/INTER/TYPE7
Block Format Keyword Interface TYPE7 is a multiusage 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
 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.
 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_ID_{s}  surf_ID_{m}  I_{stf}  I_{the}  I_{gap}  I_{bag}  I_{del}  I_{curv}  I_{adm}  
Fscale_{gap}  Gap_{max}  Fpenmax  I_{TIED}  
St_{min}  St_{max}  %mesh_size  dtmin  Irem_gap  Irem_i2 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

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

Stfac  Fric  Gap_{min}  T_{start}  T_{stop}  
I_{BC}  Inacti  VIS_{s}  VIS_{F}  Bumult  
I_{fric}  I_{filtr}  X_{freq}  I_{form}  sens_ID  fct_ID_{F}  Ascale_{F}  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) 

NR_{adm}  P_{adm}  Angl_{adm} 
(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} 
Definitions
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_ID_{s}  Secondary nodes group
identifier. (Integer) 

surf_ID_{m}  Main surface
identifier. (Integer) 

I_{stf}  Interface stiffness definition flag.
3
For SPH, only I_{stf}=0,
1 and 1000 are available.
(Integer) 

I_{the}  Heat contact flag.
(Integer) 

I_{gap}  Gap/element option flag. 11
(Integer) 

I_{bag}  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.
(Integer) 

I_{del}  Node and segment deletion flag.
(Integer) Note: I_{del} = 1 and
1 has a higher CPU cost when compared with I_{del} = 2 and
2.


I_{curv}  Gap envelope with curvature. 5
(Integer) 

I_{adm}  Computing local curvature flag for
adaptive meshing. 6
7
8
(Integer) 

Fscale_{gap}  Gap scale factor (used only when I_{gap} = 2 and
3). Default = 1.0 (Real) 

Gap_{max}  Maximum gap (used only when I_{gap} = 2 and
3). (Real) 
$\left[\text{m}\right]$ 
Fpenmax  Maximum fraction of initial penetration.
13 (Real) 

I_{TIED}  Tie contact nodes flag.
(Integer) 

St_{min}  Minimum stiffness (used only when I_{stf} = 2,
3, 4, or
5). (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
St_{max}  Maximum stiffness (used only when I_{stf} = 2,
3, 4, or 5). Default = 10^{30} (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
%mesh_size  Percentage of mesh size (used only when
I_{gap} = 3). Default = 0.4 (Real) 

dtmin  Minimum interface time step. 23
(Real) 
$\left[\text{s}\right]$ 
Irem_gap  Flag for deactivating secondary nodes if
element size < gap value, in case of selfimpact contact. 14
(Integer) 

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


node_ID_{1}  First node
identifier. (Integer) 

node_ID_{2}  Second node identifier (ignored when I_{gap} =
1). (Integer) 

Stfac  Stiffness scale factor applied to main
side of the interface (if I_{stf}
$\ne $
1). Default = 1.0 (Real) 

Interface stiffness (if I_{stf} = 1). Default = 1.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$  
Fric  Coulomb friction (if fct_ID_{F} = 0). Default = 0.0 (Real) 

Coulomb friction scale factor (if fct_ID_{F}
$\ne $
0). 20 Default = 1.0 (Real) 

Gap_{min}  Minimum gap for impact activation. For default values, see 10 (Real) 
$\left[\text{m}\right]$ 
T_{start}  Start time. (Real) 
$\left[\text{s}\right]$ 
T_{stop}  Time for temporary
deactivation. (Real) 
$\left[\text{s}\right]$ 
I_{BC}  Deactivation flag of boundary conditions
at impact. (Boolean) 

Inacti  Deactivation flag of stiffness in case
of initial penetrations. 13
(Integer) 

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

VIS_{F}  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) 

I_{fric}  Friction formulation flag. 1617 Only used if fric_ID is not defined.
(Integer) 

I_{filtr}  Friction filtering flag. 18
(Integer) 

X_{freq}  Filtering coefficient. Default value depends on I_{filtr} (Real) 

I_{form}  Friction penalty formulation type. 19
(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 T_{start} or T_{stop}. (Integer) 

fct_ID_{F}  Friction coefficient with temperature
function identifier. Default = 0 (Integer) 

Ascale_{F}  Abscissa scale factor on fct_ID_{F}. Default = 1.0 (Real) 

fric_ID  Friction identifier for friction
definition for selected pairs of parts.
(Integer) 

C_{1}  Friction law
coefficient. (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) 

K_{the}  Heat exchange coefficient (if fct_ID_{K} = 0). Default = 0.0 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
Heat exchange coefficient (if fct_ID_{K}
$\ne $
0). 20
Default = 1.0 (Real) 

fct_ID_{K}  Function identifier for thermal 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. 20 (Real) 
$\left[\text{K}\right]$ 
I_{the_form}  Heat contact formulation flag.
(Integer) 

