LS-DYNA Theory Manual - March 2006 · LS-DYNA Theory Manual Material Models 19.43 Material Model...
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LS-DYNA Theory Manual Material Models 19.43 Material Model 22: Chang-Chang Composite Failure Model Five material parameters are used in the three failure criteria. These are [Chang and Chang 1987a, 1987b]: • 1 S , longitudinal tensile strength • 2 S , transverse tensile strength • 12 S , shear strength • 2 C , transverse compressive strength • α , nonlinear shear stress parameter. 1 2 12 S , S , S , and 2 C are obtained from material strength measurement. α is defined by material shear stress-strain measurements. In plane stress, the strain is given in terms of the stress as ( ) ( ) 1 1 1 2 1 2 2 2 1 2 3 12 12 12 12 1 1 1 2 E E G ε σ υσ ε σ υσ ε τ ατ = − = − = + (19.22.1) The third equation defines the nonlinear shear stress parameter α . A fiber matrix shearing term augments each damage mode: 2 4 12 12 12 2 4 12 12 12 3 2 4 3 2 4 G S S G τ ατ τ α + = + (19.22.2) which is the ratio of the shear stress to the shear strength. The matrix cracking failure criteria is determined from 2 2 matrix 2 F S σ τ = + (19.22.3) where failure is assumed whenever matrix 1 F > . If matrix 1 F > , then the material constants 2 12 1 , , , E G υ and 2 υ are set to zero. The compression failure criteria is given as
Transcript of LS-DYNA Theory Manual - March 2006 · LS-DYNA Theory Manual Material Models 19.43 Material Model...
LS-DYNA Theory Manual Material Models
19.43
Material Model 22: Chang-Chang Composite Failure Model Five material parameters are used in the three failure criteria. These are [Chang and Chang 1987a, 1987b]:
• 1S , longitudinal tensile strength
• 2S , transverse tensile strength
• 12S , shear strength
• 2C , transverse compressive strength
• α , nonlinear shear stress parameter.
1 2 12S , S , S , and 2C are obtained from material strength measurement. α is defined by material
shear stress-strain measurements. In plane stress, the strain is given in terms of the stress as
( )
( )
1 1 1 21
2 2 2 12
312 12 12
12
1
1
12
E
E
G
ε σ υ σ
ε σ υ σ
ε τ ατ
= −
= −
= +
(19.22.1)
The third equation defines the nonlinear shear stress parameter α . A fiber matrix shearing term augments each damage mode:
2412
12122
41212
12
32 4
32 4
G
SS
G
τ αττ
α
+=
+ (19.22.2)
which is the ratio of the shear stress to the shear strength. The matrix cracking failure criteria is determined from
2
2matrix
2
FS
σ τ= + (19.22.3)
where failure is assumed whenever matrix 1F > . If matrix 1F > , then the material constants
2 12 1, , ,E G υ and 2υ are set to zero. The compression failure criteria is given as
Material Models LS-DYNA Theory Manual
19.44
2 2
2 2 2
12 12 2
12 2comp
CF
S S C
σ σ τ= + − + (19.22.4)
where failure is assumed whenever 1combF > . If 1combF > , then the material constants
2 1, ,E υ and 2υ are set to zero. The final failure mode is due to fiber breakage.
2
1
1fiberF
S
σ τ= + (19.22.5)
Failure is assumed whenever 1fiberF > . If 1fiberF > , then the constants 1, 2 12 1, , ,E E G υ and 2υare set to zero.
Material Model 23: Thermal Orthotropic Elastic with 12 Curves In the implementation for three-dimensional continua a total Lagrangian formulation is used. In this approach the material law that relates second Piola-Kirchhoff stress S to the Green-St. Venant strain E is
tlS C E T C T E= ⋅ = ⋅ (19.23.1)
where T is the transformation matrix [Cook 1974].
( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )
2 2 21 1 1 1 1 1 1 1 12 2 22 2 2 2 2 2 2 2 22 2 23 3 3 3 3 3 3 3 3
1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 2 1
2 3 2 3 2 3 2 3 3 2 2 3 3 2 2 3 3 2
3 1 3 1 3 1 3 1 1 3 3 1 1 3 3 1 1 3
2 2 2
2 2 2
2 2 2
l m n l m m n n l
l m n l m m n n l
l m n l m m n n lT
l l m m n n l m l m m n m n n l n l
l l m m n n l m l m m n m n n l n l
l l m m n n l m l m m n m n n l n l
=+ + ++ + ++ + +
(19.23.2)
il , im , in are the direction cosines
'1 2 3 1, 2,3i i i ix l x m x n x for i= + + = (19.23.3)
and 'ix denotes the material axes. The temperature dependent constitutive matrix lC is defined
in terms of the material axes as
