/INTER/TYPE19
Block Format Keyword This is a combination of two symmetric TYPE7 interfaces and one TYPE11 interface, with common input based on the same secondary/main surfaces. Secondary node group for interface TYPE7, as well as secondary and main line segments used by equivalent TYPE11 interface are virtually generated from these input surfaces.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/INTER/TYPE19/inter_ID/unit_ID  
inter_title  
surf_ID_{s}  surf_ID_{m}  I_{stf}  I_{the}  I_{gap}  I_{edge}  I_{bag}  I_{del}  I_{curv}  
Fscale_{gap}  Gap_{max}  
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  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) 

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 Identifier. (Integer, maximum 10 digits) 

inter_title  Interface title. (Character, maximum 100 characters) 

surf_ID_{s}  Secondary surface
identifier. (Integer) 

surf_ID_{m}  Main surface
identifier. (Integer) 

I_{stf}  Stiffness definition flag. 8
(Integer) 

I_{the}  Heat contact flag. 25
(Integer) 

I_{gap}  Gap/element option flag. 6
7
(Integer) 

I_{edge}  Edges to edge contact flag. 24
(Integer) 

I_{bag}  Airbag vent holes closure flag in case
of contact.
(Integer) 

I_{del}  Node and segment deletion flag. 5
(Integer) 

I_{curv}  Secondary gap with curvature. 11
12
13
(Integer) 

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

Gap_{max}  Maximum gap (used only when I_{gap} = 3).
(Real) 
$\left[\text{m}\right]$ 
St_{min}  Minimum stiffness. (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
St_{max}  Maximum stiffness. 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 or
lines, if element size < gap value, in case of selfimpact contact. 15
(Integer) 

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


node_ID_{1}  First node
identifier. (Integer) 

node_ID_{2}  Second node
identifier. (Integer) 

Stfac  Interface stiffness (if I_{stf} = 1). Default = 1.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
Stiffness scale factor for the interface
(if I_{stf} ≠ 1). Default = 0.0 (Real) 

Fric  Coulomb friction. (Real) 

Gap_{min}  Minimum gap for impact activation. 7 (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. 14
(Integer) 

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

VIS_{F}  Critical damping coefficient on
interface friction. Default set to 1.0 (Real) 

Bumult  Sorting factor. Default set to 0.20 (Real) 

I_{fric}  Friction formulation flag. 19
20 Only used if fric_ID is not defined.
(Integer) 

I_{filtr}  Friction filtering flag. 21
(Integer) 

X_{freq}  Filtering coefficient. 21
(Real) 

I_{form}  Friction penalty formulation type.
(Integer) 

sens_ID  Sensor identifier to activate/deactivate
the interface. 2
If an identifier sensor is defined, the activation/deactivation of interface is based on sensor and not with T_{start} or T_{stop}. (Integer) 

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 (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
Heat exchange scale factor (if fct_ID_{K} ≠ 0). Default = 1.0 (Real) 25 

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

T_{int}  Interface temperature. 25 (Real) 
$\left[\text{K}\right]$ 
I_{the_form}  Heat contact formulation flag.
(Integer) 

Ascale_{K}  Abscissa scale factor on fct_ID_{K}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
F_{rad}  Radiation factor. 27 (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.
26 (Real) 

Fheat_{m}  Frictional heating factor of
main. (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}  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
 The contact main and secondary
surfaces and be defined in the following ways.Single surface selfimpacting and edge to edge selfimpacting contact:
 surf_ID_{s} > 0 and surf_ID_{m} = 0
 surf_ID_{s} = 0 and surf_ID_{m} > 0
Symmetric surface to surface and edge to edge contact surf_ID_{s} > 0 and surf_ID_{m} > 0
 When sens_ID is defined for activation/deactivation of the interface, T_{start} and T_{stop} are not taken into account.
 In case of SPMD, each main segment defined by surf_ID_{m} must be associated to an element (possibly to a void element).
 For flag I_{bag}, refer to the monitored volume option (Monitored Volumes (Airbags)).
 Flag I_{del} = 1 has a CPU cost higher than I_{del} = 2.
 Variable gap is computed as:
 If I_{gap} = 1:
(1) $$\mathrm{max}\left[Ga{p}_{\mathrm{min}},\left({g}_{s}+{g}_{m}\right)\right]$$  If I_{gap} = 3:
(2) $$\mathrm{max}\left\{Ga{p}_{\mathrm{min}},\mathrm{min}\left[Fscal{e}_{gap}\cdot \left({g}_{s}+{g}_{m}\right),\%mesh\_size\cdot \left({g}_{s\_l}+{g}_{m\_l}\right),Ga{p}_{\mathrm{max}}\right]\right\}$$  If I_{gap} = 4:Node to surface contact uses variable gap
(3) $$\mathrm{max}\left\{Ga{p}_{\mathrm{min}},\mathrm{min}\left[Fscal{e}_{gap}\cdot \left({g}_{s}+{g}_{m}\right),Ga{p}_{\mathrm{max}}\right]\right\}$$For selfcontact, if element size < gap value, then secondary nodes are deactivated for nearby main segments. This is the same as using /INTER/TYPE7, Irem_gap = 2. Edge to edge contact uses a constant gap as defined by Gap_{min}.