NR_{adm}  Number of elements through a 90 degrees
radius. (Integer) 

P_{adm}  Criteria on the percentage of
penetration. Default = 1.0 (Real) 

Angl_{adm}  Angle criteria. (Real) 
$\left[\mathrm{deg}\right]$ 
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) 
$\left[\text{m}\right]$ 
Fheat_{s}  Frictional heating factor of secondary.
21
(Real) 

Fheat_{m}  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 

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

I_{BCX} 
(Boolean) 

I_{BCY} 
(Boolean) 

I_{BCZ} 
(Boolean) 
Comments
 In case of SPMD, each mainr segment defined by surf_ID_{m} must be associated to an element (possibly to a void element).
 For the flag I_{bag}, refer to the monitored volume option (Monitored Volumes (Airbags)).
 Contact stiffness, K
is computed as:If I_{stf} =1:
(1) $$K=Stfac$$If I_{stf} = 2, 3, 4 or 5:(2) $$K=\text{max}\left[S{t}_{\text{min}},\text{min}\left(S{t}_{\text{max}},{K}_{n}\right)\right]$$If I_{stf} =1000:(3) $$K={K}_{m}$$Where, ${K}_{n}$ is computed from both main segment stiffness ${K}_{m}$ and secondary node stiffness ${K}_{s}$ :
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, ${K}_{n}=\frac{{K}_{m}\cdot {K}_{s}}{{K}_{m}+{K}_{s}}$
${K}_{m}$ is the main segment stiffness and computed as:
When the main segment lies on a shell or is shared by shell and solid:(4) $${K}_{m}=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$$When the main segment lies on a solid:(5) $${K}_{m}=\mathit{Stfac}\cdot B\cdot \frac{{S}^{2}}{V}$$Where, $S$
 Segment area
 $V$
 Volume of the solid
 $B$
 Bulk modulus
${K}_{s}$ is an equivalent nodal stiffness considered for interface TYPE7, and computed as:
When the node is connected to a shell element:(6) $${K}_{s}=\frac{1}{2}\cdot E\cdot t$$When the node is connected to a solid element:(7) $${K}_{s}=B\cdot \sqrt[3]{V}$$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.
 I_{stf} = 2, 3, 4, or 5 are not compatible with SPH formulation.
 If I_{curv} = 1, a spherical curvature
is defined for the gap with node_ID_{1} (center of the sphere).
If I_{curv} = 2, a cylindrical curvature is defined for the gap with node_ID_{1} and node_ID_{2} (on the axis of the cylinder).
If I_{curv} = 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).  In case of adaptive meshing and I_{adm} = 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).
 In case of adaptive meshing and I_{adm} = 2:
If the contact occurs in a zone (main side) whose radius of curvature is lower than NR_{adm} 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 Angl_{adm} and the percentage of penetration is greater than P_{adm}, the element on the secondary side will be divided (if not yet at maximum level).  The coefficients NR_{adm}, P_{adm}, and Angl_{adm} are used only if adaptive meshing and I_{adm}=2.
 If Gap_{max}=0, there is no maximum value for the gap.
 If Gap_{min}=0 or blank, a default value
is computed as:
If main segments are shell and solid elements, Gap_{min} = min ( $t{}_{m}$ , $\frac{{l}_{\mathrm{min}}}{2}$ ).
Where, $t{}_{m}$
 The average thickness of the main shell elements, for I_{gap}=0
 $t{}_{m}$
 The minimum thickness of the main shell elements, for I_{gap}=1, 2, or 3
 ${l}_{\mathrm{min}}$
 The smallest side length of all main segments (shell or brick)
If main segments are all solid elements Gap_{min} = $\frac{{l}_{\mathrm{min}}}{10}$
Where, ${l}_{\mathrm{min}}$ being the smallest side of all main brick segments.
 Variable gap:If I_{gap} =1, variable gap is computed as:
(8) $$\text{max}\left[{\mathit{Gap}}_{\text{min}},\left({g}_{s}+{g}_{m}\right)\right]$$If I_{gap} =2, variable gap is computed as:(9) $$\text{max}\left\{{\mathit{Gap}}_{\text{min}},\text{min}\left[\mathit{Fscal}{e}_{gap}\cdot \left({g}_{s}+{g}_{m}\right),{\mathit{Gap}}_{\text{max}}\right]\right\}$$If I_{gap} =3, variable gap is computed for selfcontact as:(10) $$\text{max}\left\{{\mathit{Gap}}_{\text{min}},\text{min}\left[\mathit{Fscal}{e}_{\mathit{gap}}\cdot \left({g}_{s}+{g}_{m}\right),\%mesh\_size\cdot \left({g}_{s\_l}+{g}_{m\_l}\right),{\mathit{Gap}}_{\text{max}}\right]\right\}$$Where,
${g}_{m}$
: main element gap
${g}_{m}=\frac{t}{2}$ : with $t$ being 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
${g}_{s}=\frac{t}{2}$ : with $t$ being the largest thickness of the shell elements connected to the secondary node
${g}_{s}=\frac{1}{2}\sqrt{S}$ : for truss and beam elements. With $S$ being the cross section of the element
 ${g}_{m\_l}$ : length of the smaller edge of element
 ${g}_{s\_l}$ : 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 Gap_{min}.

${g}_{m}$
: main element gap
 Deactivation of the boundary condition is applied to secondary nodes group (grnd_ID_{s}).
 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.
If Fpenmax is not equal to zero, nodes stiffness is deactivated if:
$Penetration\ge Fpenmax\cdot Gap$ whatever the value of Inacti.
 With Irem_gap = 2, it allows to have the element size 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.
 One node can belong to the two surfaces at the same time.
 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.
For friction formulation:
If the friction flag I_{fric}=0 (default), the old static friction formulation is used:
${F}_{t}\le \mu \cdot {F}_{n}$ with $\mu $ being the Coulomb friction coefficient If fct_ID_{F} = 0:I_{fric} is the Coulomb friction.
(11) $$\mu =\mathit{Fric}$$  If fct_ID_{F} ≠ 0:Fric becomes a scale factor of Coulomb friction coefficient which depends on the temperature.
(12) $$\mu =\mathit{Fric}\cdot {\mathrm{f}}_{F}\left({\mathit{Ascale}}_{F},{T}_{\mathit{interface}}\right)$$
While ${T}_{\mathit{interface}}$ is the temperature which is taken as the mean temperature of secondary and main:(13) $${T}_{\mathit{interface}}=\frac{{T}_{\mathit{secondary}}+{T}_{\mathit{main}}}{2}$$For flag I_{fric} > 0, 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
 If fct_ID_{F} = 0:
 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):
(14) $$\mu =\mathit{Fric}+{C}_{1}.p+{C}_{2}\cdot V+{C}_{3}.p\cdot V+{C}_{4}\cdot {p}^{2}+{C}_{5}\cdot {V}^{2}$$  I_{fric} = 2 (Modified Darmstad
law):
(15) $$\mu =\mathit{Fric}+{C}_{1}.{e}^{\left({C}_{2}V\right)}.{p}^{2}+{C}_{3}.{e}^{\left({C}_{4}V\right)}.p+{C}_{5}.{e}^{\left({C}_{6}V\right)}$$  I_{fric} = 3 (Renard
law):
(16) $$\mu ={C}_{1}+\left({C}_{3}{C}_{1}\right)\cdot \frac{V}{{C}_{5}}\cdot \left(2\frac{V}{{C}_{5}}\right)\hspace{0.17em}\text{if}\hspace{0.17em}V\in \left[0,{C}_{5}\right]$$(17) $$\begin{array}{l}\mu ={C}_{3}\left(({C}_{3}{C}_{4}\right)\cdot {\left(\frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)}^{2}\cdot \left(32\cdot \frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)\hspace{0.17em})\hspace{0.17em}\text{if}\hspace{0.17em}V\in [{C}_{5}{C}_{6}]\\ \end{array}$$(18) $$\mu ={C}_{2}\frac{1}{\frac{1}{{C}_{2}{C}_{4}}+{\left(V{C}_{6}\right)}^{2}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\text{\hspace{0.17em}}V\ge {C}_{6}$$
Where for I_{fric}=3: ${C}_{1}={\mu}_{s}$ , 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
 ${C}_{4}={\mu}_{\mathrm{min}}$ , mimimum coefficient of friction
 ${C}_{5}={V}_{\mathit{cr}1}$ , first critical velocity, must be > 0
 ${C}_{6}={V}_{cr2}$ , second critical velocity, must be $>{V}_{cr1}$
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 $\left[\frac{\text{m}}{\text{s}}\right]$ $\left[\frac{\text{m}}{\text{s}}\right]$  I_{fric} = 1 (Generalized
Viscous Friction law):
 Friction filtering:If I_{filtr} flag $\ne $ 0, the tangential forces are smoothed using a filter:
(19) $${F}_{Tf}=\alpha {F}_{T}(t)+\left(1\alpha \right){F}_{Tf}(tdt)$$Where, ${F}_{Tf}$
 Filtered tangential force.
 ${F}_{T}(t)$
 Calculated tangential force at time t before filtering.
 ${F}_{Tf}(tdt)$
 Filtered tangential force at the previous time step
 $t$
 Current simulation time
 $dt$
 Current simulation time step
 $\alpha $
 Filtering coefficient
Where α coefficient is calculated from: If I_{filtr} = 1: $\alpha ={X}_{freq}$ , simple numerical filter with a value between 0 and 1.
 If I_{filtr} = 2: $\alpha =\frac{2\cdot \pi}{{X}_{freq}}$ , standard 3dB filter, with the number of time steps to filter defined as ${X}_{\mathit{freq}}=\frac{dt}{T}$ , and $T$ is the filtering period.
 If I_{filtr} = 3: $\alpha =2\cdot \pi \cdot {X}_{\mathit{freq}}\cdot \mathit{dt}$ , standard 3dB filter, with X_{freq} = cutting frequency.
