/FAIL/SAHRAEI
Block Format Keyword This orthotropic strainbased failure model can be used to predict failure and shortcut in battery cells. It is available for solid elements only.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/SAHRAEI/mat_ID/unit_ID 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Fct_ratio  NUM  DENOM  ORDIN  VOL_STRAIN  Fct_ID_{el}  El_ref 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

COMP_DIR  IDEL  MAX_COMP_STRAIN  RATIO 
(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  (Optional) Unit
identifier. (Integer, maximum 10 digits) 

Fct_ratio  Strain ratio function
identifier. (Integer) 

NUM  Numerator strain flag.
(Integer) 

DENOM  Denominator strain flag.
(Integer) 

ORDIN  Maximum strain at failure flag.
(Integer) 

VOL_STRAIN  Trigger volumetric strain for
damage. (Real) 

Fct_ID_{el}  Element size regularization
function identifier. (Integer) 

El_ref  Reference element
size. (Real) 
$\left[\text{m}\right]$ 
COMP_DIR  Direction component for compression
failure. (Integer) 

IDEL  Element deletion activation in
compression flag.
(Integer) 

MAX_COMP_STRAIN  Maximum strain value in compression
for element failure. (Real) 

RATIO  Strain ratio for failure in
compression. (Real) 

fail_ID  (Optional) Failure criteria
identifier. (Integer, maximum 10 digits) 
Example
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/LAW28/1
MAIN_1
# Init. dens. Ref. dens.
2.5E6 0
# E_11 E_22 E_33
10 8 8
# G_12 G_23 G_31
5 5 5
# Y11 Y22 Y33 Iflag1 Fscale11 Fscale22 Fscale33
10 11 11 1 0 0 0
# Eps_max_11 Eps_max_22 Eps_max_33
0 0 0
# Y12 Y23 Y31 Iflag2 Fscale12 Fscale23 Fscale31
12 12 12 1 0 0 0
# Eps_max_12 Eps_max_23 Eps_max_31
0 0 0
/FAIL/SAHRAEI/1
#Fct_ratio NUM DENOM ORDIN VOL_STRAIN Fct_IDEL EL_REF
3000 6 4 1 .5 3001 5
# COMP_DIR MAX_COMP_STRAIN RATIO
0 1 0
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# 2. FUNCTIONS:
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/FUNCT/10
Load 1st direction
1 5
0 .1
1 .1
#12345678910
/FUNCT/11
Load 2nd and 3rd direction
1 4
0 .08
1 .08
#12345678910
/FUNCT/12
Shear
1 .05
0 .05
1 .05
#12345678910
/FUNCT/3000
fail strain as ratio of E33/E11 vs. failure strain
# X Y
0 0.335081967
0.141129032 0.330491803
0.181451613 0.312131148
0.27 0.271967213
0.403225807 0.222622951
0.483870968 0.203114754
0.705645161 0.149180328
0.826612903 0.110163934
1.008064516 0.082622951
1.411290323 0.059672131
1.975806452 0.055081967
2.661290323 0.061967213
3.286290323 0.063114754
4.032258065 0.064262295
4.677419355 0.064262295
5.705645161 0.061967213
6.693548387 0.061967213
7.540322581 0.050491803
9. 0.032131148
10. 0.032131148
#12345678910
/FUNCT/3001
fail strain as ratio of E33/E11 vs. failure strain
# X Y
0 1
1 1
5 .5
10 .5
#12345678910
#enddata
#12345678910
Comments
 The SAHRAEI failure criterion considers the evolution of a strain at
failure with a strain ratio. This strain ratio is userdefined by a
numerator (NUM) and a denominator
(DENOM):$${\epsilon}_{MAX}=f\left(\frac{{\epsilon}_{num}}{{\epsilon}_{denom}}\right)$$
 The strain used as a numerator
${\epsilon}_{num}$
can be:
 Strain along X axis ${\epsilon}_{x}$
 Strain along Y axis ${\epsilon}_{y}$
 Strain along Z axis ${\epsilon}_{z}$
 First principal strain ${\epsilon}_{1}$
 Second principal strain ${\epsilon}_{2}$
 Third principal strain ${\epsilon}_{3}$
 The strain used as the denominator
${\epsilon}_{denom}$
can be:
 The equivalent strain in XZ plane defined as:$${\epsilon}_{eq}^{XZ}=\frac{{\epsilon}_{x}+{\epsilon}_{z}}{2}+\sqrt{{\left(\frac{{\epsilon}_{x}{\epsilon}_{z}}{2}\right)}^{2}+{\epsilon}_{xz}^{2}}$$
 The equivalent strain in XY plane defined as:$${\epsilon}_{eq}^{XY}=\frac{{\epsilon}_{x}+{\epsilon}_{y}}{2}+\sqrt{{\left(\frac{{\epsilon}_{x}{\epsilon}_{y}}{2}\right)}^{2}+{\epsilon}_{xy}^{2}}$$
 The equivalent strain in YZ plane defined as:$${\epsilon}_{eq}^{YZ}=\frac{{\epsilon}_{y}+{\epsilon}_{z}}{2}+\sqrt{{\left(\frac{{\epsilon}_{y}{\epsilon}_{z}}{2}\right)}^{2}+{\epsilon}_{yz}^{2}}$$
 First principal strain ${\epsilon}_{1}$
 Second principal strain ${\epsilon}_{2}$
 Third principal strain ${\epsilon}_{3}$
 The equivalent strain in XZ plane defined as:
 The strain computation for maximum value
${\epsilon}_{MAX}$
can be:
 Maximum value between normal strains $\mathrm{max}\left({\epsilon}_{x},{\epsilon}_{y},{\epsilon}_{z}\right)$
 Strain along X axis ${\epsilon}_{x}$
 Strain along Y axis ${\epsilon}_{y}$
 Strain along Z axis ${\epsilon}_{z}$
 First principal strain ${\epsilon}_{1}$
 Equivalent strain in XZ plane ${\epsilon}_{eq}^{XZ}$
 Equivalent strain in XY plane ${\epsilon}_{eq}^{XY}$
 Equivalent strain in YZ plane ${\epsilon}_{eq}^{YZ}$
 The evolution ${\epsilon}_{MAX}=f\left(\frac{{\epsilon}_{num}}{{\epsilon}_{denom}}\right)$ is given by the tabulated function ID, Fct_ratio. An example of the recommended shape is:
 The damage variable computation starts when the absolute value of
volumetric strain is higher than the limit you defined. The damage evolution
is:$$D=\frac{{\epsilon}_{ORDIN}}{{\epsilon}_{MAX}}$$
Where, ${\epsilon}_{ORDIN}$ is computed the same way as ${\epsilon}_{MAX}$ .
 A failure in compression can also be defined using
COMP_DIR, RATIO and
MAX_COMP_STRAIN (denoted
${\epsilon}_{MAX\_COMP}<0$
).
 If COMP_DIR = 1, failure is
reached when:
$\begin{array}{ccc}{\epsilon}_{y}<{\epsilon}_{MAX\_COMP}& \text{or}& {\epsilon}_{z}<{\epsilon}_{MAX\_COMP}\times ratio\end{array}$
 If COMP_DIR = 2, failure is
reached when:
$\begin{array}{ccc}{\epsilon}_{z}<{\epsilon}_{MAX\_COMP}& \text{or}& {\epsilon}_{x}<{\epsilon}_{MAX\_COMP}\times ratio\end{array}$
 If COMP_DIR = 3, failure is
reached when:
$\begin{array}{ccc}{\epsilon}_{x}<{\epsilon}_{MAX\_COMP}& \text{or}& {\epsilon}_{y}<{\epsilon}_{MAX\_COMP}\times ratio\end{array}$
 If COMP_DIR = 1, failure is
reached when:
 It is possible to consider element size in material failure by
function fct_ID_{el} to scale
the failure strain:$$facto{r}_{el}=fct\_I{D}_{el}\left(\frac{Siz{e}_{el}}{El\_ref}\right)$$
Where, $Siz{e}_{el}$ is the reference element mesh size.
 The failure in compression only sets the damage variable to the value 1 without any element deletion (it is used as an indicator). If you want to activate the element deletion in compression, set the flag IDEL to 1.