Where,

 ${g}_{m}$ : main element gap
 ${g}_{m}=\frac{t}{2}$ , with $t$ thickness of the main element for shell 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.

 ${g}_{m\_l}$ : length of the smaller edge of element
 If the secondary node is connected to multiple shells and/or beams or trusses, the largest computed secondary gap is used.

 If I_{gap} = 1:
 A default value for Gap_{min} is computed as:
(4) $$Ga{p}_{\mathrm{min}}={g}_{m\_\mathrm{min}}+{g}_{s\_\mathrm{min}}$$While, ${g}_{m\_\mathrm{min}}=\mathrm{min}\left(t,\frac{l}{20},\frac{{l}_{\mathrm{min}}}{2}\right)$
 Main surface gap
 $t$
 Average thickness of the main elements for shell elements
 $l$
 Average side length of the main brick elements
 ${l}_{\mathrm{min}}$
 Smallest side length of all main segments (shell or brick)
 ${g}_{s\_\mathrm{min}}$
 Secondary surface gap.
 Contact stiffness:For node to 3node and 4node segments or 2node segments to 2node segments contacts computation as:
(5) $$K=\mathrm{max}\left[S{t}_{\mathit{min}},\mathit{min}\left(S{t}_{\mathrm{max}},{K}_{n}\right)\right]$$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 main segment stiffness and computed as:When main segment lies on a shell or is shared by shell and solid:
(6) $${K}_{m}=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$$When main segment lies on a solid:(7) $${K}_{m}=\mathit{Stfac}\cdot B\cdot \frac{{S}^{2}}{V}$$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 node is connected to a shell element:
(8) $${K}_{s}=\frac{1}{2}\cdot E\cdot t$$When node is connected to solid element:(9) $${K}_{s}=B\cdot \sqrt[3]{V}$$
There is no limitation value to the stiffness factor Stfac (but a value can be larger than 1.0 to 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.

