/MAT/LAW78

Block Format Keyword

/MAT/LAW78 - Yoshida-Uemori Material

Description

This law is the Yoshida-Uemori model for describing the large-strain cyclic plasticity of metals. The law is based on the framework of two surfaces theory: the yielding surface and the bounding surface. During the plastic deformation, a yield surface will move within the bounding surface and will never change its size, and the bounding surface can change both in size and location. The plastic-strain dependency of the Young’s modulus and the work-hardening stagnation effect are also taken into account.

Concerning SPH, it is compatible with solid only, this can be verified with the /SPH/WavesCompression test. The solid version is only isotropic. The shell version is anisotropic based on Hill criterion.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW78/mat_ID/unit_ID
mat_title

E
Y		b		C		h		B0
m		Rsat		OptR	C1		C2
r00		r45		r90
fct_IDE		Einf		CE

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)
Y	Yield stress (Real)
b	Center of the bounding surface (Real)
C	Parameter for kinematic hardening rule of yield surface (Real)
h	Material parameter for controlling work hardening stagnation (Real)
B0	Initial size of the bounding surface (Real)
m	Parameter for isotropic and kinematic hardening of the bounding surface (Real)
Rsat	Saturated value of the isotropic hardening stress (Real)
OptR	Modified isotropic hardening rule flag (available for shells only): =0 :Yoshida formulation (Default) =1: modified formulation (define C1 and C2) (Integer)
C1, C2	Constant used in the modified formulation of the isotropic hardening of bounding surface (available for shells only) (Real)
r0, r45, r90	Material parameters determining anisotropy in Hill’s (48) yield criterion (in shell version) Default = 1.0 (Real)
fct_IDE	ID of the function defining the scale factor of Young’s modulus evolution versus effective plastic strain (Comment 7). (Integer)
Einf	Asymptotic value of Young’s modulus (Real)
CE	Parameter controlling the dependency of Young’s modulus on the effective plastic strain (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/LAW78/1/1

DP600-HDG

# RHO_I

7.8E-9

# E NU

206000 .3

# Y B C H B0

420 112 200 0 555

# m RSAT OPTR C1 C2

12 190 0 1 1

# R0 R45 R90

1 1 1

# fct_IDE EINF CE

0 1 163000

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

#ENDDATA

/END

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

1.	For solid elements, von Mises yield criterion is used, so the yield function is expressed as:

whereas for shell elements, Hill’s (48) yield criterion is used, which allows modeling anisotropic materials and it is expressed as follows:

where, () is expressed as:

2.	Yield stress, Poisson ratio and Young’s modulus should be strictly positive. The other parameters should be non-negative value.

3.	The schematic illustration of the two-surface model is shown in the following figure.

Where, 0 is the original center of the yield surface, the yield surface with its center and its radii Y, is moving kinematically, within a bounding surface that has a size indicated by B+R and tensor indicating its center position.

law78_2-surface_model

Schematic drawing of the two-surface model

4.	The yield surface is subjected to a kinematic hardening. The kinematic motion is described by that has the following evolution:

	for shell elements
	for solid elements

where,

is the equivalent plastic strain rate,

C and a are material parameters. And

is the total back stress

5.	The bounding surface is subjected to an isotropic-kinematic hardening. The evolution equation for isotropic hardening is:

	Default (if OptR = 0) Yoshida expression
	Available for shell elements, if OptR = 1

The evolution equation for kinematic hardening of bounding surface is:

6.	The work-hardening stagnation during unloading is described using a J2-type surface with a radius r and a center q:

where, should be either inside or on the surface .

7.	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, is the accumulated equivalent plastic strain.

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

8.	This material law is not available for implicit analysis.

/MAT/LAW78

/MAT/LAW78

/MAT/LAW78

See Also: