/FAIL/TENSSTRAIN
Block Format Keyword Describes a strainbased failure model that is compatible with shell and solids elements.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/TENSSTRAIN/mat_ID/unit_ID  
${\epsilon}_{t1}$  ${\epsilon}_{t2}$  fct_ID  ${\epsilon}_{f1}$  ${\epsilon}_{f2}$  SFlag 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{el}  Fscale_{el}  El_{ref}  
fct_ID_{T}  Fscale_{T} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fail_ID 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

${\epsilon}_{t1}$  Equivalent strain when
damage begins, if SFlag=1 or 2. Maximum principal tensile strain when damage begins, if SFlag=3. Default = 1.E30 (Real) 

${\epsilon}_{t2}$  Equivalent strain when the
element is deleted, if SFlag=1 or 2. Maximum principal tensile strain when the element is deleted, if SFlag=3. Default = 2.E30 (Real) 

fct_ID  Strain rate scale function
identifier to scale
${\epsilon}_{t1}$
and
${\epsilon}_{t2}$
depending on the strain
rate. (Integer) 

${\epsilon}_{f1}$  First principal strain for
failure and element deletion. Only used with
SFlag =1. 3
(Real) 

${\epsilon}_{f2}$  Second principal strain
for failure and element deletion. Only used with
SFlag =1. 3
(Real) 

SFlag  Options failure flag.
(Integer) 

fct_ID_{el}  Element size scale factor
function identifier. 4
(Integer) 

Fscale_{el}  Element size function
scale factor. Default = 1.0 (Real) 

El_ref  Reference element size. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
fct_ID_{T}  Temperature scale factor function
identifier. (Integer) 

Fscale_{T}  Temperature function scale factor. Default = 1.0 (Real) 

fail_ID  Failure criteria identifier. 6
(Integer, maximum 10 digits) 
Example (Aluminum)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
Mg mm s
#12345678910
/MAT/PLAS_TAB/1/1
Aluminium
# RHO_I
2.788714E9 0
# E Nu Eps_p_max Eps_t Eps_m
68000 .3 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f
1 0 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 1 0 0 0
# func_ID1 func_ID2 func_ID3 func_ID4 func_ID5
2
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
0
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0
#12345678910
/FAIL/TENSSTRAIN/1
# EPS_t1 EPS_t2 funct_ID EPS_f1 EPS_f2 SFLAG
.05 .1 16 .02 .06 0
#12345678910
/FUNCT/16
scale factor for Eps_t1 and Eps_t2
# strain rate scale factor
# X Y
0 1
50 .5
10000 .5
#12345678910
/FUNCT/2
True StressTrue plastic strain
# X Y
0 124
.01 150
.02 165
.04 184
.06 196
.08 203
.1 206
.12 210
.14 213
.16 217
.18 220
.5 240
1000 240
#12345678910
#enddata
#12345678910
Example with Element Size Regularization
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
Mg mm s
#12345678910
/MAT/PLAS_TAB/1/1
Aluminium
# RHO_I
2.788714E9 0
# E Nu Eps_p_max Eps_t Eps_m
68000 .3 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f
1 0 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 1 0 0 0
# func_ID1 func_ID2 func_ID3 func_ID4 func_ID5
2
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
0
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0
#12345678910
/FAIL/TENSSTRAIN/1
# EPS_t1 EPS_t2 funct_ID EPS_f1 EPS_f2 SFLAG
.05 .1 16 .02 .06 2
#FCT_ID_EL FSCALE_EL EI_REF
21 1 1
# FCT_ID_T FSCALE_T
22 1
#12345678910
/FUNCT/21
Element length regularisation
# X Y
# relative ele. size scale factor
.5 1
1 1
2 0.8
/FUNCT/22
Temperature scale function
# X Y
0 1.0
350 1.0
1000 0.5
#12345678910
/FUNCT/16
scale factor for Eps_t1 and Eps_t2
# strain rate scale factor
# X Y
0 1
50 .5
10000 .5
#12345678910
/FUNCT/2
True StressTrue plastic strain
# X Y
0 124
.01 150
.02 165
.04 184
.06 196
.08 203
.1 206
.12 210
.14 213
.16 217
.18 220
.5 240
1000 240
#12345678910
#enddata
#12345678910
Comments
 The failure criteria is based
on the damage calculation:
(1) $$D=\frac{\epsilon {\epsilon}_{t1}}{{\epsilon}_{t2}{\epsilon}_{t1}}$$Where, $\epsilon $ is either the equivalent strain or maximum principal tensile strain depending on the SFlag option. The stress is then reduced using the calculated damage value using this equation:(2) $$\sigma =\left(1D\right)\sigma $$The damage, $D$ , can be plotted using /ANIM/Eltype/DAMA or /H3D/Eltype/DAMA. The progressive damage value is calculated based on the ratio of total strain and the final calculated total strain limit. The highest value is retained until the element reaches the failure limit. There is no accumulation and no load path dependency.
 Equivalent strain is
calculated using tensile strain equivalent of Rankine criterion:
(3) $${\epsilon}_{T}=\frac{1}{3}{I}_{1}+\frac{2}{\sqrt{3}}\sqrt{{J}_{2}^{d}}\mathrm{cos}\theta $$Where, ${I}_{1}$
 First invariant of strain tensor.
 ${J}_{2}^{d}$
 Second invariant of strain deviator.
For 2D (shells) this definition is reduced to:(4) $${\epsilon}_{T}=\frac{1}{\text{2}}\left({\epsilon}_{xx}+{\epsilon}_{yy}+\sqrt{{\left({\epsilon}_{xx}{\epsilon}_{yy}\right)}^{2}+{\epsilon}_{xy}{}^{2}}\right)$$  When SFlag=1, elements
can be deleted when
$D$
=1 for one integration point, the first pricinple
strain
${\epsilon}_{1}>{\epsilon}_{f1}$
, or the second principal strain
${\epsilon}_{2}>{\epsilon}_{f2}$
is reached. Failure based on the principal
tension strain for failure and element deletion,
${\epsilon}_{f1}$
or
${\epsilon}_{f2}$
, does not include damage and instead fails
immediately.
When SFlag= 2 or 3, elements can be deleted when $D$ =1 for one integration point and ${\epsilon}_{f1}$ or ${\epsilon}_{f2}$ are not used.
 When SFlag= 2 or 3, it
is possible to scale the defined total failure strain values, (
${\epsilon}_{f1}$
or
${\epsilon}_{f2}$
) based on element size or temperature using the
following factors:
(5) $$facto{r}_{el}=Fscal{e}_{el}\cdot {\mathrm{f}}_{el}\left(\frac{Siz{e}_{el}}{El\_ref}\right)$$Where, ${\mathrm{f}}_{el}$
 Element size correction factor function defined via fct_ID_{el}
 Size_{el}
 Characteristic element size
(6) $$facto{r}_{T}=Fscal{e}_{T}\cdot {\mathrm{f}}_{{}_{T}}\left({T}^{*}\right)$$Where, ${\mathrm{f}}_{{}_{T}}\left({T}^{*}\right)$ is the function, $fct\_I{D}_{T}$ and Temperature ${T}^{*}$ is computed via:(7) $${T}^{\ast}=\frac{T{T}_{ini}}{{T}_{melt}{T}_{ini}}$$It is recommended to use /HEAT/MAT to define the thermal parameters for material laws that support thermoplasticity.
 When SFlag =3, the strain calculation is based on 1st principal strain value. For material numbers < 28 with shell elements, damage is not applied and failure is immediate.
 The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL. 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 the .sta file with /STATE/BRICK/FAIL option).