/MAT/LAW48 (ZHAO)

Block Format Keyword

/MAT/LAW48 - Zhao Material Law

Description

This law describes the Zhao material law used to model an elasto-plastic strain rate dependent materials. The law is applicable only for solids and shells. The global plasticity option for shells (N=0 in shell property keyword) is not available in the actual version.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW48/mat_ID/unit_ID or /MAT/ZHAO/mat_ID/unit_ID
mat_title

E
A		B		n		Chard
C		D		m		c		k
		Fcut

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)
A	Plasticity yield stress (Real)
B	Plasticity hardening parameter (Real)
n	Plasticity hardening exponent Default = 1.0 (Real)
Chard	Plasticity Iso-kinematic hardening factor Default = 0.0 (Real) = 0: hardening is full isotropic model = 1: hardening uses the kinematic Prager-Ziegler model = between 0 and 1: hardening is interpolated between the two models
	Plasticity maximum stress Default = 1030 (Real)
C	Relative strain rate coefficient Default = 1.0 (Real)
D	Strain rate plasticity factor Default = 0.0 (Real)
m	Relative strain rate exponent Default = 1.0 (Real)
c	Strain rate coefficient Default = 0.0 (Real)
k	Strain rate exponent Default = 1.0 (Real)
	Reference strain rate (Real)
Fcut	Cutoff frequency for strain rate filtering Default = 0.0 (Real)
	Failure plastic strain Default = 1030 (Real)
	Tensile failure strain 1 Default = 1030 (Real)
	Tensile failure strain 2 Default = 1030 (Real)

#RADIOSS STARTER

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/UNIT/1

unit for mat

g mm ms

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#- 2. MATERIALS:

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/MAT/LAW48/1/1

metal

# RHO_I

.008

# E NU

200000 .3

# A B n C_hard SIGMA_max

145 550 .42 1 0

# C D m c k

35 47 .3 185 .3

# EPS_rate_0 Fcut

.05 0

# EPS_max EPS_t1 EPS_t2

0 0 0

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

#ENDDATA

/END

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1.	The stress-strain function is based on the formula published by Zhao:

Where, is the plastic strain and is the strain rate.

2.	Except for the strain rate formulation, the plasticity curve is strictly identical to a Johnson-Cook model:

mat_law48

However, compared to Johnson-Cook, the Zhao law allows a better approximation of a nonlinear strain rate dependent behavior.

3.	Yield stress should be strictly positive.

4.	The hardening exponent n must be less than 1.

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5.	If , the term , and the equation is:

6.	The strain rate filtering is used to smooth strain rate. It is only available for shell and solid elements.

7.	When reaches 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.

8.	If ( is the largest principal strain), the stress is reduced as follows:

9.	If , the stress is reduced to 0 (but the element is not deleted).