/MAT/LAW36 (PLAS

Block Format Keyword

/MAT/LAW36 - Elastic Plastic Piecewise Linear Material

Description

This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve (for example, plastic strain vs. stress) for different strain rates.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW36/mat_ID/unit_ID or /MAT/PLAS_TAB/mat_ID/unit_ID
mat_title

E
Nfunct	Fsmooth	Chard		Fcut
fct_IDp	Fscale		fct_IDE	Einf		CE

Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
fct_ID1	fct_ID2	fct_ID3	fct_ID4	fct_ID5

Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
Fscale1		Fscale2		Fscale3		Fscale4		Fscale5

Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards

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

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)
E	Young’s modulus (Real)
	Poisson’s ratio (Real)
	Failure plastic strain Default = 1030 (Real)
	Tensile failure strain at which stress starts to reduce Default = 1030 (Real)
	Maximum tensile failure strain at which the stress in element is set to zero Default = 2.0 x 1030 (Real)
Nfunct	Number of functions () Default = 0 (Integer)
Fsmooth	Smooth strain rate option flag Default = 0 (Integer) = 0: no strain rate smoothing = 1: strain rate smoothing active
Chard	Hardening coefficient (Real) = 0: the hardening is a full isotropic model = 1: the hardening uses the kinematic Prager-Ziegler model = value between 0 and 1: the hardening is interpolated between the two models
Fcut	Cutoff frequency for strain rate filtering Only available for shell and solid elements. Default = 1.0 x 1030 (Real)
	Tensile strain for element deletion Default = 3.0 x 1030 (Real)
fct_IDp	Yield factor vs. pressure function (Comment 7) Default = 0 (Integer)
Fscale	Scale factor for yield factor in fct_IDp Default = 1.0 (Real)
fct_IDE	Function identifier for the scale factor of Young modulus, when Young modulus is function of the plastic strain (Comment 16): Default = 0: in this case the evolution of Young depends on Einf and CE. (Integer)
Einf	Saturated Young’s modulus for infinitive plastic strain (Real)
CE	Parameter for Young’s modulus evolution (Real)
fct_ID1	Yield stress function identifier 1 corresponding to strain rate (Integer)
fct_ID2	Yield stress function identifier 2 corresponding to strain rate (Integer)
fct_ID3	Yield stress function identifier 3 corresponding to strain rate (Integer)
fct_ID4	Yield stress function identifier 4 corresponding to strain rate (Integer)
fct_ID5	Yield stress function identifier 5 corresponding to strain rate (Integer)
Fscale1	Scale factor for ordinate (stress) in fct_ID1 Default = 1.0 (Real)
Fscale2	Scale factor for ordinate (stress) in fct_ID2 Default = 1.0 (Real)
Fscale3	Scale factor for ordinate (stress) in fct_ID3 Default = 1.0 (Real)
Fscale4	Scale factor for ordinate (stress) in fct_ID4 Default = 1.0 (Real)
Fscale5	Scale factor for ordinate (stress) in fct_ID5 Default = 1.0 (Real)
	Strain rate 1 (Real)
	Strain rate 2 (Real)
	Strain rate 3 (Real)
	Strain rate 4 (Real)
	Strain rate 5 (Real)

#RADIOSS STARTER

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

/UNIT/1

unit for mat

g mm ms

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

#- 2. MATERIALS:

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

/MAT/PLAS_TAB/1/1

Aluminum_example

# RHO_I

.0027

# E NU Eps_p_max Eps_t Eps_m

60400 .33 0 0 0

# N_funct F_smooth C_hard F_cut Eps_f

14 0 0 0 0

# fct_IDp Fscale Fct_IDE EInf CE

0 0 0 0 0

# fct_ID1 fct_ID2 fct_ID3 fct_ID4 fct_ID5

1 2 3 4 5

6 7 8 9 10

11 12 13 14

# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5

1 1.2 1.4 1.6 1.9

10 10.2 10.4 10.6 10.9

20 20.2 20.4 20.6

# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5

0 20 30 40 50

110 120 130 140 150

210 220 230 240

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

#- 3. FUNCTIONS:

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

/FUNCT/1

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/2

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/3

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/4

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/5

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/6

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/7

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/8

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/9

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/10

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/11

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/12

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/13

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

/FUNCT/14

function_36

# X Y

0 90

2.5E-4 100

.001 104

.009 121

.017 136

.021 143

.036 156

.045 162

.055 165

.072 170

.075 170

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

#ENDDATA

/END

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

1.	The first point of yield stress functions (plastic strain vs stress) should have a plastic strain value of zero. If the last point of the first (static) function equals 0 in stress, default value of is set to the corresponding value of .

2.	Element deletion:

•	Once (plastic strain) reaches , in one integration point, the element is deleted.

•	If reaches , the stress is reduced using the following relation:

•	If (largest principal strain) reaches (), the stress in element is reduced to 0 (but the element is not deleted).

•	Once (largest principal strain) reaches (maximum tensile failure strain), the element is deleted.

3.	The kinematic hardening model is not available in global formulation (N=0 in shell property keyword) that is, hardening is fully isotropic.

4.	In case of kinematic hardening and strain rate dependency, the yield stress depends on the strain rate.

5.	Strain rate filtering is used to smooth strain rates.

The first function in fct_ID1 is used for strain rate values from 0 to its corresponding strain rate, strain rate 1. However, the last function used in the model does not extend to the maximum strain rate; for higher strain rates, a linear extrapolation will be applied. This could lead to instability and/or unusual deformation. This instability can be overcome by repeating the stress strain curve, corresponding to the last strain rate, again with a much higher strain rate.

clip0079

fct_IDp is used to distinguish the behavior in tension and compression for certain materials (pressure dependent yield). This is available for both shell and solid elements. The effective yield stress is then obtained by multiplying the nominal yield stress by the yield factor corresponding to the actual pressure.

8.	If , the yield stress is interpolated between and .

9.	If , function is used.

10.	Above , yield stress is extrapolated.

mat_law36_yield_stress

11.	Separate functions must be defined for different strain rates.

12.	Strain rate values must be given in strictly ascending order.

13.	The evolution of Young’s modulus:

•	If fct_IDE > 0, the curve defines a scale factor for Young modulus evolution with equivalent plastic strain, which means the Young Modulus is scaled by the function :

The initial value of the scale factor should be equal to 1 and it decreases.

•	If fct_IDE = 0, the Young Modulus is calculated as:

Where, E and Einf are respectively the initial and asymptotic value of Young’s modulus, and is the accumulated equivalent plastic strain.

Note: If fct_IDE = 0 and CE = 0, Young modulus E is kept constant.

/MAT/LAW36 (PLAS_TAB)

/MAT/LAW36 (PLAS_TAB)

/MAT/LAW36 (PLAS_TAB)

See Also: