/INTER/TYPE25
Block Format Keyword TYPE25 is a general nodes to surface contact interface using the penalty method. The penalty stiffness is constant and therefore the time step is not affected.
Solid elements have zero contact gap thickness. Contact inputs can be defined as a single surface, surface to surface, or nodes to surface.
This contact interface can replace interface TYPE3, TYPE5, TYPE7, TYPE19 or TYPE24.
This interface is not available with the implicit solution.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/INTER/TYPE25/inter_ID/unit_ID  
inter_title  
surf_ID_{1}  surf_ID_{2}  I_{stf}  I_{the}  I_{gap}  Irem_i2  I_{del}  I_{edge}  
grnd_ID_{s}  Gap_scale  %mesh_size  Gap_max_s  Gap_max_m  
St_{min}  St_{max}  I_{gap0}  I_{shape}  Edge_angle 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Stfac  Fric  T_{start}  T_{stop}  
I_{BC}  IVIS2  Inacti  VIS_{s}  
I_{fric}  I_{filtr}  X_{freq}  sens_ID  fric_ID 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

C_{1}  C_{2}  C_{3}  C_{4}  C_{5} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

C_{6} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

ViscFluid  SigMaxAdh  ViscAdhFact 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{the}  fct_ID_{K}  T_{int}  I_{the_form}  Ascale_{K}  
F_{rad}  D_{rad}  Fheat_{s}  Fheat_{m}  fct_ID_{F}  
fct_ID_{c}  Dcond 
Definitions
Field  Contents  SI Unit Example 

inter_ID  Interface
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

inter_title  Interface
title. (Character, maximum 100 characters) 

surf_ID_{1}  First surface identifier. 1 (Integer) 

surf_ID_{2}  Second surface
identifier. (Integer) 

I_{stf}  Interface stiffness
definition flag. 2
(Integer) 

I_{the}  Heat transfer flag.
Thermal exchange is not available for edge to edge. (Integer) 

I_{gap}  Gap/element option flag.
3


Irem_i2  Deactivating flag for the
secondary node, if the same contact pair (nodes) has been defined in
interface TYPE2.


I_{del}  Node and segment deletion flag.


I_{edge}  Edge contact options.
Contact occurs between main and secondary edges which are
automatically extracted from surf_ID_{1} and surf_ID_{2}. Sharp edges for external solid faces are defined using the angle
Edge_angle.
(Integer) 

grnd_ID_{s}  Nodes group
identifier. 1 If defined, node group will be added as secondary nodes. (Integer) 

Gap_scale  Gap scale factor for all
I_{gap} options. Default = 1.0 (Real) 

%mesh_size  Percentage of mesh size
(used only when I_{gap} = 3). Default = 0.4 (Real) 

Gap_max_s  Secondary maximum gaps.
3 Default = 10^{30} (Real) 
$\left[\text{m}\right]$ 
Gap_max_m  Main maximum gaps. 3 Default = 10^{30} (Real) 
$\left[\text{m}\right]$ 
St_{min}  Minimum stiffness (used
only when I_{stf} >
1 and I_{stf} < 7). 2 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
St_{max}  Maximum stiffness (used
only when I_{stf} > 1
and I_{stf} < 7). 2 Default = 10^{30} (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
I_{gap0}  Gap modification flag for
secondary shell nodes on the free edges or shell elements. 3
(Integer) 

I_{shape}  Flag defining the shape of
the gap along the surface(s) external border in the node to surface contact.
(Integer) 

Edge_angle  Edge angle Only used with I_{edge} =11,13. Sharp edges are included in edge contact, if the angle between two segments which share the same edge is smaller than Edge_angle value. Default = 135° (Real) 
$\left[\mathrm{deg}\right]$ 
Stfac  Interface stiffness scale
factor. 2 Default = 1.0 (Real) 

Fric  Coulomb friction (if fct_ID_{F}= 0). Coulomb friction scale factor (if fct_ID_{F}≠ 0). Default = 0.0 (Real) 

T_{start}  Start time. 10
(Real) 
$\left[\text{s}\right]$ 
T_{stop}  Temporary deactivation
time. 10 Default = 10^{30} (Real) 
$\left[\text{s}\right]$ 
I_{BC}  Deactivation flag of
boundary conditions at impact. (Boolean) 

Inacti  Initial penetration flag.
(Integer) 

VIS_{s}  Critical damping
coefficient on interface stiffness. Default = 0.05 (Real) 

