/FAIL/TAB1
Block Format Keyword This advanced failure model allows the plastic failure strain to be defined as a function of: stress triaxiality, strain rate, Lode angle, element size, temperature, and instability strain. Damage is accumulated based on userdefined functions.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/TAB1/mat_ID/unit_ID  
I_{fail_sh}  I_{fail_so}  P_thick_{fail}  P_thin_{fail}  Ixfem 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

D_{crit}  D_{p}  n  D_{adv}  fct_ID_{d} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

table1_ID  Yscale1  Xscale1  table2_ID  Yscale2  Xscale2 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{el}  Fscale_{el}  El_ref  inst_start  Fad_exp  Ch_i_f 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{T}  Fscale_{T}  Shrf  Biaxf 
(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) 

I_{fail_sh}  Shell failure flag. If Ixfem =0: failure  element deleted. 1 If Ixfem =1: failure  element cracked. 2 (Integer)


I_{fail_so}  Solid failure flag.
(Integer) 

Ixfem  XFEM flag (for
/SHELL and /SH_SANDW
properties only).
(Integer) 

P_thick_{fail}  Ratio of through thickness
integration points that must fail before the element is deleted.
(shells only). Only used when
I_{fail_sh}=2
or 3. 2
6
7
(Real) 

P_thin_{fail}  Ratio of thickness
reduction before failure (shells only and only active for
Ifail_sh >
1). (Real) 

D_{crit}  Critical accumulated
damage value (failure criteria). Default = 0.999 (Real) 

D_{p}  Damage accumulation
parameter. Default = 1.0 (Real) 

n  Damage accumulation
parameter. Default = 1.0 (Real) 

D_{adv}  Criterion for the crack
advancement (Only active if
Ixfem=1). (Real, between 0 and 1) Default = 0 means D_{adv} = D_{crit} 4 

fct_ID_{d}  Damage scale factor
function identifier as function of current damage. 5 Default = 0 (Integer) 

table1_ID  Failure strain table
identifier. 3 (Integer) 

Yscale1  Scale factor for the
ordinate of table1 (failure strain). Default = 1.0 (Real) 

Xscale1  Scale factor for the
abscissa table1 (strain rate). Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
table2_ID  Instability strain table
identifier. 9 (Integer) 

Yscale2  Scale factor for the
ordinate of table2 (instability strain). Default = 1.0 

Xscale2  Scale factor for the
abscissa of table2 (strain rate). Default = 1.0 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
fct_ID_{el}  Element size factor
function identifier. (Integer) 

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

El_ref  Reference element
size. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
inst_start  Instability strain (Only
used if table2_ID is not defined). Default = D_{p} (Real) 

Fad_exp  Fading exponent. 9


Ch_i_f  Choice of instability or
fracture regularization flag.


Shrf  Shear triaxiality limit
for applying element size regularization on instability
curve. Default = 1.0 (Real) 

Biafx  Bitraction triaxiality
limit for applying element size regularization on instability
curve. Default = 1.0 (Real) 

fct_ID_{T}  Temperature factor
function identifier. (Integer) 

