/INTER/TYPE7

Block Format Keyword Interface TYPE7 is a multi-usage impact interface, modeling contact between a main surface and a group of secondary nodes. It is also possible to consider heat transfer and heat friction.

Description

All limitations that were encountered with interfaces TYPE3, TYPE4 and TYPE5 are solved with this interface:
  • A node can at the same time be a secondary and a main node.
  • Each secondary node can impact each main segment; except if it is connected to this segment.
  • A node can impact on more than one segment.
  • A node can impact on the two sides, on the edges and on the corners of each segments.
  • It is a fast search algorithm without limitations.
The main limitations of this interface are:
  • Time step is reduced in case of high impact speed or contacts with small gap.
  • It does not work properly if used with a rigid body at high impact speed or rigid body with small gap.
  • It does not solve edge to edge contact (to solve this, /INTER/TYPE11 should be used along with TYPE7).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/INTER/TYPE7/inter_ID/unit_ID
inter_title
grnd_IDs surf_IDm Istf Ithe Igap   Ibag Idel Icurv Iadm
Fscalegap Gapmax Fpenmax     ITIED  
Stmin Stmax %mesh_size dtmin Irem_gap Irem_i2
Insert if Icurv = 1 or 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
node_ID1 node_ID2                
Required Fields
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Stfac Fric Gapmin Tstart Tstop
IBC     Inacti VISs VISF Bumult
Ifric Ifiltr Xfreq Iform sens_ID fct_IDF AscaleF fric_ID
If Ifric > 0
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
C1 C2 C3 C4 C5
If Ifric > 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
C6                
If Iadm = 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
NRadm Padm Angladm          
If Ithe = 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Kthe fct_IDK   Tint Ithe_form AscaleK  
Frad Drad Fheats Fheatm    

Definition

Field Contents SI Unit Example
inter_ID Interface identifier.

(Integer, maximum 10 digits)

 
unit_ID unit_ID.

(Integer, maximum 10 digits)

 
inter_title Interface title.

(Character, maximum 100 characters)

 
grnd_IDs Secondary nodes group identifier.

(Integer)

 
surf_IDm Main surface identifier.

(Integer)

 
Istf Interface stiffness definition flag. 3
For SPH, only Istf=0, 1 and 1000 are available.
= 0
Set to value defined in /DEFAULT/INTER/TYPE7.
= 1
Interface stiffness is entered as Stfac.
= 2
Interface stiffness is the average of the main and secondary stiffness.
= 3
Interface stiffness is the maximum of the main and secondary stiffness.
= 4
Interface stiffness is the minimum of the main and secondary stiffness.
= 5
Interface stiffness is the main and secondary stiffness in series.
= 1000 Default, if /DEFAULT/INTER/TYPE7 is not defined
Interface stiffness is only based on the main side stiffness.

(Integer)

 
Ithe Heat contact flag.
=0
No heat transfer or heat friction.
=1
Heat transfer or heat friction activated.

(Integer)

 
Igap Gap/element option flag. 11
= 0
Set to value defined in /DEFAULT/INTER/TYPE7.
= 1
Variable gap varies according to the characteristics of the impacted main surface and the impacting secondary node.
= 2
Variable gap + gap scale correction of the computed gap.
= 3
Variable gap + gap scale correction of the computed gap + size of the mesh is taken into account to avoid initial penetrations during self-contact.
= 1000 Default, if /DEFAULT/INTER/TYPE7 is not defined
Constant gap; equal to the minimum gap Gapmin.

(Integer)

 
Ibag Airbag vent holes closure flag in case of contact.
This flag is also used to activate Sol2SPH particles, if the corresponding solid element is in contact.
= 0
Set to value defined in /DEFAULT/INTER/TYPE7.
= 1
Closure.
= 2 Default, if /DEFAULT/INTER/TYPE7 is not defined
No closure.

