汎用接触(TYPE7)

このインターフェースは、最も一般的なタイプの接触と衝撃をシミュレーションします。TYPE7インターフェースには次の特性があります。
  1. TYPE5インターフェース同様に、メインサーフェスと一群のセカンダリ節点との間で衝撃が発生します。
  2. 節点は、1つ以上のメインセグメントに衝撃を与えることができます。
  3. 節点は、サーフェスのどちらの側にも衝撃を与えることができます。
  4. 各セカンダリ節点は、現在のセグメントに結合しているメインセグメントを除き、各メインセグメントに衝撃を与えることができます。
  5. 図 1に示すように、節点はメインサーフェスと一群のセカンダリ節点に属することができます。
  6. 節点は、メインセグメントのエッジと角に衝撃を与えることができます。これは、ここまでに取り上げたインターフェースでは不可能です。
  7. このインターフェースでは、メインセグメントのエッジとセカンダリセグメントのエッジとの接触は解決できません。

制限事項

インターフェースTYPE3、TYPE4、およびTYPE5にあるすべての制限が、このインターフェースでは解決されています。

制約なしの高速検索アルゴリズムです。


図 1. セカンダリ節点とメイン節点の接触

このインターフェースでは、節点とサーフェスとの接触に関連する検索上の制限がありません。考えられる接触がすべて検出されます。

同じインターフェース上で大型のセグメントと小型のセグメントを制限なく使用できます。妥当な結果を得るためにアスペクト比が良好な要素または規則的なメッシュの使用をお勧めしますが、必ずしも必須ではありません。

スプリングの剛性係数の大きさに対する制限はありません。デフォルトの剛性係数である1.0では、TYPE3とTYPE5のインターフェースよりもスプリングの剛性がはるかに高くなります。これは節点の貫通がギャップサイズよりも大きくなることを避けるための措置であり、他のインターフェースであれば発生する問題を排除できます。

Interface Stiffness

When two surfaces contact, a massless stiffness is introduced to reduce the penetration of one surface node to the other 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.

The interface spring stiffness calculation is not as simple as for TYPE3, TYPE4 and TYPE5. The initial stiffness is calculated using the methods for TYPE3 interfaces. However, after initial penetration, the stiffness is given as a function of the penetration distance and the rate of penetration.

A critical viscous damping coefficient given on the input card (visc) allows damping to be applied to the interface stiffness.(1) F = f ( p ) + v i s c 2 K M d p d t

The stiffness is much larger than the other interfaces to accommodate high speed impacts with minimal crossing of surfaces. The consequence of this is that a stable time step is calculated to maintain solution stability.

Interface Friction

TYPE7 interface allows sliding between contact surfaces.

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

In TYPE7 interface a critical viscous damping coefficient is defined, allowing viscous damped sliding.

The friction on a surface may be calculated by two methods. The first method suitable for contact tangential velocity greater that 1m/s consist in computing a viscous tangential growth by:(2) Δ F t = C t V t
In the second method an artificial stiffness K S is input. The change of tangent force F is obtained using:(3) Δ F t = K S δ t
Where,
δ t
Tangent displacement
The normal force computation is given by:(4) F n = K s P + C d P d t
Where,
K s = K 0 ( G a p G a p P )
C = V I S s 2 K s M
K 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIWaaabeaaaaa@37AC@
Initial interface spring stiffness (as in TYPE5)
V I S s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiaadM eacaWGtbWaaSbaaSqaaiaadohaaeqaaaaa@399B@
Critical damping coefficient on interface stiffness (input)


図 2. Coulomb Friction
C 0
Contact Point at time t
C 1
Contact Point at time t = t + Δ t


図 3. Friction on TYPE7 Interface - Scheme
The tangential force computation is given by:(5) F t =min( μ* F n , F ad ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaaS baaSqaaiaadshaaeqaaOGaeyypa0JaciyBaiaacMgacaGGUbWaaeWa aeaacqaH8oqBcaGGQaGaamOramaaBaaaleaacaWGUbaabeaakiaacY cacaWGgbWaaSbaaSqaaiaadggacaWGKbaabeaaaOGaayjkaiaawMca aaaa@4592@
Where,
F a d = C t V t
Adhesion force
C = V I S F 2 K s M
V t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwbWaaS baaSqaaiaadshaaeqaaaaa@385F@
Tangential velocity calculated from the movement of the node from c 0 to c 1 in 図 2.
注: The friction coefficient μ may be obtained by Coulomb, Darmstad and Renard models as described in Interface Friction.
Time integration of the frictional forces is performed by:(6) F t n e w = F t o l d + Δ F t
Where, Δ F t is obtained from 式 2 or 式 3.