 Friction penalty formulation I_{form}:
 If I_{form} = 1 (default) viscous
formulation, the friction forces are:
(20) $${F}_{t}=\text{min}\left(\mu {F}_{n},{F}_{\text{adh}}\right)$$While an adhesion force is computed as:(21) $${F}_{\text{adh}}=C\cdot {V}_{t}\text{\hspace{0.17em}}\text{with}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C={\mathit{VIS}}_{F}\cdot \sqrt{2\mathit{Km}}$$  If I_{form} = 2, stiffness
formulation), the friction forces are:
(22) $${F}_{t}^{\mathit{new}}=\text{min}\left(\mu {F}_{n},{F}_{\mathit{adh}}\right)$$While an adhesion is computed as:
${F}_{adh}={F}_{t}^{old}+\text{\Delta}{F}_{t}$ with $\text{\Delta}{F}_{t}=K\cdot {V}_{t}\cdot dt$
Where, ${V}_{t}$ is the tangential velocity of the secondary node relative to the main segment.
I_{form} = 2 is recommended for implicit and explicit analysis.
 If I_{form} = 1 (default) viscous
formulation, the friction forces are:
 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 shell and constant temperature contact T_{int}.
 If I_{the_form} = 1, then heat exchange is between all contact pieces.
T_{int} is used only when I_{the_form}= 0. In this case, the temperature of main side assumed to be constant (equal to T_{int}). If I_{the_form}=1, then T_{int} is not taken into account, for the nodal temperature of main side will be considered.
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, then K_{the} is a scale factor and the heat exchange
will depend on the contact pressure:
(23) $$K={K}_{\mathit{the}}\cdot {f}_{K}\left({\mathit{Ascale}}_{K},P\right)$$  While ${\mathrm{f}}_{K}$ is the function of fct_ID_{K}.
 Heat Friction:
 Frictional energy is converted into heat when I_{the} > 0 for interface.
 Fheat_{s} and
Fheat_{m} are defined as the
fraction of frictional energy and distributed respectively to the secondary side and
main side. So generally:
(24) $${\mathit{Fheat}}_{s}+{\mathit{Fheat}}_{m}\le 1.0$$When both Fheat_{s} and Fheat_{m} are equal to 0, the conversion of the frictional sliding energy to heat is not activated.
 The frictional heat Q_{Fric} is
defined:
 If I_{form}= 2 (a stiffness
formulation):Secondary side:
(25) $${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{s}\cdot \frac{\left({F}_{\mathit{adh}}{F}_{t}\right)}{K}\cdot {F}_{t}$$Main side:(26) (I_{the_form}= 1)$${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{m}\cdot \frac{\left({F}_{\mathit{adh}}{F}_{t}\right)}{K}\cdot {F}_{t}$$  If I_{form}= 1 (a penalty
formulation):Secondary side:
(27) $${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{s}\cdot C\cdot {{V}_{t}}^{2}\cdot dt$$Main side:(28) (I_{the_form}= 1)$${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{m}\cdot C\cdot {{V}_{t}}^{2}\cdot dt$$
 If I_{form}= 2 (a stiffness
formulation):
 Radiation:Radiation is considered in contact if ${F}_{rad}\ne 0$ and the distance, ${d}_{}$ , of the secondary node to the main segment is:
(29) $$\mathit{Gap}<d<{D}_{\mathit{rad}}$$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
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:(30) $${h}_{\mathit{rad}}={F}_{\mathit{rad}}\left({{T}_{m}}^{2}+{{T}_{s}}^{2}\right)\cdot \left({T}_{m}+{T}_{s}\right)$$with(31) $${F}_{\mathit{rad}}=\frac{\sigma}{\frac{1}{{\epsilon}_{1}}+\frac{1}{{\epsilon}_{2}}1}$$Where, $\sigma =5.669\times {10}^{8}\left[\frac{\text{W}}{{\text{m}}^{2}{\text{K}}^{4}}\right]$
 Stefan Boltzman constant
 ${\epsilon}_{1}$
 Emissivity of secondary surface
 ${\epsilon}_{2}$
 Emissivity of main surface
 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.
 When sens_ID is defined for activation/deactivation of the interface, T_{start} and T_{stop} are not taken into account.