(Integer)

 
Idel Node and segment deletion flag.
= 0
Set to the value defined in /DEFAULT/INTER/TYPE7.
= 1
When all the elements (4-node shells, 3-node shells, solids) associated to one segment are deleted, the segment is removed from the main side of the interface. It is also removed in case of explicit deletion using Radioss Engine keyword /DEL in the Engine file.
Additionally, non-connected nodes are removed from the secondary side of the interface.
= 2
When a 4-node shell, a 3-node shell or a solid element is deleted, the corresponding segment is removed from the main side of the interface. It is also removed in case of explicit deletion using Radioss Engine keyword /DEL in the Engine file.
Additionally, non-connected nodes are removed from the secondary side of the interface.
= 1000 Default, if /DEFAULT/INTER/TYPE7 is not defined
No deletion.
= -1
Same as = 1, except non-connected nodes are not removed from the secondary side of the interface.
= -2
Same as =2, except non-connected nodes are not removed from the secondary side of the interface.

(Integer)

Note: Idel = 1 and -1 has a higher CPU cost when compared with Idel = 2 and -2.
 
Icurv Gap envelope with curvature. 5
=0 (Default)
No curvature.
=1
Spherical curvature.
=2
Cylindrical curvature.
=3
Automatic bicubic surface.

(Integer)

 
Iadm Computing local curvature flag for adaptive meshing. 6 7 8
=0 (Default)
Not activated.
=1
Interface update according mesh size.
=2
Interface update according mesh size, penetration and angle.

(Integer)

 
Fscalegap Gap scale factor (used only when Igap = 2 and 3).

Default = 1.0 (Real)

 
Gapmax Maximum gap (used only when Igap = 2 and 3).

(Real)

[ m ]
Fpenmax Maximum fraction of initial penetration. 13

(Real)

 
ITIED Tie contact nodes flag.
=0 (Default)
The nodes are not tied due to time step.
=1
Secondary node is tied with possible rebound when the contact time step is less than /DT/INTER/DEL or dtmin defined in the contact.
=2
Secondary node is tied without possible rebound when the contact time step is less than /DT/INTER/DEL or dtmin defined in the contact.

(Integer)

 
Stmin Minimum stiffness (used only when Istf = 2, 3, 4, or 5).

(Real)

[ N m ]
Stmax Maximum stiffness (used only when Istf = 2, 3, 4, or 5).

Default = 1030 (Real)

[ N m ]
%mesh_size Percentage of mesh size (used only when Igap = 3).

Default = 0.4 (Real)

 
dtmin Minimum interface time step. 23

(Real)

[ s ]
Irem_gap Flag for deactivating secondary nodes if element size < gap value, in case of self-impact contact. 14
= 0
Set to the value defined in /DEFAULT/INTER/TYPE7.
= 1 Default, if /DEFAULT/INTER/TYPE7 is not defined
No deactivation of secondary nodes.
= 2
Deactivation of secondary nodes.

(Integer)

 
Irem_i2 Flag for deactivating the secondary node, if the same contact pair (nodes) has been defined in interface TYPE2.
= 0
Set to the value defined in /DEFAULT/INTER/TYPE7.
= 1
Secondary nodes in /INTER/TYPE2 tied contacts are removed from this contact.
= 3 Default, if /DEFAULT/INTER/TYPE7 is not defined
No change to secondary nodees.
 
node_ID1 First node identifier.

(Integer)

 
node_ID2 Second node identifier (ignored when Icurv = 1).

(Integer)

 
Stfac Stiffness scale factor applied to main side of the interface (if Istf 1).

Default = 1.0 (Real)

 
Interface stiffness (if Istf = 1).

Default = 1.0 (Real)

[ N m ]
Fric Coulomb friction (if fct_IDF = 0).

Default = 0.0 (Real)

 
Coulomb friction scale factor (if fct_IDF 0). 20

Default = 1.0 (Real)

Gapmin Minimum gap for impact activation.

For default values, see 10 (Real)

[ m ]
Tstart Start time.