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

fail_ID  (Optional) Failure
criteria identifier. 10 (Integer, maximum 10 digits) 
Example (Shell)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/PLAS_JOHNS/1/1
Steel
# RHO_I
7.9E6 0
# E Nu Iflag
210 .3 0
# a b n EPS_p_max SIG_max0
.05 .52 .1 0 0
# c EPS_DOT_0 ICC Fsmooth F_cut Chard
.022 .001 0 1 1 0
# m T_melt rhoC_p T_r
1.03 1796 3.91 300
/FAIL/TAB1/1/1
# failure for shell
# Ifail_sh Ifail_so P_THICKFAIL P_THINFAIL I_Xfem
2 1 1 0 0
#12345678910
##CARD2  Damage accumulation parameters
# DCRIT D N Dadv fct_IDd
1 .1 1 0 0
#12345678910
#CARD3  Failure strain functions for each defined strain rate (Nrate lines, at least one)
#Table1_ID Yscale1 Xscale1 Table2_ID Yscale2 Xscale2
4711 1 1 4712 1 1
#12345678910
#CARD4  Element size scale function
#FCT_ID_EL FSCALE_EL EI_REF INST_START FAD_EXP Ch_i_f
21 1 1 0 10 0
#12345678910
#CARD5  Temperature scale function and triaxiality limits for element size factors
# FCT_ID_T FSCALE_T Shrf Biaxf
22 1
#12345678910
#CARD6  Function identifier (optional card)
# Fail_Id
1
#12345678910
# 3. FUNCTIONS:
#12345678910
/TABLE/1/4711
failure plasticstrain vs triaxiality for material failure
#
1
# Triaxiality Failure_Strain
1. 0.50
1. 0.50
#12345678910
/TABLE/1/4712
failure plasticstrain vs triaxiality for diffuse necking
#
1
# Triaxiality Failure_Strain
1. 0.30
1. 0.30
#12345678910
/FUNCT/21
Element length regularisation
# X Y
# relative ele. size scale factor
.1 1
.25 1
#12345678910
/FUNCT/22
Temperature scale function
# X Y
0 1.0
1000 1.0
#12345678910
#enddata
/END
#12345678910
Example (Solid)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/PLAS_JOHNS/1/1
Steel
# RHO_I
7.9E6 0
# E Nu Iflag
210 .3 0
# a b n EPS_p_max SIG_max0
.05 .52 .1 0 0
# c EPS_DOT_0 ICC Fsmooth F_cut Chard
.022 .001 0 1 1 0
# m T_melt rhoC_p T_r
1.03 1796 3.91 300
/FAIL/TAB1/1/1
# Ifail_sh Ifail_so P_THICKFAIL P_THINFAIL I_Xfem
1 1 1 0 0
# DCRIT D N Dadv fct_IDd
1 1 1 0 0
#Table1_ID Yscale1 Xscale1 Table2_ID Yscale2 Xscale2
4711 1 1 0 0 0
#FCT_ID_EL FSCALE_EL EI_REF INST_START FAD_EXP Ch_i_f
21 1 1 0 0 0
# FCT_ID_T FSCALE_T Shrf Biaxf
22 1
# Fail_Id
1
#12345678910
# 3. FUNCTIONS:
#12345678910
/TABLE/1/4711
curve_list Failure Function vs. strain rates vs Lode angle
#DIMENSION
3
# FCT_ID strain_rate Lode_angle
3000 1E4 1 0
3001 1E4 0 0
3002 1E4 1 0
3003 1 1 0
3004 1 0 0
3005 1 1 0
#12345678910
/FUNCT/3000
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/3001
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/3002
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/3003
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/3004
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/3005
fail strain vs triaxiality
# triaxiality fail strain
# X Y
0 .5
1 .5
#12345678910
/FUNCT/21
Element length regularisation
# X Y
# relative ele. size scale factor
0 1
10 1
#12345678910
/FUNCT/22
Temperature scale function
# X Y
0 1
1000 1
#12345678910
#enddata
/END
#12345678910
Comments
 Using Ixfem=0, failure leads to element or layer deletion. In this case, if I_{fail_sh}=1, then P_thick_{fail} has to be set to zero for proper working failure criteria.
 Using
Ixfem=1 (XFEM formulation), failure leads to
element crack:
XFEM formulation is only compatible with Belytchko (I_{shell}=1 or 2), I_{shell}=3 or 4 and QEPH (I_{shell}=24) shell elements.
Two XFEM options are available: monolayer and multilayer. The XFEM option depends on the property type associated to the failure criterion applied to the material identifier: If /PROP/SHELL (TYPE1) is used, then monolayer XFEM
will be applied.