${K}_{n}$
is computed from both main segment stiffness
${K}_{m}$
and secondary node stiffness
${K}_{s}$
:
 The values given in Line 4 are ignored, if I_{gap} ≠ 3.
 The values given in Line 5 are ignored, if I_{stf} ≤ 1.
 Spherical curvature (I_{curv} = 1) is defined with node_ID_{1} (center of the sphere).
 The node_ID_{2} given in Line 6 is ignored, if I_{curv} = 1.
 Cylindrical curvature (I_{curv} = 2) is defined with node_ID_{1} and node_ID_{2} (on the axis of the cylinder).
 Inacti = 3 may create initial
energy if the node belongs to a spring element.Inacti = 6 is recommended instead of Inacti =5, to avoid high frequency effects into the interface.
 With Irem_gap = 2, it allows to have the element size smaller than gap values:
In case of selfimpact contact, when Curvilinear is smaller than $\sqrt{2}\cdot Gap$ (in initial configuration), then this secondary entity (node / line) will not be taken into account by this main entity (surface / line). The secondary entity will not be deleted from the contact for other other main entities. This also applies both nodes to surface and edge to edge contact as stated in the /INTER/TYPE7 and /INTER/TYPE11 comments.
 The sorting factor, Bumult is used to speed up the sorting algorithm.
 The sorting factor, Bumult is machine dependent.
 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:
 Whatever the friction flag I_{fric}, the Coulomb friction coefficient
used in the TYPE11 interface is:
(10) $$\mu =Fric$$  The friction flag I_{fric} only applies to the TYPE7 interface(s).
 If the friction flag I_{fric} = 0 (default), the
old static friction formulation is used:
(11) $${F}_{t}\le \mu \cdot {F}_{n}$$While, $\mu =\mathit{Fric}$ with $\mu $ is Coulomb Friction coefficient.
 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
 Whatever the friction flag I_{fric}, the Coulomb friction coefficient
used in the TYPE11 interface is:
 Currently, the coefficients C_{1} through C_{6} are used to define a variable friction
coefficient
$\mu $
for
new friction formulations.
 I_{fric} = 1 (Generalized
Viscous Friction law):
(12) $$\mu =\mathit{Fric}+{C}_{1}\cdot p+{C}_{2}\cdot V+{C}_{3}\cdot p\cdot V+{C}_{4}\cdot {p}^{2}+{C}_{5}\cdot {V}^{2}$$  I_{fric} = 2 (Modified Darmstad
law):
(13) $$\mu =Fric+{C}_{1}\cdot {e}^{\left({C}_{2}V\right)}\cdot {p}^{2}+{C}_{3}\cdot {e}^{\left({C}_{4}V\right)}\cdot p+{C}_{5}\cdot {e}^{\left({C}_{6}V\right)}$$  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,${C}_{1}={\mu}_{s}$ ${C}_{4}={\mu}_{\mathrm{min}}$ ${C}_{2}={\mu}_{d}$ ${C}_{5}={V}_{\mathit{cr}1}$ ${C}_{3}={\mu}_{\mathrm{max}}$ ${C}_{6}={V}_{cr2}$  First critical velocity ${V}_{cr1}={C}_{5}$ must be different to 0 ( ${C}_{5}\ne 0$ ).
 First critical velocity ${V}_{cr1}={C}_{5}$ must be lower than the second critical velocity ${V}_{cr2}={C}_{6}$ ( ${C}_{5}<{C}_{6}$ ).
 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 $\left[\frac{\text{m}}{\text{s}}\right]$ $\left[\frac{\text{m}}{\text{s}}\right]$  I_{fric} = 1 (Generalized
Viscous Friction law):
 Friction filtering:If I_{filtr} ≠ 0, the tangential forces are smoothed using a filter:
(14) $${F}_{t}=\alpha \cdot {{F}^{\prime}}_{t}+\left(1\alpha \right)\cdot {F}_{t}^{1}$$Where α coefficient is calculated from: If I_{filtr}= 1: $\alpha ={X}_{\mathit{freq}}$ , simple numerical filter.
 If I_{filtr} = 2: $\alpha =\frac{2\cdot \pi}{{X}_{\mathit{freq}}}$ , standard 3dB filter, with ${X}_{\mathit{freq}}=\frac{dt}{T}$ , and $T$ is filtering period.
 If I_{filtr} = 3:
$\alpha =2\cdot \pi \cdot {X}_{freq}\cdot dt$
, standard 3dB filter, with
${X}_{freq}$
is cutting frequency.
The filtering coefficient ${X}_{freq}$ should have a value between 0 and 1.
 Friction penalty formulation I_{form}
 If I_{form} = 1, (default) viscous
formulation, the friction forces are:
(15) $${F}_{t}=\mathrm{min}\left(\mu {F}_{n},{F}_{adh}\right)$$While an adhesion force is computed as:
${F}_{adh}=C\cdot {V}_{t}$ with $C=VI{S}_{F}\cdot \sqrt{2Km}$
 If I_{form} = 2, stiffness
formulation, the friction forces are:
(16) $${F}_{t}^{new}=\mathrm{min}\left(\mu {F}_{n},{F}_{adh}\right)$$While an adhesion force 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.
 If I_{form} = 1, (default) viscous
formulation, the friction forces are:
 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.
 Edges to edge contact flag I_{edge}:
 I_{edge} = 1: only external edges are generated from contact surfaces which defined by SHELL parts, it is recommended for optimized performance. Cannot be used when the surface contains only solid parts which lead to an empty line and then error message will be printed.
 I_{edge} = 2: all edges are generated from contact surfaces.
 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:
(17) $$K={K}_{\mathit{the}}\cdot {f}_{K}\left({\mathit{Ascale}}_{K},P\right)$$  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:
(18) $${\mathit{Fheat}}_{s}+{\mathit{Fheat}}_{m}\le 1.0$$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:
(19) $${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{s}\cdot \frac{\left({F}_{\mathit{adh}}{F}_{t}\right)}{K}\cdot {F}_{t}$$Main side:(20) (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:
(21) $${Q}_{\mathit{Fric}}={\mathit{Fheat}}_{s}\cdot C\cdot {{V}_{t}}^{2}\cdot dt$$Main side:(22) (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:
(23) $$\mathit{Gap}<d<{D}_{\mathit{rad}}$$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:(24) $${h}_{\mathit{rad}}={F}_{\mathit{rad}}\left({{T}_{m}}^{2}+{{T}_{s}}^{2}\right)\cdot \left({T}_{m}+{T}_{s}\right)$$with(25) $${F}_{\mathit{rad}}=\frac{\sigma}{\frac{1}{{\epsilon}_{1}}+\frac{1}{{\epsilon}_{2}}1}$$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