(Real)

[ s ]
Tstop Time for temporary deactivation.

(Real)

[ s ]
IBC Deactivation flag of boundary conditions at impact.

(Boolean)

 
Inacti Deactivation flag of stiffness in case of initial penetrations. 13
= 0
Set to the value defined in /DEFAULT/INTER/TYPE7.
= 1
Deactivation of stiffness on nodes.
= 2
Deactivation of stiffness on elements.
= 3
Change node coordinates to avoid initial penetrations.
= 5
Gap is variable with time and initial gap is adjusted as:
gap 0 = Gap P 0 , where P 0 is the initial penetration
= 6
Gap is variable with time, but initial gap is adjusted as (the node is slightly depenetrated):
gap 0 = Gap P 0 5 % ( Gap P 0 )
= 1000 Default, if /DEFAULT/INTER/TYPE7 is not defined
No action.

(Integer)

 
VISs Critical damping coefficient on interface stiffness.

Default set to 0.05 (Real)

 
VISF Critical damping coefficient on interface friction. 22

Default set to 1.0 (Real)

 
Bumult Sorting factor is used to speed up the sorting algorithm and is machine dependent.

Default set to 0.20 (Real)

 
Ifric Friction formulation flag. 1617
Only used if fric_ID is not defined.
= 0 (Default)
Static Coulomb friction law.
= 1
Generalized viscous friction law.
= 2
(Modified) Darmstad friction law.
= 3
Renard friction law.

(Integer)

 
Ifiltr Friction filtering flag. 18
= 0 (Default)
No filter is used.
= 1
Simple numerical filter.
= 2
Standard -3dB filter with filtering period.
= 3
Standard -3dB filter with cutting frequency.

(Integer)

 
Xfreq Filtering coefficient.

Default value depends on Ifiltr (Real)

 
Iform Friction penalty formulation type. 19
= 0
Set to the value defined in /DEFAULT/INTER/TYPE7.
= 1 Default, if /DEFAULT/INTER/TYPE7 is not defined
Viscous (total) formulation.
= 2
Stiffness (incremental) formulation.

(Integer)

 
sens_ID Sensor identifier to activate/deactivate the interface. 24

If an identifier sensor is defined, the activation/deactivation of interface is based on sensor and not on Tstart or Tstop.

(Integer)

 
fct_IDF Friction coefficient with temperature function identifier.

Default = 0 (Integer)

 
AscaleF Abscissa scale factor on fct_IDF.

Default = 1.0 (Real)

 
fric_ID Friction identifier for friction definition for selected pairs of parts.
= 0 (Default)
Use friction parameters defined in this interface.
0
Use /FRICTION/fric_ID.

(Integer)

 
C1 - C6 Friction law coefficient.

(Real)

See Table 1
Kthe Heat exchange coefficient (if fct_IDK = 0).

Default = 0.0

[ W m 2 K ]
Heat exchange coefficient (if fct_IDK 0). 20

Default = 1.0 (Real)

fct_IDK Function identifier for thermal heat exchange definition with contact pressure.

Default = 0 (Integer)

 
AscaleK Abscissa scale factor on fct_IDK.

Default = 1.0 (Real)

[ Pa ]
Tint Interface temperature. 20

(Real)

[ K ]
Ithe_form Heat contact formulation flag.
= 0 (Default)
Exchange only between interface (constant temperature) and shells (secondary side).
= 1
Heat exchange between all pieces in contact.

(Integer)

 
NRadm Number of elements through a 90 degrees radius.

(Integer)

 
Padm Criteria on the percentage of penetration.

Default = 1.0 (Real)

 
Angladm Angle criteria.

(Real)

[ deg ]
Frad Radiation factor.

(Real)

[ W m 2 K 4 ]
Drad Maximum distance for radiation computation.