I_{fric}  Friction formulation
flag. Only used if fric_ID is not defined.
For edge to edge contact, only static Coulomb friction law is available. (Integer) 

I_{filtr}  Friction filtering flag.
(Integer) 

X_{freq}  Filtering
coefficient. Default = 1.0 (Real) 

sens_ID  Sensor identifier to
activate/deactivate the interface. (Integer) 

fric_ID  Friction identifier for
friction definition for selected pairs of parts.
For edge to edge contact, only isotropic friction is considered. If the corresponding model is orthotropic, only coefficient in direction 1 of contacted part is taken into account for edge to edge contact. (Integer) 

C_{1}  Friction law coefficient.
5 (Real) 

C_{2}  Friction law
coefficient. (Real) 

C_{3}  Friction law
coefficient. (Real) 

C_{4}  Friction law
coefficient. (Real) 

C_{5}  Friction law
coefficient. (Real) 

C_{6}  Friction law
coefficient. (Real) 

IVIS2  Interface adhesion flag.
12
(Interger) 

ViscFluid  Viscosity of the fluid at
the interface. 12 (Real) 
$\left[\text{Pa}\cdot \text{s}\right]$ 
SigMaxAdh  Maximum transverse
adhesive stress at interface. 12 (Real) 
$\left[\text{Pa}\right]$ 
ViscAdhFact  Tangential viscous
resistant force scaling factor. 12 (Real) 

K_{the}  Conductive heat exchange
coefficient (if fct_ID_{K} = 0). Default = 0.0 (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
Heat exchange scale factor
(if fct_ID_{K}≠ 0) Default = 0.0 (Real) 

fct_ID_{K}  Function identifier for
heat exchange definition with contact pressure. Default = 0 (Integer) 

Ascale_{K}  Abscissa scale factor on
fct_ID_{K}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
T_{int}  Interface temperature.
(Real) 
$\left[\text{K}\right]$ 
I_{the_form}  Heat contact formulation
flag.
(Integer) 

F_{rad}  Radiation factor.
(Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}{\text{K}}^{\text{4}}}\right]$ 
D_{rad}  Maximum distance for
radiation computation. (Real) 
$\left[\text{m}\right]$ 
fct_ID_{c}  Function identifier for
the conductive heat exchange coefficient definition as a function of
distance. Default = 0 (Integer) 

Dcond  Maximum distance for
conductive heat exchange. Default = 0.0 (Real) 
$\left[\text{m}\right]$ 
Fheat_{s}  Frictional heating factor
of secondary. (Real) 

Fheat_{m}  Frictional heating factor
of main. (Real) 

fct_ID_{F}  Friction coefficient with
temperature function identifier. Default = 0 (Integer) 
Flags for Deactivation of Boundary Conditions: IBC
(1)1  (1)2  (1)3  (1)4  (1)5  (1)6  (1)7  (1)8 

I_{BCX}  I_{BCY}  I_{BCZ} 
Definitions
Field  Contents  SI Unit Example 

I_{BCX}  Deactivation flag of X
boundary condition at impact.
(Boolean) 

I_{BCY}  Deactivation flag of Y
boundary condition at impact.
(Boolean) 

