/LEAK/MAT

Block Format Keyword Specifies effective leakage area of porous airbag fabric materials LAW19 and LAW58 as function of time, pressure, area and other parameters.

Format

(1)	(3)	(5)
/LEAK/MAT/`mat_ID`/`unit_ID`
`mat_title`
`Ileakage`	`Ascale`_T	`Ascale`_P

Define leakage for area in contact

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`AC'`		`fct_ID`_AC'		`Fscale`_AC'

Insert if Ileakage =1

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`LC`		`AC`

Insert if Ileakage =2, 3 or 4

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_LC	`fct_ID`_AC	`Fscale`_LC		`Fscale`_AC

Insert if Ileakage =5

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`L`		`R`
`C`₁		`C`₂		`C`₃

Insert if Ileakage =6

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`X`₀		`X`₁		`X`₂		`X`₃

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier (Integer, maximum 10 digits)
`mat_title`	Material title (Character, maximum 100 characters)
`Ileakage`	Effective leakage area formulation flag. = 0 No leakage = 1, 2, 3, 4 2 = 5 Fabric leakage model = 6 Anagonye and Wang leakage model (Integer)
`Ascale`_T	Abscissa time scale factor on function Default = 1 (Real)
`Ascale`_P	Abscissa pressure scale factor on function Default = 1 (Real)
`AC'`	Area coefficient for area in contact $0 \leq A C' \leq 1$ Default = 0 (Real)
`fct_ID`_AC'	Area coefficient function identifier AC'(t) if AC' is equal to 0 (Integer)
`Fscale`_AC'	Scale factor on function AC' Default = 1 (Real)
`LC`	Leakage coefficient Default function is 0 (Real)
`AC`	Area coefficient Default = 0 (Real)
`fct_ID`_LC	Leakage coefficient function identifier LC(t), if `Ileakage` =2 or 3 Leakage coefficient function identifier $L C (A r e a / A r e a_{0})$ , if `Ileakage` =4 Default function is 0 (Integer)
`Fscale`_LC	Scale factor on function LC Default = 1 (Real)
`fct_ID`_AC	Area coefficient function identifier $A C (P)$ , if `Ileakage` =2. Area coefficient function identifier $A C (P - P_{e x t})$ , if `Ileakage` =3. Area coefficient function identifier $A C (P_{e x t} / P)$ , if `Ileakage` =4. Default function is 0 (Integer)
`Fscale`_AC	Scale factor on function AC Default = 1 (Real)
`L`	Characteristic length Default = 1 (Real)	$[m]$
`R`	Fiber thickness Default = L (Real)	$[m]$
`C`₁	Coefficient C1 (Real)
`C`₂	Coefficient C2 Default = 1 (Real)
`C`₃	Coefficient C3 (Real)
`X`₀, `X`₁, `X`₂, `X`₃	Coefficients of Anagonye-Wang leakage area law (Real)

Comments

The mat_ID must be the same as /MAT/LAW19 (FABRI) or /MAT/LAW58 (FABR_A). Material porosity is active only when corresponding components are referred as external surfaces in /MONVOL/AIRBAG1, /MONVOL/COMMU1, and /MONVOL/FVMBAG1 airbag cards.
Effective leakage area ( $A_{e f f}$ ) formulation:
Ileakage =1:(1)
$A_{e f f} = \sum_{n} L C \cdot A C \cdot A r e a_{n}$

Ileakage =2:(2)
$A_{e f f} = \sum_{n} LC (t) \cdot AC (P) \cdot A r e a_{n}$

Ileakage =3:(3)
$A_{e f f} = \sum_{n} LC (t) \cdot AC (P - P e x t) \cdot A r e a_{n}$

Ileakage =4:(4)
$A_{e f f} = \sum_{n} LC (A r e a_{n} / A r e a_{0}) \cdot AC (P_{e x t} / P) \cdot A r e a_{n}$

Where,

$A r e a_{0}$

Initial area of the airbag surface

Note: By default all coefficients and functions are zero.

Ileakage =5:(5)
$A_{e f f} = \sum_{n} \frac{A r e a_{0}}{L^{2}} [(C_{1} Δ P^{C_{2}} - C_{3}) {(L - R)}^{2} + C_{3} (L λ_{1} - R / \sqrt{λ_{2}}) (L λ_{2} - R / \sqrt{λ_{1}})] \cdot \sin α_{12}$

$Δ P = P / P_{e x t} - 1$

Where, $λ_{1}$ and $λ_{2}$ are the stretches in warp and weft directions and $α_{12}$ is the angle between warp and weft directions.
Note: For LAW19 $α_{12} = 90^{\circ}$

Ileakage =6:(6)
$A_{e f f} = \sum_{n} A r e a_{0} (X_{0} + X_{1} r_{s} + X_{2} r_{p} + X_{3} r_{s} r_{p})$

with $r_{s} = A r e a_{n} / A r e a_{0}$ and $r_{p} = P_{e x t} / P$
Blockage of airbag fabric, due to contact, can be activated in corresponding /MONVOL card. Effective leakage area is calculated with account of the blockage as:
(7)
$A r e a_{n} = A r e a_{n o n_i m p a c t e d} + A C^{'} \cdot A r e a_{i m p a c t e d}$