(Real)

[ m ]
Fheats Frictional heating factor of secondary. 21

(Real)

 
Fheatm Frictional heating factor of main. 21

(Real)

 

Flags for Deactivation of Boundary Conditions: IBC

(1)-1 (1)-2 (1)-3 (1)-4 (1)-5 (1)-6 (1)-7 (1)-8
          IBCX IBCY IBCZ

Definition

Field Contents SI Unit Example
IBCX
=1
Deactivation flag of X boundary condition at impact.

(Boolean)

 
IBCY
=1
Deactivation flag of Y boundary condition at impact.

(Boolean)

 
IBCZ
=1
Deactivation flag of Z boundary condition at impact.

(Boolean)

 

Comments

  1. In case of SPMD, each mainr segment defined by surf_IDm must be associated to an element (possibly to a void element).
  2. For the flag Ibag, refer to the monitored volume option (Monitored Volumes (Airbags)).
  3. Contact stiffness, K is computed as:
    If Istf =1:(1)
    K = S t f a c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbGaey ypa0Jaam4uaiaadshacaWGMbGaamyyaiaadogaaaa@3CBE@
    If Istf = 2, 3, 4 or 5:(2)
    K = max [ S t min , min ( S t max , K n ) ]
    If Istf =1000:(3)
    K = K m

    Where, K n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaaaa@384D@ is computed from both main segment stiffness K m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaaaa@384D@ and secondary node stiffness K s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaaaa@384D@ :

    Istf = 2, K n = K m + K s 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaOGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaSqa aiaad2gaaeqaaOGaey4kaSIaam4samaaBaaaleaacaWGZbaabeaaaO qaaiaaikdaaaaaaa@3F01@

    Istf = 3, K n = max ( K m , K s ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaOGaeyypa0JaciyBaiaacggacaGG4bWaaeWa aeaacaWGlbWaaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUeadaWgaa WcbaGaam4CaaqabaaakiaawIcacaGLPaaaaaa@4260@

    Istf = 4, K n = min ( K m , K s ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaOGaeyypa0JaciyBaiaacMgacaGGUbWaaeWa aeaacaWGlbWaaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUeadaWgaa WcbaGaam4CaaqabaaakiaawIcacaGLPaaaaaa@425E@

    Istf = 5, K n = K m K s K m + K s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaOGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaSqa aiaad2gaaeqaaOGaeyyXICTaai4samaaBaaaleaacaGGZbaabeaaaO qaaiaadUeadaWgaaWcbaGaamyBaaqabaGccqGHRaWkcaWGlbWaaSba aSqaaiaadohaaeqaaaaaaaa@4479@

    K m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaaaa@384D@ is the main segment stiffness and computed as:

    When the main segment lies on a shell or is shared by shell and solid:(4)
    K m = Stfac 0.5 E t
    When the main segment lies on a solid:(5)
    K m = Stfac B S 2 V
    Where,
    S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGtbaaaa@39AF@
    Segment area
    V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGtbaaaa@39AF@
    Volume of the solid
    B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGtbaaaa@39AF@
    Bulk modulus

    K s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaad6gaaeqaaaaa@384D@ is an equivalent nodal stiffness considered for interface TYPE7, and computed as:

    When the node is connected to a shell element:(6)
    K s = 1 2 E t
    When the node is connected to a solid element:(7)
    K s = B V 3

    There is no limitation to the value of stiffness scale factor Stfac (but, a value greater than 1.0 can reduce the initial time step).

    When using /PROP/VOID and /MAT/VOID, material properties and thickness for the VOID material must be entered; otherwise, the contact stiffness of the void elements will be zero. This is especially important if VOID shell elements share elements with solid elements as the stiffness of the shell elements is used in the contact calculation.

  4. Istf = 2, 3, 4, or 5 are not compatible with SPH formulation.
  5. If Icurv = 1, a spherical curvature is defined for the gap with node_ID1 (center of the sphere).

    If Icurv = 2, a cylindrical curvature is defined for the gap with node_ID1 and node_ID2 (on the axis of the cylinder).