図 4. Friction on TYPE7 Interface

Interface Gap

TYPE7 interfaces have a gap that determines when contact between two segments occurs.

This gap is user-defined, but some interfaces will calculate an automatic default gap. Shown in Interface Stiffness, is a segment TYPE7 interface with three nodes in close proximity. The gap, as shown, determines the distance for which the segment interacts with the three nodes. If a node moves within the gap distance, such as nodes 1 and 2, reaction forces act on the nodes.


図 5. TYPE7 Interface Gap

TYPE7 interface has a gap that covers both edges of the segments, as shown in 図 5.

Time Step

A time step is calculated to maintain stability when a TYPE7 interface is used.

The kinematic or interface time step is calculated if d P d t > 0 by:(7) Δ t min = 0.5 [ G a p p d P d t ]
The stable time step or nodal time step is given by:(8) Δ t n o d = 2 M K
Where,
M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaaaa@36C8@
Nodal mass
K = ( K int e r + K e l )
Nodal stiffness

The time step used for the interface is the smaller of the two. If the interface spring stiffness is too great, the time step can be reduced dramatically. If the two materials involved in the contact are the same, the default interface stiffness factor can be retained. This is the case when modelling sheet metal. However, the stiffness factor may need adjustment if the two materials stiffness' vary too much; for example, steel and foam.

Methods to Increase Time Step

The time step can be altered by two different methods, by altering the size of the gap and by increasing the initial stiffness. 図 6 shows three force-penetration curves for a TYPE7 interface. Both methods change the nature of the stiffness which affects the time step.


図 6. Force - Penetration Curves

Using a larger gap size, curves 1 and 2 keep the same initial stiffness; hence the initial time step remains the same. Since the impact slowing force is applied over a greater distance, the stiffness is not changed as much, but increases.

Increasing the initial interface stiffness, although decreasing the time step initially; will increase the time step if penetration is large.

Detection and Gap Size

A slave node can be detected near a master segment from all directions, as shown in 図 7.

The size of the gap can be user defined, but Radioss automatically calculates a default gap size, based on the size of the interface elements. For shell elements, the computed gap is the average thickness. For brick elements it is equal to one tenth of the minimum side length.

Variable Gap

By default the gap is constant on all master segments.

If the variable gap option is activated, a different gap is used for each contact taking into account the physical thickness on the master and slave sides.


図 7. Variable Gap

For shell elements, the master gap is equal to one half of the shell thickness. The slave gap is equal to one half of the largest thickness of all connected shell elements.

For solid elements, the master gap is zero. If the slave node is only connected to solid elements, the slave gap is zero.

For beam or truss elements connected to the slave node, the slave gap is one half of the square root of the section area.

If a slave node is connected to different elements (shell, brick, beam, and truss) the largest gap value is used.

The total gap is the sum of the slave and master gaps. The total gap cannot be smaller than a minimum gap (user input gap).

Gap Correction

TYPE7 interface is very sensitive to initial penetrations. One method for solving the resulting problems is to use an automatic gap correction (Inacti = 5).

With automatic gap correction the effective gap is corrected to take into account the initial penetration. The correction is only applied to the initially penetrated nodes. If the node penetration decreases, the correction is reduced. The computed penetration is illustrated in 図 8.


図 8. Corrected Gap

Penetration Reaction

Like the other interface types, TYPE7 has a spring stiffness as a slave node penetrates the interface gap (previous section). However, there are some fundamental differences in the determination of the reaction force. 図 9 shows a graph of force versus penetration of a node on a master segment. This figure also shows a pictorial diagram of node penetration and the associated forces.


図 9. Penetration Reaction Force

The reaction force is not a linear relation like the previous interfaces. There is a viscous damping which acts on the rate of penetration.