In this case, the whole element thickness is considered as a single layer. The failure criterion is calculated in each integration point but only one single crack can appear in this element. This approach is compatible with all shell flag options (I_{fail_sh}=1, 2 or 3), as well as P_Thick_{fail} values. The crack direction is determined by the principal constraints in the last failed integration point.
 If /PROP/SH_SANDW (TYPE11) is used, then multilayer
XFEM will be applied.
In this case, each integration point over thickness is considered as a distinct layer. The failure criterion is calculated separately, and the crack direction may be different for each layer. Crack direction in each layer will independently propagate from one element to another. Multilayer XFEM is not compatible with I_{fail_sh}=1 and P_thick_{fail}>0. Their values will be automatically set to I_{fail_sh}=2 and P_thick_{fail}=0.
Warning: Monolayer and multilayer XFEM formulations cannot be mixed in the same model, yet. The choice between them must be made for the whole model.  If /PROP/SHELL (TYPE1) is used, then monolayer XFEM
will be applied.
 The plastic failure strain is defined
as:
(1) $${\epsilon}_{f}=Yscale1\cdot Table1({\sigma}^{*},\frac{\dot{\epsilon}}{Xscale1},\xi )\cdot facto{r}_{el}\cdot facto{r}_{T}$$Where, $f({\sigma}^{*},\dot{\epsilon},\xi )$
 Described in table1_ID and is calculated by interpolating between the failure strain versus stress triaxiality functions for strain rate $\dot{\epsilon}$ and Lode angle $\xi $ .
 ${\sigma}^{*}\text{=}\frac{{\sigma}_{m}}{{\sigma}_{VM}}$
 Stress triaxiality
 ${\sigma}_{m}$
 Hydrostatic stress
 ${\sigma}_{VM}$
 von Mises stress
The first function from table1_ID is used for strain rate values from 0 to its corresponding strain rate. For strain rates above the last defined function, the failure strain value is extrapolated using the last two curves and their corresponding strain rates.
It is possible to consider element size in material failure by function fct_ID_{el} to scale the failure strain depending on the normalized element size with Ch_i_f=1 or 3.(2) $$facto{r}_{el}=Fscal{e}_{el}\cdot {\mathrm{f}}_{el}\left(\frac{Siz{e}_{el}}{El\_ref}\right)$$Where, ${\mathrm{f}}_{el}\left(\frac{Siz{e}_{el}}{El\_ref}\right)$ is the function of fct_ID_{el}.
Element size scale factor is only applied between triaxiality limits defined by Shrf and Biaxf.(3) $$Shrf<{\sigma}^{*}<Biaxf$$Outside this triaxiality range, the element size scaling is not applied to failure or instability curves.Note: If nonlocal regularization is used (with /NONLOCAL/MAT), the element size scaling factor is not used. If a scaling function is still defined (fct_ID_{el} > 0), the parameters are scaled using LE_MAX parameter of the nonlocal card (either specified directly by you or computed from the Rlen parameter value).Temperature dependency can be considered in material failure by defining a function to scale the failure strain depending on the normalized temperature:(4) $$facto{r}_{T}=Fscal{e}_{T}\cdot {\mathrm{f}}_{T}\left({T}^{*}\right)$$Here, ${\mathrm{f}}_{T}\left({T}^{*}\right)$ is defined using fct_ID_{T} and Temperature ${T}^{*}$ is computed as:(5) $${T}^{\ast}=\frac{T{T}_{ini}}{{T}_{melt}{T}_{ini}}$$It is recommended to use /HEAT/MAT to define the thermal parameter for material laws (which support thermoplasticity).
 Two different failures (rupture or crack) are
introduced in this failure model. The failure criteria is calculated
as:Element rupture (Ixfem=0):
 Element rupture (deleted), if
(6) $$\sum \text{\Delta}D>{D}_{\mathit{crit}}$$Where, ${D}_{crit}$ is the only rupture criterion used when Ixfem=0.
Element crack (Ixfem=1): Element cracked, if:
(7) $$\sum \text{\Delta}D>{D}_{\mathit{crit}}$$in case no failed neighbors for this element. ${D}_{crit}$ is used for new crack initialization.(8) $$\sum \text{\Delta}D>{D}_{\mathit{adv}}$$in case there is failed neighbors for this element, ${D}_{adv}$ is used for crack advancement.