    If Icurv = 3, the main surface shape is obtained with a bicubic interpolation, respecting continuity of the coordinates and the normal from one segment to the other. In case of a fast and large change in curvature, this formulation might become unstable (will be improved in future version).

    inter_type7_Icurv
    Figure 1.
  6. In case of adaptive meshing and Iadm = 1:
    If the contact occurs in a zone (main side) whose radius of curvature is lower than the element size (secondary side), the element on the secondary side will be divided (if not yet at maximum level).

    inter_type7_Iadm
    Figure 2.
  7. In case of adaptive meshing and Iadm = 2:

    If the contact occurs in a zone (main side) whose radius of curvature is lower than NRadm times the element size (secondary side), the element on the secondary side will be divided (if not yet at maximum level).

    If the contact occurs in a zone (main side) where the angles between the normals are greater than Angladm and the percentage of penetration is greater than Padm, the element on the secondary side will be divided (if not yet at maximum level).


    Figure 3.
  8. The coefficients NRadm, Padm, and Angladm are used only if adaptive meshing and Iadm=2.
  9. If Gapmax=0, there is no maximum value for the gap.
  10. If Gapmin=0 or blank, a default value is computed as:

    If main segments are shell and solid elements, Gapmin = min ( t m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBe aaleaacaWGTbaabeaaaaa@380E@ , l min 2 ).

    Where,
    t m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBe aaleaacaWGTbaabeaaaaa@380E@
    The average thickness of the main shell elements, for Igap=0
    t m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBe aaleaacaWGTbaabeaaaaa@380E@
    The minimum thickness of the main shell elements, for Igap=1, 2, or 3
    l min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGSbWaaS baaSqaaiGac2gacaGGPbGaaiOBaaqabaaaaa@3A4D@
    The smallest side length of all main segments (shell or brick)

    If main segments are all solid elements Gapmin = l min 10

    Where, l min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGSbWaaS baaSqaaiGac2gacaGGPbGaaiOBaaqabaaaaa@3A4D@ being the smallest side of all main brick segments.

  11. Variable gap:
    If Igap =1, variable gap is computed as:(8)
    max [ Gap min , ( g s + g m ) ]
    If Igap =2, variable gap is computed as:(9)
    max { Gap min , min [ Fscal e g a p ( g s + g m ) , Gap max ] }
    If Igap =3, variable gap is computed for self-contact as:(10)
    max { Gap min , min [ Fscal e gap ( g s + g m ) , % m e s h _ s i z e ( g s _ l + g m _ l ) , Gap max ] }
    Where,
    • g m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbWaaS baaSqaaiaad2gaaeqaaaaa@3868@ : main element gap

      g m = t 2 : with t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0baaaa@3758@ being the thickness of the main element for shell elements

      g m = 0 : for brick elements

    • g s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbWaaS baaSqaaiaadohaaeqaaaaa@386E@ : secondary node gap

      g s = 0 : if the secondary node is not connected to any element or is only connected to brick or spring elements

      g s = t 2 : with t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0baaaa@3758@ being the largest thickness of the shell elements connected to the secondary node

      g s = 1 2 S : for truss and beam elements. With S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0baaaa@3758@ being the cross section of the element

    • g m _ l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbWaaS baaSqaaiaad2gacaGGFbGaamiBaaqabaaaaa@3A3C@ : length of the smaller edge of element
    • g s _ l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbWaaS baaSqaaiaad2gacaGGFbGaamiBaaqabaaaaa@3A3C@ : length of the smaller edge of elements connected to the secondary node

    If the secondary node is connected to multiple shells and/or beams or trusses, the largest computed secondary gap is used.

    The variable gap is always at least equal to Gapmin.

  12. Deactivation of the boundary condition is applied to secondary nodes group (grnd_IDs).
  13. Inacti = 3 may create initial energy if the node belongs to a spring element.
    Inacti = 6 is recommended instead of Inacti =5, in order to avoid high frequency effects into the interface.


