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/MAT/LAW58 (FABR_A)

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/MAT/LAW58 - Hyperelastic Anisotropic Fabric Material

Description

This law describes a hyperelastic anisotropic fabric material. It uses an anisotropic coordinate system with anisotropy angle, following element deformation. The material formulation provides coupling between warp and weft directions in order to reproduce physical interaction between fibers. The shear degree of freedom is fully decoupled from the translational degrees of freedom. Optionally, nonlinear stress-strain curves can be specified for warp, weft directions and in shear.

Format

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(2)

(3)

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(5)

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(10)

/MAT/LAW58/mat_ID/unit_ID or /MAT/FABR_A/mat_ID/unit_ID

mat_title

 

 

 

 

 

 

 

 

E1

B1

E2

B2

Flex

G0

GT

Gsh

 

sens_ID

Df

Ds

Gfrot

 

ZeroStress

N1

N2

S1

S2

Flex1

Flex2

Optional lines:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

fct_ID1

 

Fscale1

 

 

 

 

 

fct_ID2

 

Fscale2

 

 

 

 

 

fct_ID3

 

Fscale3

 

 

 

 

 

fct_ID4

fct_ID5

Fscale4

Fscale5

fct_ID6

Fscale6

 

hmtoggle_plus1Flag Definition

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)

E1

Young’s modulus in the warp direction

(Real)

B1

Softening coefficient in the warp direction

Default = 0.00  (Real)

E2

Young’s modulus in the weft direction

(Real)

B2

Softening coefficient in the weft direction

Default = 0.00  (Real)

Flex

Fiber bending modulus reduction factor

Default = 0.01 (Real)

 

G0

Initial shear modulus

(Real)

Default = G, where

GT

Tangent shear modulus at

(Real)

Shear lock angle

(Real)

Gsh

Traverse shear modulus (only used with multi-layer property)

Default  (Real)

If G0 = 0, then

sens_ID

Sensor identifier to activate reference geometry (Comment 7)

(Integer, maximum 10 digits)

 

Df

Damping coefficient in the warp and weft directions (0.0 < Df < 1.0) (Comment 9)

Default = 0.00  (Real)

 

Ds

Friction coefficient between fibers in shear (0.0 < Ds < 1.0) (Comment 10)

Default = 0.00  (Real)

 

Gfrot

Shear friction modulus (Comment 10)

Default  (Real)

If G0 = 0, then

 

ZeroStress

Zero stress flag for initial stresses in tension and compression by using reference state geometry (Comment 6)

(Real)

= 0: No stress reduction

= 1: Full stress reduction

 

N1

Fiber density (number of fiber per length unit) in warp direction (Comment 17)

Default = 1  (Integer)

 

N2

Fiber density (number of fiber per length unit) in weft direction (Comment 17)

Default = 1  (Integer)

 

S1

Straightening strain in the warp direction (Comment 4)

Default = 0.10  (Real)

 

S2

Straightening strain in the weft direction (Comment 4)

Default = 0.10  (Real)

 

Flex1

Fiber bending modulus reduction factor in warp direction (Comment 11)

Default = Flex  (Real)

 

Flex2

Fiber bending modulus reduction factor in weft direction (Comment 11)

Default = Flex  (Real)

 

fct_ID1

(Optional) Function identifier for true stress vs true strain in warp direction

Default = 0  (Integer)

 

Fscale1

(Optional) Scale factor for ordinate of function 1

Default = 1.0  (Real)

fct_ID2

(Optional) Function identifier for true stress vs true strain in weft direction

Default = 0  (Integer)

 

Fscale2

(Optional) Scale factor for ordinate of function 2

Default = 1.0  (Real)

fct_ID3

(Optional) Function identifier for true shear stress vs the complementary angle (in degrees) between fiber directions (axes of anisotropy) (Comment 5)

Default = 0  (Integer)

 

Fscale3

(Optional) Scale factor for ordinate of function 3

Default = 1.0  (Real)

fct_ID4

(Optional) Function identifier for unloading for true stress vs true strain in warp direction

Default = 0  (Integer)

 

Fscale4

(Optional) Scale factor for ordinate of function 4

Default = 1.0  (Real)

fct_ID5

(Optional) Function identifier for unloading for true stress vs true strain in weft direction

Default = 0  (Integer)

 

Fscale5

(Optional) Scale factor for ordinate of function 5

Default = 1.0  (Real)

fct_ID6

(Optional) Function identifier for true shear stress vs the complementary angle (in degrees) between fiber directions (axes of anisotropy)

Default = 0  (Integer)

 

Fscale6

(Optional) Scale factor for ordinate of function 6

Default = 1.0  (Real)

hmtoggle_plus1Example (Fabric)

#RADIOSS STARTER

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

/UNIT/1

unit for mat

                 kg                   m                   s

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

#-  2. MATERIALS:

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

/MAT/LAW58/1/1

FABRIC

#              RHO_I

               722.5

#                 E1                  B1                  E2                  B2                FLEX

           450000000                   0           450000000                   0                0.01

#                 G0                  GT              AlphaT                 Gsh             sens_ID

                   0            10000000                  60                   0                   0

#                 Df                  Ds               GFROT                             ZERO_STRESS

                 .05                 .05                   0                                       0

