/FAIL/EMC
Block Format Keyword Describes failure dependent on effective plastic strain.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/EMC/mat_ID/unit_ID  
a  n  b_{0}  c 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

$\gamma $  ${\dot{\epsilon}}_{0}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fail_ID 
Definition
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

a  Hosford exponent. Default = 1.0 (Real) 

n  Stress state sensitivity
exponent. (Real) 

b_{0}  Strain to fracture for uniaxial tension. 2 Default = 1.0 (Real) 

c  Friction parameter for triaxiality. Default = 0.0 (Real) 

$\gamma $  Strain rate sensitivity
parameter. (Real) 

${\dot{\epsilon}}_{0}$  Reference strain rate. Default = 10^{30} (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
fail_ID  (Optional) Failure criteria identifier. 3 (Integer, maximum 10 digits) 
Example (Metal)
Fracture parameters could be identified with tests like uniaxial tension ( $\eta =1/3,\theta =1$ ), pure shear ( $\eta =0,\theta =0$ ), and axisymmetric compression ( $\eta =2/3,\theta =1$ ).
#RADIOSS STARTER
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/UNIT/1
unit for mat
Mg mm s
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# 2. MATERIALS:
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/MAT/LAW84/1/1
Swiftvoce (metal)
# RHO_I
8E9
# E NU
206000. 0.30
# P12 P22 P33 QVOCE BVOCE
0.5 1. 3. 524.0000 25.
# G11 G22 G33 K0 ALPHA
0.5 1. 3. 100. 0.5
# AN EPS0 NN CEPSP DEPS0
1000. 0.00128 0.200 0.014 0.0011
# ETA CP TINI TREF TMELT
0.9 420e+8 293 293. 1700.
# MTEMP DEPSAD
0.921 1.379
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/FAIL/EMC/1/1
# exponent_a exponent_n coef_b coef_c
1.9 0.2 0.20 0.0
# GAMA DEPS0
0.0 1.0
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#ENDDATA
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Comments
 The failure
criteria is calculated as:
(1) $${D}_{fail}={\displaystyle \sum \text{\Delta}D}>1$$Where,(2) $$\text{\Delta}D=\frac{\text{\Delta}{\overline{\epsilon}}_{p}}{{\overline{\epsilon}}_{p,fail}}$$Where,(3) $${\overline{\epsilon}}_{p,fail}=b\cdot {\left(1+c\right)}^{\frac{1}{n}}\cdot {\left\{{\left[\frac{1}{2}\left({\left({f}_{1}{f}_{2}\right)}^{a}+{\left({f}_{2}{f}_{3}\right)}^{a}+{\left({f}_{1}{f}_{3}\right)}^{a}\right)\right]}^{\frac{1}{a}}+c\left(2\eta +{f}_{1}+{f}_{3}\right)\right\}}^{\frac{1}{n}}$$Where, ${f}_{1}$ , ${f}_{2}$ and ${f}_{3}$ are functions of the Lode angle $\theta $ :(4) $${f}_{1}=\frac{2}{3}\text{cos}\left[\frac{\pi}{6}\left(1\theta \right)\right]$$(5) $${f}_{2}=\frac{2}{3}\text{cos}\left[\frac{\pi}{6}\left(3+\theta \right)\right]$$(6) $${f}_{3}=\frac{2}{3}\text{cos}\left[\frac{\pi}{6}\left(1+\theta \right)\right]$$With(7) $$\theta =1\frac{2}{\pi}\text{arccos}\left[\frac{3\sqrt{3}}{2}\frac{{\text{J}}_{3}}{{\left({\text{J}}_{2}\right)}^{3/2}}\right]$$Where, $\eta $ is the traixiality $\eta =\frac{{\sigma}_{m}}{{\sigma}_{VM}}=\frac{{I}_{1}}{3\sqrt{3{J}_{2}}}$ .
 The
coefficient, b is computed as:
$b={b}_{0}\left[1+\gamma \mathrm{ln}\left(\frac{{\dot{\overline{\epsilon}}}_{p}}{{\dot{\overline{\epsilon}}}_{0}}\right)\right]$ if ${\dot{\overline{\epsilon}}}_{p}>{\dot{\overline{\epsilon}}}_{0}$ else $b={b}_{0}$
 The fail_ID is used with
/STATE/BRICK/FAIL and
/INIBRI/FAIL for brick. There
is no default value. If the line is blank, no
value will be output for failure model variables
in the /INIBRI/FAIL (written in
.sta
file with /STATE/BRICK/FAIL for brick).