    Figure 4.

    If Fpenmax is not equal to zero, nodes stiffness is deactivated if:

    P e n e t r a t i o n F p e n m a x G a p whatever the value of Inacti.

  14. With Irem_gap = 2, it allows to have the element size smaller than gap values:

    inter_type7_master_seg
    Figure 5. Secondary nodes removed from node to surface contact

    For self-impact contact, when Curvilinear Distance (from a node of the main segment to a secondary node) is smaller than 2 G a p (in initial configuration), this secondary node will not be taken into account by this main segment, and it will not be deleted from the contact for the other main segments.

  15. One node can belong to the two surfaces at the same time.
  16. If fric_ID is defined, the contact friction is defined in /FRICTION and the friction inputs (Ifric, C1, etc.) in this input card are not used.

    For friction formulation:

    If the friction flag Ifric=0 (default), the old static friction formulation is used:

    F t μ F n with μ being the Coulomb friction coefficient
    • If fct_IDF = 0:
      Ifric is the Coulomb friction.(11)
      μ = Fric
    • If fct_IDF0:
      Fric becomes a scale factor of Coulomb friction coefficient which depends on the temperature.(12)
      μ = Fric f F ( Ascale F , T interface )
    While T interface is the temperature which is taken as the mean temperature of secondary and main:(13)
    T interface = T secondary + T main 2

    For flag Ifric > 0, new friction models are introduced. In this case, the friction coefficient is set by a function ( μ = μ ( ρ , V ) ).