I_{BCZ}  Deactivation flag of Z
boundary condition at impact.
(Boolean) 
Comments
 Contact main/secondary pairs
can be defined in three ways:
 Single selfimpacting surface only: surf_ID_{1} > 0, and surf_ID_{2} = 0
 Symmetric surface to surface: surf_ID_{1} > 0, and surf_ID_{2} > 0
 Nodes to surface: grnd_ID_{s} > 0, surf_ID_{1} = 0, and surf_ID_{2} > 0
grnd_ID_{s} > 0 is used to define node to surface contact type, but it may also be used in other contact types. In that case, the node group will be added simply as supplementary secondary nodes, which is useful when users want to add spring element nodes, main node of rigid body, etc. into the contact (as secondary nodes).
If the surface is defined with shells, two contact segments (shifted by half thickness (t)) with opposite normal directions will be generated:In case of SPMD, each main segment defined by surf_ID_{i} (i=1, 2) must be associated to an element (possibly to a void element).
In cases where quadratic elements are used, it is recommended to define the surfaces by using /SURF/PART/EXT as in that case, middle nodes of quadratic elements are used in the contact treatment.
The surface definition /SURF/PART/ALL is not available with TYPE25.
 Contact stiffness,
$K$
is computed as:
(1) $$K=\mathrm{max}\left[S{t}_{\mathrm{min}},\mathrm{min}\left(S{t}_{\mathrm{max}},{K}_{n}\right)\right]$$Where, ${K}_{n}$ depends on I_{stf}: I_{stf} = 1000, ${K}_{n}={K}_{m}$
 I_{stf} = 2, ${K}_{n}=\frac{{K}_{m}+{K}_{s}}{2}$
 I_{stf} = 3, ${K}_{n}=\mathrm{max}\left({K}_{m},{K}_{s}\right)$
 I_{stf} = 4, ${K}_{n}=\mathrm{min}\left({K}_{m},{K}_{s}\right)$
 I_{stf} = 5, ${K}_{n}=\frac{{K}_{m}\cdot {K}_{s}}{{K}_{m}+{K}_{s}}$
${K}_{m}$ : main segment stiffness and computed as: ${K}_{m}=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , when the main segment lies on a shell.
 ${K}_{m}=\mathit{Stfac}\cdot B\cdot \frac{{S}^{2}}{V}$ , when main segment lies on a solid.
 ${K}_{m}=\mathrm{max}\left(\mathit{Stfac}\cdot 0.5\cdot E\cdot t,\mathit{Stfac}\cdot B\cdot \frac{{S}^{2}}{V}\right)$ , when main segment is shared by shell and solid.
${K}_{s}$ : Secondary node stiffness is an equivalent nodal stiffness considered for interface TYPE25, and computed as: ${K}_{m}=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , when node is connected to a shell element,
 ${K}_{s}=Stfac\cdot B\cdot \sqrt[3]{V}$ , when node is connected to solid element.
Where, $S$
 Segment area
 $V$
 Volume of the solid
 $B$
 Bulk modulus
 $t$
 Thickness of the shell
The Stfac value can be larger than 1.0. There is no limitation value to the stiffness factor (a value larger 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.
 The gap is computed
automatically for each impact as:
 If I_{gap} = 1, variable gap is computed as:
(2) $$\mathrm{min}({g}_{s},Gap\_\mathrm{max}\_s)+\mathrm{min}({g}_{m},Gap\_\mathrm{max}\_m)$$  If I_{gap}=2, variable gap is computed as:
(3) $$\mathrm{min}({g}_{s},Gap\_\mathrm{max}\_s)+\mathrm{min}({g}_{m},Gap\_\mathrm{max}\_m)$$with deactivation of secondary nodes when the element size is smaller than gap values:For selfimpact contact, when Curvilinear Distance (from a node of the main segment to a secondary node) is smaller than $\sqrt{2}\cdot Gap$ (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.
 If I_{gap}= 3, variable gap is computed as:
(4) $$\mathrm{min}\left[\mathrm{min}({g}_{s},Gap\_\mathrm{max}\_s)+\mathrm{min}({g}_{m},Gap\_\mathrm{max}\_m),\%mesh\_size\cdot \left({g}_{s\_l}+{g}_{m\_l}\right)\right]$$Where,
${g}_{m}$
: main element gap:
${g}_{m}=Gap\_scale*\frac{t}{2}$ , with $t$ is the thickness of the main element for shell elements
${g}_{m}=0$ , for brick elements

${g}_{s}$
: 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.
${g}_{s}=Gap\_scale*\frac{t}{2}$ , if the secondary node is connected to a shell element, with $t$ being the largest thickness of the shell elements connected to the secondary node.
${g}_{s}=Gap\_scale*\frac{\sqrt{S}}{2}$ , if the secondary node is connected to truss or beam elements, with $S$ being the cross section of the 1D element.
If the gap modification flag for secondary shell nodes on the free edges I_{gap0} is set to 1: ${g}_{s}$ is reset to zero if the secondary node lies on the free edges of the secondary surface. The gap modification flag for secondary shell nodes on the free edges has no effect if the secondary node is defined through the optional node group (grnod_IDs).
If the secondary node is connected to multiple shells and/or beams or trusses, the largest computed secondary gap is used.

${g}_{m}$
: main element gap:
 $gm\_l$ : length of the smallest edge of the main segment.