Element is deleted, if a second crack arrives to the same element.
Note: ${D}_{adv}$ should always be less than ${D}_{crit}$ ( ${D}_{adv}$ < ${D}_{crit}$ ). If not, then ${D}_{adv}$ is set to ${D}_{crit}$ _{crit} ( ${D}_{adv}$ = ${D}_{crit}$ ).  Element rupture (deleted), if
 Damage accumulation is computed in Radioss one of two different ways:
 With parameter input, if
fct_ID_{d} =
0:
(9) $$\text{\Delta}D=\frac{\text{\Delta}{\epsilon}_{p}}{{\epsilon}_{f}}\cdot n\cdot {D}_{p}{}^{\left(1\frac{1}{n}\right)}$$Where, $\text{\Delta}{\epsilon}_{p}$
 Change in plastic strain of the integration point.
 ${\epsilon}_{f}$
 Plastic failure strain.
 D_{p} and n
 Damage parameters.
 With curve input, if
fct_ID_{d} ≠
0:
(10) $$\text{\Delta}D=\frac{\text{\Delta}{\epsilon}_{p}}{{\epsilon}_{f}}\cdot {\mathrm{f}}_{d}$$Where, ${\mathrm{f}}_{d}$ is the damage scale factor as a function of current damage defined in fct_ID_{d}.
 With parameter input, if
fct_ID_{d} =
0:
 P_thick_{fail} is only compatible with shell elements (except, shells with /PROP/TYPE11 (SH_SANDW)) and is only used when I_{fail_sh}=2 or I_{fail_sh}=3. If Ixfem=1, P_thick_{fail} is only compatible with monolayer XFEM formulation. 1
 When
P_thick_{fail} is used,
the shell complete rupture occurs when the thickness of broken layers is greater
than the ratio of shell total thickness. Any P_thickfail
value defined in the shell properties is ignored and the value entered in this
failure model is used instead.
Only adjacent layers that fail consecutively are accounted for the thickness sum (usually from one of external skin to the midsurface).
 The first variable of
table1_ID is the plastic failure strain versus stress
triaxiality function, the second variable is strain rate and the third is the
Lode angle parameter
$\xi $
(for solids).
For shell, only 2D tables are available (no dependency of Lode angle).
 Instability (diffuse necking):
 Only available for shells
 The fading exponent describes the softening behvior and starts of
instability (diffuse necking). The recommended value of
Fad_exp is 5 to 10.
If Fad_exp < 0 and Ch_i_f=2 or 3, then the absolute value of the fading exponent is a function identifier fct_ID_{el} which defines the fading exponent as a function of element length.
 The start of instability can be described as a function or constant
value:
 table2_ID is a function of instability strain
versus triaxiality where the instability strain defines when
diffuse necking starts. Strain rate dependency for diffuse
necking could be considered as well using
dimension=2 in
/TABLE.
(11) $${\epsilon}_{f}=Yscale2\cdot Table2({\sigma}^{*},\frac{\dot{\epsilon}}{Xscale2})\cdot facto{r}_{el}\cdot facto{r}_{T}$$  If table2_ID is not defined, inst_start is used as constant flat line for instability starting value over the triaxiality, where the default value is D_{p}.
 table2_ID is a function of instability strain
versus triaxiality where the instability strain defines when
diffuse necking starts. Strain rate dependency for diffuse
necking could be considered as well using
dimension=2 in
/TABLE.
 The diffuse necking softening is based according to this
equation:
(12) $${\sigma}_{reduced}=\sigma \cdot \left(1{\left(\frac{{D}_{instability}inst\_start}{1inst\_start}\right)}^{Fad\_\mathrm{exp}}\right)$$Where, ${D}_{instability}={\displaystyle \sum \frac{\text{\Delta}{\epsilon}_{p}}{{\epsilon}_{f}}}$ with ${\epsilon}_{f}$ being the diffuse necking strain.
Currently, diffuse necking (material instability) in /FAIL/TAB1 could be used with material laws greater than 28.
 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).