    Where,
    ρ
    Pressure of the normal force on the main segment
    V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwbaaaa@373A@
    Tangential velocity of the secondary node relative to the main segment
  17. Currently, the coefficients C1 through C6 are used to define a variable friction coefficient μ for new friction formulations.
    The following formulations are available:
    • Ifric = 1 (Generalized Viscous Friction law):(14)
      μ = Fric + C 1 . p + C 2 V + C 3 . p V + C 4 p 2 + C 5 V 2
    • Ifric = 2 (Modified Darmstad law):(15)
      μ = Fric + C 1 . e ( C 2 V ) . p 2 + C 3 . e ( C 4 V ) . p + C 5 . e ( C 6 V )
    • Ifric = 3 (Renard law):(16)
      μ = C 1 + ( C 3 C 1 ) V C 5 ( 2 V C 5 ) if V [ 0 , C 5 ]
      (17)
      μ = C 3 ( ( C 3 C 4 ) ( V C 5 C 6 C 5 ) 2 ( 3 2 V C 5 C 6 C 5 ) ) if V [ C 5 C 6 ]
      (18)
      μ = C 2 1 1 C 2 C 4 + ( V C 6 ) 2 if V C 6
    Where for Ifric=3:
    • C 1 = μ s , static coefficient of friction, must be μ min < μ s < μ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiabgYda8iabeY7aTnaa BaaaleaacaWGZbaabeaakiabgYda8iabeY7aTnaaBaaaleaaciGGTb GaaiyyaiaacIhaaeqaaaaa@44BF@
    • C 2 = μ d , dynamic coefficient of friction, must be μ min < μ d < μ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiabgYda8iabeY7aTnaa BaaaleaacaWGKbaabeaakiabgYda8iabeY7aTnaaBaaaleaaciGGTb GaaiyyaiaacIhaaeqaaaaa@44B0@
    • C 3 = μ max , maximum coefficient of friction
    • C 4 = μ min , mimimum coefficient of friction
    • C 5 = V cr 1 , first critical velocity, must be > 0
    • C 6 = V c r 2 , second critical velocity, must be > V c r 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH+aGpca WGwbWaaSbaaSqaaiaadogacaWGYbGaaGymaaqabaaaaa@3B08@
    Table 1. Units for Friction Formulations
    Ifric Fric C1 C2 C3 C4 C5 C6
    1 [ 1 P a ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaaGymaaqaaiaaccfacaGGHbaaaaGaay5waiaaw2faaaaa @3AD5@ [ s m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4Caaqaaiaab2gaaaaacaGLBbGaayzxaaaaaa@3A46@ [ s Pa m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4CaaqaaiaabcfacaqGHbGaeyyXICTaaeyBaaaaaiaa wUfacaGLDbaaaaa@3E47@ [ 1 Pa 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaaGymaaqaaiaabcfacaqGHbWaaWbaaSqabeaacaaIYaaa aaaaaOGaay5waiaaw2faaaaa@3BC6@ [ s 2 m 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4CamaaCaaaleqabaGaaGOmaaaaaOqaaiaab2gadaah aaWcbeqaaiaaikdaaaaaaaGccaGLBbGaayzxaaaaaa@3C2C@
    2 [ 1 Pa 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaaGymaaqaaiaabcfacaqGHbWaaWbaaSqabeaacaaIYaaa aaaaaOGaay5waiaaw2faaaaa@3BC6@ [ s m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4Caaqaaiaab2gaaaaacaGLBbGaayzxaaaaaa@3A46@ [ 1 P a ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaaGymaaqaaiaaccfacaGGHbaaaaGaay5waiaaw2faaaaa @3AD5@ [ s m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4Caaqaaiaab2gaaaaacaGLBbGaayzxaaaaaa@3A46@ [ s m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaae4Caaqaaiaab2gaaaaacaGLBbGaayzxaaaaaa@3A46@
    3 [ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@ [ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
  18. Friction filtering:
    If Ifiltr flag 0, the tangential forces are smoothed using a filter:(19)
    F T f = α F T ( t ) + ( 1 α ) F T f ( t d t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGubGaamOzaaqabaGccqGH9aqpcqaHXoqycaWHgbWaaSba aSqaaiaadsfaaeqaaOGaaiikaiaadshacaGGPaGaey4kaSYaaeWaae aacaaIXaGaeyOeI0IaeqySdegacaGLOaGaayzkaaGaaCOramaaBaaa leaacaWGubGaamOzaaqabaGccaGGOaGaamiDaiabgkHiTiaadsgaca WG0bGaaiykaaaa@4D30@
    Where,
    F T f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGubGaamOzaaqabaaaaa@38B5@
    Filtered tangential force.
    F T ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGubaabeaakiaacIcacaWG0bGaaiykaaaa@3A26@
    Calculated tangential force at time t before filtering.
    F Tf (tdt) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGubGaamOzaaqabaGccaGGOaGaamiDaiabgkHiTiaadsga caWG0bGaaiykaaaa@3DE0@
    Filtered tangential force at the previous time step
    t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaads haaaa@37D8@
    Current simulation time
    dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaads haaaa@37D8@
    Current simulation time step
    α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3796@
    Filtering coefficient
    Where α coefficient is calculated from:
    • If Ifiltr = 1: α = X f r e q , simple numerical filter with a value between 0 and 1.
    • If Ifiltr = 2: α = 2 π X f r e q , standard -3dB filter, with the number of time steps to filter defined as X freq = d t T , and T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGubaaaa@39B0@ is the filtering period.
    • If Ifiltr = 3: α = 2 π X freq dt , standard -3dB filter, with Xfreq = cutting frequency.
  19. Friction penalty formulation Iform:
    • If Iform = 1 (default) viscous formulation, the friction forces are:(20)
      F t = min ( μ F n , F adh )
      While an adhesion force is computed as:(21)
      F adh = C V t with C = VIS F 2 Km
    • If Iform = 2, stiffness formulation), the friction forces are:(22)
      F t new = min ( μ F n , F adh )

      While an adhesion is computed as:

      F a d h = F t o l d + Δ F t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaaS baaSqaaiaadggacaWGKbGaamiAaaqabaGccqGH9aqpcaWGgbWaa0ba aSqaaiaadshaaeaacaWGVbGaamiBaiaadsgaaaGccqGHRaWkcaqGuo GaamOramaaBaaaleaacaWG0baabeaaaaa@43D7@ with Δ F t = K V t d t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaqGuoGaam OramaaBaaaleaacaWG0baabeaakiabg2da9iaadUeacqGHflY1caWG wbWaaSbaaSqaaiaadshaaeqaaOGaeyyXICTaamizaiaadshaaaa@43C9@

      Where, V t is the tangential velocity of the secondary node relative to the main segment.