$gs\_l$
: if the secondary node belongs to the
main surface,
$gs\_l$
is the length of the smallest edge of
main segments connected to the secondary node,
$gs\_l$
=1E+30, otherwise.
In any case, ${g}_{m}$ and ${g}_{s}$ are limited separately by Gap_max_m and Gap_max_s before the gap is computed.
If the secondary node does not belong to the main surface, the gap remains(5) $$\mathrm{min}({g}_{s},Gap\_\mathrm{max}\_s)+\mathrm{min}({g}_{m},Gap\_\mathrm{max}\_m)$$
 If I_{gap} = 1, variable gap is computed as:
 For node to surface contact,
the gap never extends more than the secondary node gap out of the surface
external border. I_{shape}
determines if the shape of this gap is square or round and the contact force
(normal) direction. I_{shape} has
no effect on the gap and its shape for edge to edge contact.Depending on I_{shape} the gap used for contact at the main surface external border and resulting force direction.
I_{shape} =1 is not available with I_{gap} =3 and will then be reset to I_{shape} =2.
 For shell element edge to
edge contact, the gap is round. The main side contact gap on the free edge is
shifted so that the edge does not extend out of the shell segment.
The secondary side contact gap on the free edge behavior depends on the value of I_{gap0} as shown in figure xyz.
 For solid elements when I_{edge}=11 and I_{edge}=13, the secondary side consists of only the sharp edges with angle smaller than Edge_angle. For I_{edge}=22, all edges from solid elements are considered on secondary side. On the main side, all edges from solid elements are included for all 3 I_{edge} cases.
 If fric_ID is defined, the contact friction is defined in /FRICTION
and the friction inputs (I_{fric}, C_{1}, etc.) in this input card are not used.The friction forces are:
(6) $${F}_{t}^{new}=\mathrm{min}\left(\mu {F}_{n},{F}_{adh}\right)$$While an adhesion force is computed as:
${F}_{adh}={F}_{t}^{old}+\mathrm{\text{\Delta}}F$ with $\mathrm{\text{\Delta}}{F}_{t}=K\cdot {V}_{t}\cdot dt$
Where, $\mu $ is the Coulomb friction coefficient and is defined as: For flag I_{fric} by default:
$\mu =Fric$ with ${F}_{T}\le \mu \cdot {F}_{N}$ (Coulomb friction)
 For flag I_{fric} > 1, new friction
models are introduced. In this case, the friction coefficient is set
by a function:
$\mu =\text{\mu}(\rho ,V)$
Where, $\rho $
 Pressure of the normal force on the main segment
 $V$
 Tangential velocity of the secondary node relative to the main segment
Currently, the coefficients C_{1} through C_{6} are used to define a variable friction coefficient $\mu $ for new friction formulations.
The following formulations are available: I_{fric} = 1
(Generalized Viscous Friction law):
(7) $$\mu =\mathit{Fric}+{C}_{1}\cdot p+{C}_{2}\cdot V+{C}_{3}\cdot p\cdot V+{C}_{4}\cdot {p}^{2}+{C}_{5}\cdot {V}^{2}$$  I_{fric} = 2
(Modified Darmstad law):
(8) $$\mu =Fric+{C}_{1}\cdot {e}^{\left({C}_{2}V\right)}\cdot {p}^{2}+{C}_{3}\cdot {e}^{\left({C}_{4}V\right)}\cdot p+{C}_{5}\cdot {e}^{\left({C}_{6}V\right)}$$  I_{fric} = 3
(Renard law):
$\mu ={C}_{1}+\left({C}_{3}{C}_{1}\right)\cdot \frac{V}{{C}_{5}}\cdot \left(2\frac{V}{{C}_{5}}\right)$ if $V\in \left[0,{C}_{5}\right]$
$\mu ={C}_{3}\left(\left({C}_{3}{C}_{4}\right)\cdot {\left(\frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)}^{2}\cdot \left(32\cdot \frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)\right)$ if $V\in \left[{C}_{5},{C}_{6}\right]$
$\mu ={C}_{2}\frac{1}{\frac{1}{{C}_{2}{C}_{4}}+{\left(V{C}_{6}\right)}^{2}}$ if $V\ge {C}_{6}$
Where, ${C}_{1}={\mu}_{s}$ , static coefficient of friction, must be ${\mu}_{\mathrm{min}}<{\mu}_{s}<{\mu}_{\mathrm{max}}$
 ${C}_{2}={\mu}_{d}$ , dynamic coefficient of friction, must be ${\mu}_{\mathrm{min}}<{\mu}_{d}<{\mu}_{\mathrm{max}}$
 ${C}_{3}={\mu}_{\mathrm{max}}$ , maximum coefficient of friction
 ${C}_{4}={\mu}_{\mathrm{min}}$ , minimum coefficient of friction
 ${C}_{5}={V}_{cr1}\ne 0$ , first critical velocity, must be > 0
 ${C}_{6}={V}_{cr2}$ , second critical velocity, must be $>{V}_{cr1}$
 First critical velocity ${V}_{cr1}={C}_{5}$ must be less than the second critical velocity ${V}_{cr2}={C}_{6}\left({C}_{5}<{C}_{6}\right)$ .
 The static friction coefficient ${C}_{1}$ and the dynamic friction coefficient ${C}_{2}$ , must be less than the maximum friction ${C}_{3}$ ( ${C}_{1}\le {C}_{3}$ and ${C}_{2}\le {C}_{3}$ ).
 The minimum friction coefficient
${C}_{4}$
must be less than the
static friction coefficient
${C}_{1}$
and the dynamic friction
coefficient
${C}_{2}$
(
${C}_{4}\le {C}_{1}$
and
${C}_{4}\le {C}_{2}$
).
Table 1. Units for Friction Formulations I_{fric} Fric C_{1} C_{2} C_{3} C_{4} C_{5} C_{6} 1 $\left[\frac{1}{\text{P}\text{a}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{\text{s}}{\text{Pa}\cdot \text{m}}\right]$ $\left[\frac{1}{{\text{Pa}}^{2}}\right]$ $\left[\frac{{\text{s}}^{2}}{{\text{m}}^{2}}\right]$ 2 $\left[\frac{1}{{\text{Pa}}^{2}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{1}{\text{P}\text{a}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ 3 $\left[\frac{\text{m}}{\text{s}}\right]$ $\left[\frac{\text{m}}{\text{s}}\right]$
 For flag I_{fric} by default:
 Friction filteringIf I_{filtr} = 1, 2 or 3, the tangential forces are smoothed using a filter:
(9) $${F}_{t}=\alpha \cdot {{F}^{\prime}}_{t}+\left(1\alpha \right)\cdot {{{F}^{\prime}}_{t}}^{1}$$Where, α coefficient is calculated from: If I_{filtr} = 1: α = X_{freq}, simple numerical filter
 If I_{filtr} = 2: $\alpha =\frac{2\cdot \pi}{{X}_{freq}}$ , standard 3dB filter, with ${X}_{freq}=\frac{dt}{T}$ , and T = filtering period
 If I_{filtr} = 3: $\alpha =2\cdot \pi \cdot {X}_{\mathit{freq}}\cdot dt$ , standard 3dB filter, with X_{freq} = cutting frequency
The filtering coefficient X_{freq} should have a value between 0 and 1.
 Inacti and Ipen_max,
initial penetration treatment:
 Inacti = 1000: The initial penetrations are ignored: no contact force is applied, but the nodes are not deactivated from the contact; if the node goes out of the contact and later gets back into contact, contact forces are then applied.
 Inacti = 1: Initial forces are applied on all penetrating nodes. High initial penetrations should be avoided, as they might generate high contact forces and lead to high energy error at the beginning of the computation.
 Inacti = 5: The main segment is shifted by the initial penetration value ( ${P}_{0}$ ); therefore, at time zero no initial forces are applied.
The main segment position is restored only in case of rebound larger than ${P}_{0}$ .
In the opposite case, when secondary node continues to penetrate, the penetration is computed as:(10) $$P\text{'}=P{P}_{0}$$ Intersections and large initial penetration (Inacti= 1 and
5):
Shells: initial intersections should be avoided, as they will lead to wrong direction of contact force and possible secondary nodes anchorage.
 When sens_ID is defined for activation/deactivation of the interface, T_{start} and T_{stop} are not taken into account.
 For output forces:
When the contact type is asymmetric surface to surface, the output normal contact forces in Time History are calculated correctly, if the two surfaces are well separated.
 IVIS2=1: is used to add
adhesion in the normal direction and viscous resistive forces in the tangential
direction. This can be used to model thermoplastic composite forming.When used, half of the contact gap is considered an adhesive zone and the other half a physical contact zone. Therefore, to maintain the same physical contact gap, the contact thickness should be doubled using Gap_scale.The adhesive force is only applied after secondary nodes have entered the physical contact zone and then move back into the adhesion zone. The adhesive force acts to prevent the node from moving out of the adhesion zone and is applied in the normal direction.
(11) Where,$${F}_{N}=\frac{SigMaxAdh\cdot Area}{\frac{1}{2}Gap}(\frac{1}{2}Gap{P}_{adh})$$ $Area$
 Area of the secondary surface
 ${P}_{adh}$
 Penetration into the adhesion zone
 $Gap$