#       N1        N2                  S1                  S2               FLEX1               FLEX2

         1         1                 .05                 .05                   0                   0

#  fct_ID1                       Fscale1

         0                             0

#  fct_ID2                       Fscale2

         0                             0

#  fct_ID3                       Fscale3

         0                             0

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

#ENDDATA

/END

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

hmtoggle_plus1Comments
1.This law is only used with shell elements with Anisotropic Layered Shell Property (/PROP/TYPE16 - SH_FABR). Only one integration point is allowed in the current version.
2.The fiber directions (warp and weft) define local axes of anisotropy. Material data are specified independently for each direction and in shear.
3.If stress-strain curves in warp and weft directions (fct_ID1 and fct_ID2) are not specified, the following analytical relationship between stress and strain is used:

4.This material allows you to account for the initial straightening effect of the woven fabric.

law58_woven_fabric

It is assumed to be softer in the tensile direction during the straightening phase. Young’s modulus in the corresponding direction is scaled by a factor Flexi. The straightening portion of the strain is given by the strains S1 and S2 for direction 1 and 2 correspondingly.

law58_straightening

In compression, the Young’s modulus of the fabric material is equal to Flexi * Ei. In biaxial tension there is no straightening phase and the fibers bear loads from the beginning of the loading phase.

law58_loading_phase

5.The shear stress (symbol_t) can be specified either as a nonlinear function (fct_ID3) of the complementary angle a which is equal to the difference between 90 degrees and the current angle between the anisotropy axes, or the following analytical relationship between shear stress and a is used:

          if    

   if    

and

,    with  

Where, aT  is the shear locking angle, GT is the shear modulus at aT, and G0 is the shear modulus at a = a0.

law58_shear

If the G0 field is set to 0, then its value is calculated to avoid discontinuity of the shear modulus at aT: G0 = G.

law58_continuous_shear

aT is an initial complementary angle, which is equal to the difference between 90 degrees and the initial angle between the anisotropy axes defined in the shell property (/PROP/TYPE16). Note that initial pre-stress exists in the fabric material if initial angle between the fiber axes specified in the property is not equal to 90 degrees.

6.The ZeroStress flag is used to remove initial stresses in the folded airbag. These initial stresses arise during the folding process. Numerically this pre-stress is specified through a reference airbag geometry which represents an unfolded airbag state. If ZeroStress=1, then compressive and tensile initial stresses are set to zero and then gradually increase to the actual value after deployment begins.
7.sens_ID is used only with ZeroStress =1 and reference airbag geometry. It activates the pre-stress based on the values output from the sensor. This is useful for airbags with time to fire > 0.
8.This material uses the anisotropic coordinate system, with the angle between the material coordinate system axes (anisotropy angle) updated based on the element deformation. Special user-defined output should be used to evaluate stresses, strains, and the shear angle alpha. In the /TH/SHEL and /TH/SH3N entries in the Starter file and in /ANIM/SHELL in the Engine file, you should specify the following:

USR1 – stress in fiber direction 1

USR2 – stress in fiber direction 2

USR3 - stress in shear direction

USR4 - strain in fiber direction 1

USR5 - strain in fiber direction 2

USR6 - tan(a)

Due to special material formulation (decoupled DOF with special interaction between fibers), the stress components does not form a stress tensor, therefore usual tensor evaluations such as von Mises stress, principal stresses, and so on, have no meaning for the material.

9.Fiber damping is used to suppress instabilities as a result of elastic material behavior. The recommended value for the damping coefficient in the fiber direction Df is 0.05.
10.Gfrot is the shear modulus used to calculate interaction shear stress () between fibers. The friction in-plane shear stress between the fibers is calculated as .
11.If the value of Flex1 or Flex2 is equal to zero, then the value of Flex will be used.
12.The nonlinear functions (fct_ID#) should begin at (0,0), be monotonically increasing, and both abscissa and ordinate should be greater than or equal to zero. For fct_ID3, the abscissa a should be set in degrees, and its value should be less than 90 degrees. The material is assumed to be hyperelastic, and the loading and unloading paths are equivalent.
13.The functions fct_ID1 and fct_ID2 correspond to biaxial tension, where the initial straightening is not taken into account. But in uniaxial tension, the soften effect is accounted for by using Flex1 and Flex2 in the stress calculation. It is similar if E1 and E2 are specified instead.
14.The values of E1, B1, E2, B2, G0, and GT are ignored if the nonlinear functions (fct_ID#) are set. However, the values E1, E2, and G0 are still required to calculate the prestress from the reference geometry. In such cases, E1, E2, and G0 should correspond to average stiffness (average slope) of the corresponding nonlinear functions (fct_ID#).
15.The nonlinear functions (fct_ID#) are not mandatory. If these functions are not specified, the corresponding values of E1, B1, E2, B2, G0, and GT are used to calculate the stress-strain relationship of the material.
16.If fct_ID4 , fct_ID5 and fct_ID6 are given the material shows hysteresis behavior with different path for loading and unloading in uniaxial and shear directions.
17.N1 and N2 are the number of fiber per length unit, which are used to calculate stress in both fiber directions.

See Also:

Material Compatibility

Law Compatibility with Failure Model

Airbag modeling in User’s Guide

FVM Airbag Guidelines

/MAT/LAW58 in FAQ

/MAT/LAW58 in Theory Manual