The force computation is given by:(9) F = K s P + C d P d t
Where,
K s = K 0 ( G a p G a p P )
C = V I S s 2 K s M
K 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIWaaabeaaaaa@37AC@
Initial interface spring stiffness (as in TYPE5)
VI S s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiaadM eacaWGtbWaaSbaaSqaaiaadohaaeqaaaaa@399B@
Critical damping coefficient on interface stiffness (input)
The instantaneous stiffness is given by:(10) K t = K 0 ( G a p 2 ( G a p P ) 2 )


図 10. Force - Penetration Graph

A critical viscous damping is required to be defined on the TYPE7 input card for both damping on the spring stiffness and for interface friction damping.

Force Orientation

Due to the gap on a TYPE7 interface extending around the edges of a segment, the reaction forces over a surface will be smooth.

Penetration Reaction, 図 10 shows the reaction forces on a node at various positions around two adjoining segments.


図 11. Force Orientation

Position 1 in 図 11 shows the force acting radially from the edge of the segment. The size of the force depends on the amount of penetration. At position 2 the force is normal to the segment surface. In position 3 two segments intersect and their gaps overlap. The result is that each segment applies a force to the node, normal to the respective segment, this may double the force for the distance of gap overlap.

Interface Hints

Main Problem

One main problem remains namely, deep penetrations are not easily tolerated. They lead to high penalty forces and stiffness', and consequently to a drop-in time step. When such a problem occurs, you may see:
  • A very small time step
  • A large contact force vector in animation
Deep penetrations (that is, close to gap value) can sometimes occur in most car crash simulations. They occur in the following cases:
  • Initial penetrations of adjacent plates
  • Edge impacts: wrong side contacts
  • Full collapse of one structural region
  • Rigid body impact on another rigid body or on fixed nodes or on very stiff structures
  • Impact between heavy stiff structures
  • High impact speed
  • Small gap
The elastic contact force is calculated with the formulation:(11) F = k g p ( g p )

With k = 0.5 S t f a c * E * t

The elastic contact energy is calculated with the formulation:(12) CE=kg( pg×ln( ( gp ) g ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaadw eacqGH9aqpcaWGRbGaam4zamaabmaabaGaeyOeI0IaamiCaiabgkHi TiaadEgacqGHxdaTciGGSbGaaiOBamaabmaabaWaaSaaaeaadaqada qaaiaadEgacqGHsislcaWGWbaacaGLOaGaayzkaaaabaGaam4zaaaa aiaawIcacaGLPaaaaiaawIcacaGLPaaaaaa@4A86@
Where,
k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E7@
Interface stiffness
g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E7@
Contact gap
p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E7@
Penetration

When node to element mid-plane distance is smaller then 10-10 gap, the node is deactivated.

The maximum potential contact energy is:
  • elastic contact energy CE = 23 kg

Drastic time step dropping is mostly due to cases where node is forced into the gap region.

Remedies to the Main Problem

There are several ways to resolve this problem:
  1. Increase Gap

    Increasing the gap is the best remedy, but check that no initial penetrations result from this.

  2. Increase Stiffness

    Increase Stfac dimensionless stiffness factor or provide an appropriate effective global stiffness value (v23 and up).

  3. /DT/INTER/DEL (Engine option)

    Some nodes will be allowed to cross the impacted surface freely before penetration reaches (1-1010 ) gap.

  4. /DT/INTER/CST (Engine option)

    Nodal mass will be modified to maintain time step constant. This option should be avoided when rigid body slave nodes are slaves of a TYPE7 interface.

    The initial penetrations are mostly due to discretization and modelization problems.

    They result in high initial forces that should be avoided.

  5. Modify geometry

    New coordinates are proposed in the listing file for all initially penetrated nodes. These are the coordinates used in the automatic coordinate change option. However, this might not suffice. Several iterations are sometimes necessary. Radioss will create a file RootD0A containing the modified geometry.

  6. Reduce gap

    When there are only small penetrations with a gap, this should be reduced; otherwise care should be taken as this will reduce potential contact energy.

  7. Deactivate node stiffness

    This solution is the simplest. It will generally not unduly affect your results. For sake of precision, use this option only for initial penetrations remaining after geometrical adjustments.

Edge Contact Problem

A special algorithm is developed for this purpose.

Modelization should eventually be adapted to prevent situations where 2 nodes of an element move to opposite sides of a surface.

For solid to solid contacts, the external closed surfaces may be used.