 Contact gap as calculated in Comment 3
The adhesive spring ruptures as the node exits the adhesion zone and will be recreated if the node enters the contact zone again.
Viscous resistive forces are applied in the tangential direction when the secondary nodes enter into the adhesion zone. A viscous tangential opposing force is applied instead of a friction force and is calculated as:(12) Where,$${F}_{T}=(ViscAdhFact)\frac{ViscFluid\cdot Area}{\frac{1}{2}Gap}{V}_{rel}$$ $Area$
 Area of the secondary surface
 ${V}_{rel}$
 Penetration into the adhesion zone
 $Gap$
 Contact gap
 Heat exchange By I_{the}=1 (heat transfer activated) to consider heat exchange and heat friction in contact.
 If I_{the_form}=0, then heat exchange is between secondary nodes and constant temperature contact T_{int}.
 If I_{the_form}=1, then heat exchange is between all contact pieces.
In this case T_{int} is used only when I_{the_form}=0. The temperature of the main side is assumed to be constant (equal to T_{int}). If I_{the_form}=1, then T_{int} is not taken into account. So, the nodal temperature of the main side will be considered.
Contact heat exchange, can involve: Thermal conduction
I_{the} =1 needs the material of the secondary side to be a thermal material using finite element formulation for heat transfer (/HEAT/MAT).
Thermal conduction is computed when the secondary node falls into gap:(13) $$gap=\mathrm{max}\left[Ga{p}_{\mathrm{min}},\mathrm{min}\left(Fscal{e}_{gap}\cdot {g}_{s},Ga{p}_{\mathrm{max}}\right)\right]$$Heat exchange coefficient If fct_ID_{K} = 0, then K_{the} is heat exchange coefficient and heat exchange depends only on heat exchange surface.
 If fct_ID_{K} ≠ 0, K_{the} is a scale factor and heat exchange depends on
contact pressure:
(14) $$\mathrm{K}={K}_{the}\cdot {\mathrm{f}}_{K}\left(Ascal{e}_{K},P\right)$$While, ${\mathrm{f}}_{K}$ is function of fct_ID_{K}.
 Thermal conduction and radiation
When fct_ID_{c} ≠ 0, the heat transfer coefficient can change as function of distance $d$ when $Gap<d\le {D}_{cond}$ . In this zone, conductive and radiative heat transfer fluxes are considered.
Abscises and ordinates of this function fct_ID_{c} must be between 0 and 1.
The heat transfer coefficient is computed as:(15) $$K={K}_{the}\left(P=0\right)\cdot {\mathrm{f}}_{c}\left(\frac{dGap}{DcondGap}\right)$$The maximum value of $K$ is equal to the value of K_{the} when K_{the} is constant. Otherwise, in case of K_{the} depending on pressure, the maximum is equal to value of K_{the} for contact pressure $P=0$ . $K$ drops to zero when distance is equal to Dcond.
 Thermal radiation Radiation is considered in contact if ${F}_{rad}\ne 0$ and the distance, $d$ , of the secondary node to the main segment is:
(16) $$Gap<d<{D}_{rad}$$While D_{rad} is the maximum distance for radiation computation. The default value for D_{rad} is computed as the maximum of: upper value of the Gap (at time 0) among all nodes
 smallest side length of secondary element
Note: It is recommended not to set the value too high for D_{rad}, which may reduce the performance of Radioss Engine.A radiant heat transfer conductance is computed as:(17) $${h}_{rad}={F}_{rad}\left({T}_{m}{}^{2}+{T}_{s}{}^{2}\right)\cdot \left({T}_{m}+{T}_{s}\right)$$with(18) $${F}_{rad}=\frac{\sigma}{\frac{1}{{\epsilon}_{1}}+\frac{1}{{\epsilon}_{2}}1}$$Where, $\sigma =5.669\times {10}^{8}\left[\frac{W}{{m}^{2}{K}^{4}}\right]$
 Stefan Boltzman constant.
 ${\epsilon}_{1}$
 Emissivity of secondary surface.
 ${\epsilon}_{2}$
 Emissivity of main surface.
 Heat friction Frictional energy can be converted into heat when I_{the} > 0 for interface.
 Fheat_{s} is defined as the fraction of this energy which is converted into heat and transferred to the secondary side.
 Fheat_{m} is defined as the fraction of this energy which is converted into heat and transferred to the secondary side.
The frictional heat ${Q}_{Fric}$ is defined for a stiffness formulation:(19) $${Q}_{Fric}=Fheat\cdot \frac{\left({F}_{adh}{F}_{t}\right)}{K}\cdot {F}_{t}$$