penetration

The penetration,

p

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

N

, and the contact point,

C

The force applied on node

N

in direction

\vec{N C}

is:(7)

F = K p

Where,

$K$: Interface spring stiffness

Reaction forces

F_{1}

F_{2}

F_{3}

and

F_{4}

are applied on each master node (shown in 図 8) in the opposite direction to the penetration force, such that:(8)

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:(9)

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:(10)

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