/MAT/LAW12 (3D

Block Format Keyword

/MAT/LAW12 - Orthotropic Composite Solid Material

Description

This law describes a solid material using the Tsai-Wu formulation that is usually used to model composites. This material is assumed to be 3D orthotropic-elastic before the Tsai-Wu criterion is reached. The material becomes nonlinear afterwards. The Tsai-Wu criterion can be set dependent on the plastic work and strain rate in each of the orthotropic directions and in shear to model material hardening. Stress based orthotropic criterion for brittle damage and failure is available. This material is a generalization and improvement of /MAT/LAW14.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW12/mat_ID/unit_ID or /MAT/3D_COMP/mat_ID/unit_ID
mat_title

E11		E22		E33

G12		G23		G31

B		n		fmax



		Ef		c				ICC

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)
E11	Young’s modulus in direction 1 (Real)
E22	Young’s modulus in direction 2 (Real)
E33	Young’s modulus in direction 3 (Real)
	Poisson’s ratio between directions 1 and 2 (Real)
	Poisson’s ratio between directions 2 and 3 (Real)
	Poisson’s ratio between directions 3 and 1 (Real)
G12	Shear modulus in direction 12 (Real)
G23	Shear modulus in direction 23 (Real)
G31	Shear modulus in direction 31 (Real)
	Stress at the beginning of composite tensile/compressive failure in direction 1 (Comment 6) Default = 1030 (Real)
	Stress at the beginning of composite tensile/compressive failure in direction 2 (Comment 6) Default = (Real)
	Stress at the beginning of composite tensile/compressive failure in direction 3 (Comment 6) Default = (Real)
	Maximum damage factor (Comment 6) Default = 0.05 (Real)
B	Global plastic hardening parameter (Real)
n	Global plastic hardening exponent Default = 1.0 (Real)
fmax	Maximum value of the Tsai-Wu criterion limit Default = 1010 (Real)
	Yield stress in tension in direction 1 Default = 0.0 (Real)
	Yield stress in tension in direction 2 Default = 0.0 (Real)
	Yield stress in compression in direction 1 Default = 0.0 (Real)
	Yield stress in compression in direction 2 Default = 0.0 (Real)
	Yield stress in tensile shear in direction 12 Default = 0.0 (Real)
	Yield stress in compressive shear in direction 12 Default = 0.0 (Real)
	Yield stress in tensile shear in direction 23 Default = 0.0 (Real)
	Yield stress in compressive shear in direction 23 Default = 0.0 (Real)
	Yield stress in tension in direction 3 Default = 0.0 (Real)
	Yield stress in compression in direction 3 Default = 0.0 (Real)
	Yield stress in tensile shear in direction 13 Default = 0.0 (Real)
	Yield stress in compressive shear in direction 13 Default = 0.0 (Real)
	Fiber volume fraction (Comment 7) (Real)
Ef	Fiber Young’s modulus (Comment 7) (Real)
c	Global strain rate coefficient (Real) = 0: no strain rate effect
	Reference strain rate (Real)
ICC	Strain rate effect flag (Integer) = 0: default set to 1 = 1: strain rate effect on fmax = 2: no strain rate effect on fmax

#RADIOSS STARTER

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

/UNIT/1

unit for mat

Mg mm s

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

#- 2. MATERIALS:

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

/MAT/LAW12/1/1

carbon

# RHO_I

1.5E-9

# E11 E22 E33

64000 60000 5000

# NU12 NU23 NU31

.07 .07 .07

# G12 G23 G31

4000 2000 2000

# sigma_t1 sigma_t2 sigma_t3 delta

0 0 0 0

# B n fmax

50 .5 0

# sigma_1yt sigma_2yt sigma_1yc sigma_2yc

600 500 600 600

# sigma_12yt sigma_12yc sigma_23yt sigma_23yc

100 100 30 30

# sigma_3yt sigma_3yc sigma_13yt sigma_13yc

50 50 100 100

# alpha Ef c EPS_RATE_0 ICC

0 0 0 0 0

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

#ENDDATA

/END

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

This material requires an orthotropic solid property (/PROP/SOL_ORTH, /PROP/TSH_ORTH or /PROP/TSH_COMP). It can only be used with solid elements for a 3-dimensional analysis. This law is compatible with 10-node tetrahedron and 4-node tetrahedron elements. The orthotropic material directions are set in the property entries.

2.	For the elastic case, the stresses and strains are related as follows:

Where, are the strains, are the stresses, and , and are the distortions in the corresponding material directions. For example, for :

mat_law12_distortion

3.	The material is assumed to be elastic until the Tsai-Wu criterion is fulfilled. After exceeding the Tsai-Wu criterion limit , the material becomes non-linear:

Where, F is the variable Tsai-Wu criterion limit defined as a function of plastic work (Wp ) and the true strain rate ():

and, B is the plastic hardening parameter, n is the plastic hardening exponent, is the reference true strain rate, and c is the strain rate coefficient.

The coefficients of the Tsai-Wu criterion are determined from the limiting stresses when the material becomes nonlinear in directions 1, 2, 3 or 12, 23, 31 (shear) in compression or tension as follows:

4.	The maximum value of the Tsai-Wu criterion limit is bounded by:

5.	ICC is a flag that defines the effect of strain rate on fmax.

If ICC = 1, then fmax is scaled by a factor of:

When the limiting stress value of

is reached in tension, the corresponding stress value is scaled as

. The value of

is updated on each time step

. After

reaches the value of 1 the stress in corresponding direction is set to 0. The damage is irreversible, that is, if a value of

is attained the material will not reach any lower damage value.

7.	These parameters allow the definition of additional fiber reinforcement in the 11 direction. Additional stress in direction 11 will be added equal to .

/MAT/LAW12 (3D_COMP)

/MAT/LAW12 (3D_COMP)

/MAT/LAW12 (3D_COMP)

Format