      Iform = 2 is recommended for implicit and explicit analysis.

  20. Heat exchange:
    By Ithe =1 (heat transfer activated) to consider heat exchange and heat friction in contact.
    • If Ithe_form = 0, then heat exchange is between shell and constant temperature contact Tint.
    • If Ithe_form = 1, then heat exchange is between all contact pieces.

      Tint is used only when Ithe_form= 0. In this case, the temperature of main side assumed to be constant (equal to Tint). If Ithe_form=1, then Tint is not taken into account, for the nodal temperature of main side will be considered.

    Heat exchange coefficient:
    • If fct_IDK = 0, then Kthe is heat exchange coefficient and heat exchange depends only on heat exchange surface.
    • If fct_IDK0, then Kthe is a scale factor and the heat exchange will depend on the contact pressure:(23)
      K = K the f K ( Ascale K , P )
    • While f K is the function of fct_IDK.
  21. Heat Friction:
    • Frictional energy is converted into heat when Ithe > 0 for interface Type 7 only.
    • Fheats and Fheatm are defined as the fraction of frictional energy and distributed respectively to the secondary side and main side. So generally:(24)
      Fheat s + Fheat m 1.0

      When both Fheats and Fheatm are equal to 0, the conversion of the frictional sliding energy to heat is not activated.

    • The frictional heat QFric is defined:
      • If Iform= 2 (a stiffness formulation):
        Secondary side: (25)
        Q Fric = Fheat s ( F adh F t ) K F t
        Main side: (26)
        Q Fric = Fheat m ( F adh F t ) K F t
        (Ithe_form= 1)
      • If Iform= 1 (a penalty formulation):
        Secondary side: (27)
        Q Fric = Fheat s C V t 2 d t
        Main side: (28)
        Q Fric = Fheat m C V t 2 d t
        (Ithe_form= 1)
  22. Radiation:
    Radiation is considered in contact if F r a d 0 and the distance, d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadkhacaWGHbGaamizaaqabaaaaa@3A1A@ , of the secondary node to the main segment is:(29)
    Gap < d < D rad
    While D r a d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadkhacaWGHbGaamizaaqabaaaaa@3A1A@ is the maximum distance for radiation computation. The default value for D r a d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadkhacaWGHbGaamizaaqabaaaaa@3A1A@ is computed as the maximum of:
    • Upper value of the Gap (at time 0) among all nodes
    • Smallest side length of secondary element

    It is recommended not to set the value too high for D r a d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadkhacaWGHbGaamizaaqabaaaaa@3A1A@ , which may reduce the performance of Radioss Engine.

    A radiant heat transfer conductance is computed as:(30)
    h rad = F rad ( T m 2 + T s 2 ) ( T m + T s )
    with(31)
    F rad = σ 1 ε 1 + 1 ε 2 1
    Where,
    σ = 5.669 × 10 8 [ W m 2 K 4 ]
    Stefan Boltzman constant
    ε 1
    Emissivity of secondary surface
    ε 2
    Emissivity of main surface
  23. If the time step of a secondary node in this contact becomes less than dtmin, the secondary node is deleted from the contact and a warning message is printed in the output file. This dtmin value takes precedence over any model interface minimum time step entered in /DT/INTER/DEL.
  24. When sens_ID is defined for activation/deactivation of the interface, Tstart and Tstop are not taken into account.
  25. It is necessary to activate the option Idel= -1 or -2 for parts with SOL2SPH formulation (/PROP/TYPE14 (SOLID)).