/MAT/LAW77

Block Format Keyword

/MAT/LAW77 - Visco-elastic Foam Tabulated Material with Air

Description

This open cell foam material law is a generalization of LAW70. It accounts for a non-viscous compressible ideal gas flow inside of the foam and its interaction with the foam structure. ALE simulation of the gas flow and Lagrangian simulation of the foam deformation is performed on the same elements system. Interaction between the gas flow and the structure is through Darcy law and direct application of the gas pressure to the structure.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW77/mat_ID/unit_ID
mat_title

E0				Emax
Fcut		Fsmooth	NL	NunL	Iflag	Shape		Hys

If NL ≠ 0

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
fct_IDL			FscaleL

If NunL ≠ 0

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
fct_IDunL			FscaleunL

The cards for the gas and external gas

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
		P0						R
		Pext		Iclos	Inc_gas
						K
fct_IDK	fct_IDR

Field	Contents	SI Unit Example
mat_ID	Material identifier (Integer, maximum 10 digits)
unit_ID	Optional unit identifier (Integer, maximum 10 digits)
mat_title	Material title (Character, maximum 100 characters)
	Initial density (Real)
E0	Initial Young’s modulus (Real)
	Poisson’s ratio (Real)
Emax	Maximum Young's modulus (Real)
	Failure plastic strain (Real)
Fcut	Cutoff frequency for strain rate filtering Default = 1030 (Real)
Fsmooth	Smooth strain rate option flag (Integer) = 0: no strain rate smoothing (default) = 1: strain rate smoothing active
NL	Number of loading functions Default = 0 (Integer)
NunL	Number of unloading functions Default = 0 (Integer)
Iflag	Unloading response control flag Default = 1 (Integer) = 0: The material behavior follows the defined curves for loading and unloading. = 1: The loading curves are used for both loading and unloading behavior. For unloading the deviatoric stress is damaged by using the quasi-static unloading curve where, D is computed by respecting the quasi-static unloading curve, are the current stresses computed respectively from the unloading and quasi-static curves. = 2: The loading curves are used for both loading and unloading behavior. For unloading the tensor stress is reduced by using the quasi-static unloading curve where, D is computed by respecting the quasi-static unloading curve, are the current stresses computed respectively from the unloading and quasi-static curves. = 3: The loading curves are used for both loading and unloading behavior. The deviatoric unloading stress is reduced by: Where, Wcur and Wmax are current and maximum energy. If Iflag = 3, the unloading curves are not used.
Shape	Shape factor describes the “convexity” of the unloading curve Default = 1.0 (Real) = 1: corresponds to linear unloading curve. < 1: convex unloading curve.
Hys	Hysteresis unloading factor Default = 1.0 (Real)
fct_IDL	Load function identifier (Integer)
	Strain rate for load function (Real)
FscaleL	Load function scale factor (Real)
fct_IDunL	Unload function identifier (Integer)
	Strain rate for unload function (Real)
FscaleunL	Unload function scale factor (Real)
	Air density Default = 0 (Real)
P0	Initial pressure Default = 0 (Real)
	Gamma constant for the gas Default (Real)
	External gas density (Real) Default is
Pext	External pressure Default = P0 (Real)
Inc_gas	Reverse flow flag Default = 0 (Integer) = 0: no reverse flow of outside air into the foam = 1: reverse flow is admitted
R	Initial porosity fraction of element volume filled with the gas) ( 0 < R < 1) = 0.0: no gas in element, no gas flow = 1.0: complete element volume is used for gas flow (Real)
	Linear parameter for generalized Darcy Law Default = 0 (Real)
	Quadratic parameter for generalized Darcy Law Default = 0 (Real)
	Transient parameter for generalized Darcy Law Default = 0 (Real)
K	Initial foam permeability modulus) Default = 0 (Real)
Iclos	Open/close the free surface of the solid block flag (surface not connected to any solid element) Default = 0 (Integer) = 0: free outflow on free surface (open) = 1: no outflow on free surface (close) = 2: no gas outflow through external surfaces which are in contact. Parameter Ibag= 1 should be activated in corresponding contact.
fct_IDK	Permeability scale factor function (scale vs relative foam density) Default = 0 (Integer) = 0: the permeability modulus is constant
fct_IDR	Porosity scale factor function (scale vs relative foam density) Default = 0 (Integer) = 0: the porosity is constant and fct_IDR= fct_IDK

#RADIOSS STARTER

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/UNIT/1

unit for mat

kg mm ms

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/MAT/LAW77/1/1

Open cell foam

# RHO_I

4.5E-8

# E0 NU EMAX EMAX1

.1 0 5 .99

# FCUT FSMOOTH N_L N_UNL IFLAG SHAPE HYS

.1 1 1 0 3 2 1E-20

# fct_ID_L SLOAD FSCALE_L

1 0 .001

# RHO_AIR P0 GAMMA R

1.2E-9 1.0E-4 1.4 1.0

# RHO_EXT P_EXT ICLOSE INC_GAS

1.2E-9 1.0E-4 2 0

# ALPHA BETA T K

1 5 0 1e07

# fct_ID_K fct_ID_R

2 3

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/FUNCT/1

LoadCurve

# X Y

-.8 -.11

-.7 -.10

-.4 -.05

-.2 -.02

0 0

.2 .004

.4 .006

.6 .01

.7 .020

.8 .050

.99 134

/FUNCT/2

Funct_2

# X Y

0.0 0.2

0.555 0.2

0.909 1.0

1.0 1.0

/FUNCT/3

Funct_3

# X Y

0.0 0.25

0.555 0.25

0.909 0.55

1.0 0.55

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

#ENDDATA

/END

1.	This material law can be used only with solid non-degenerated hexa elements. This material is available only for the following parameters in the solid property:

•	Isolid = 1 (Belytschko)

•	Ismtr = 1 (small strain)

•	Iframe = 1 (non co-rotational)

2.	For stresses above the last load function, the behavior is extrapolated by using the last two load functions. In order to avoid huge stress values, it is recommended to repeat the last load function.

3.	We consider non-viscous flow of a perfect gas using the ALE approach.

4.	When reaches , in one integration point, the deviatoric stress of the corresponding integral point is permanently set to 0, however, the solid element is not deleted.

5.	For coupling between the foam and the gas, use the modified Darcy’s law (Dupuit-Forchiemer):

Where,

V is the velocity of the fluid,

P is the fluid pressure

K is the permeability modulus.

6.	In order to save the structural stress, strain and gas flow data, the following options have to be used in Engine file:

/STATE/BRICK/STRAIN/FULL

/STATE/BRICK/STRESS/FULL

/STATE/BRICK/AUX/FULL

7.	Pre-stress of the foam and initial state of the air inside of the foam can be defined from pre-stress simulation and read into the model with /INIBRI/STRS_F, /INIBRI/STRA_F and /INIBRI/AUX cards.

8.	The following user variables are available to output gas flow data into animation (/ANIM/BRICK/) or time history (/TH/BRIC) file:

USR1: gas density

USR20: gas pressure

USR21: R value

USR22: K value

Gas velocity vector field can be output in animation with /ANIM/VECT/GVEL.