/MAT/LAW2 (PLAS

Block Format Keyword

/MAT/LAW2 - Johnson-Cook Material

Description

This law represents an isotropic elasto-plastic material using the Johnson-Cook material model. This model expresses material stress as a function of strain, strain rate and temperature. A built-in failure criterion based on the maximum plastic strain is available.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW2/mat_ID/unit_ID or /MAT/PLAS_JOHNS/mat_ID/unit_ID
mat_title

E				Iflag
a (or )		b (or UTS)		n (or )
c				ICC	Fsmooth	Fcut		Chard
m		Tmelt				Tr

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)
Iflag	Input type flag (Integer) = 0: Classic input for Johnson-Cook parameter a,b,n is active (default) = 1: New, simplified input type is active: Yield stress, UTS (engineering stress), or Strain at UTS (Comment 17)
a (or )	If Iflag = 0: Plastic yield stress If Iflag = 1: Yield stress (Real)
b (or UTS)	If Iflag = 0: Plastic hardening parameter b If Iflag = 1: Ultimate Tensile Stress - UTS (engineering stress) (Real)
n (or )	If Iflag = 0: Plastic hardening exponent n (Comment 5) If Iflag = 1: , Engineering strain at UTS Default = 1.0 (Real)
	Failure plastic strain Default = 1030 (Real)
	Maximum stress Default = 1030 (Real)
c	Strain rate coefficient Default = 0.00 (Real) = 0: no strain rate effect
	Reference strain rate (Real) If , no strain rate effect
ICC	Strain rate computation flag (Comment 8) (Integer) = 0: default set to 1 = 1: strain rate effect on = 2: no strain rate effect on
Fsmooth	Strain rate smoothing flag (Integer) = 0: strain rate smoothing is inactive (default) = 1: strain rate smoothing is active
Fcut	Cutoff frequency for strain rate smoothing (Comments 9 and 10) Default = 1030 (Real)
Chard	Hardening coefficient (unloading) (Real) = 0: isotropic model = 1: kinematic Prager-Ziegler model = value between 0 and 1: the hardening behavior is interpolated between the two models (Comment 16)
m	Temperature exponent Default = 1.00 (Real)
Tmelt	Melting temperature Default = 1030 (Real) = 0: no temperature effect
	Specific heat per unit volume (Comment 12) (Real)
Tr	Room temperature (Comment 12) Default = 298 K (Real)

#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/PLAS_JOHNS/1/1

Steel

# RHO_I

7.8E-9

# E NU Iflag

210000 .3 0

# a b n EPS_max SIG_max0

270 793.9521092213 0.7520058067932 0 0

# c EPS_DOT_0 ICC Fsmooth F_cut Chard

0 0 0 0 0 0

# m T_melt rhoC_p T_r

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----|

#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/PLAS_JOHNS/1/1

Steel (use ultimate tensile stress(UTS) and engineering strain )

# RHO_I

7.8E-9

# E NU Iflag

210000 .3 1

# SIG_y UTS EPS_UTS EPS_max SIG_max0

270 450 .6 0 0

# c EPS_DOT_0 ICC Fsmooth F_cut Chard

0 0 0 0 0 0

# m T_melt rhoC_p T_r

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----|

1.	This is an elasto-plastic material model that includes strain rate and temperature effects.

2.	In this model the material behaves as a linear-elastic material when the equivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic and the stress is calculated as shown below.

where,

is the plastic strain, is the strain rate, T is the temperature, Tr is the ambient temperature, and Tmelt is the melting temperature.

3.	The plastic yield stress should always be greater than zero. To model pure elastic behavior, the plastic yield stress will be set to 1030.

4.	When reaches the value of in one integration point, then based on the element type:

•	Shell elements: The corresponding shell element is deleted.

•	Solid elements: The deviatoric stress of the corresponding integral point is permanently set to 0, however, the solid element is not deleted.

5.	The plastic hardening exponent, n must be less than or equal to 1.

6.	The strain rate has no effect on truss elements.

7.	To eliminate the effect of the strain rate, you can either set the value of c equal to 0 or the reference strain rate () can be set equal to 1030. There is no effect of strain rate when is less than .

8.	The ICC flag defines the effect of strain rate on the maximum material stress . The figure below shows the value of for the corresponding ICC flag.

mat_law27

9.	Strain rate smoothing is a process used to filter out higher strain rate frequencies.

10.	The strain rate smoothing input (Fcut) is available only for shell and solid elements.

11.	There is no effect of temperature on trusses and beams.

12.	The temperature is constant (T = Tr), if .

13.	Adiabatic conditions are assumed for thermal simulations with initial temperature equal to room temperature (Tr) and:

Where, is the internal deformation energy.

14.	The strain rate dependence must be activated to account for thermal effects.

15.	When /HEAT/MAT (with Iform =1) references this material model, the values of Tr and defined in this card will be overwritten by the corresponding T0 and defined in /HEAT/MAT.

16.	The hardening coefficient is used to describe the hardening model (during unloading). The values of the hardening coefficient should be between 0 and 1.

17.	The simplified input of Yield-Stress, Ultimate-Stress (UTS in engineering stress), and strain at UTS (which is between 0.5 – 0.9 of failure strain) will be recalculate to the Johnson-Cook values a,b,n internally. The Starter output file has the values.

/MAT/LAW2 (PLAS_JOHNS)

/MAT/LAW2 (PLAS_JOHNS)

/MAT/LAW2 (PLAS_JOHNS)

See Also: