/FAIL/TBUTCHER
Block Format Keyword Describes a TulerButcher failure model.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/TBUTCHER/mat_ID/unit_ID  
$\lambda $  K  ${\sigma}_{r}$  I_{fail_sh}  I_{fail_so}  I_{duct}  Ixfem  
a  b  D_{adv} 
(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) 

$\lambda $  Exponent. (Positive real) 

K  Critical damage
integral. (Real) 
$\left[P{a}^{\lambda}\cdot s\right]$ 
${\sigma}_{r}$  Fracture
stress. (Real) 
$\left[\text{Pa}\right]$ 
I_{fail_sh}  Shell failure flag.
If Ixfem =0: failure  element deleted If Ixfem =1: failure  element cracked. 2 (Integer) 

I_{fail_so}  Solid failure flag.
(Integer) 

I_{duct}  Ductilebrittle materials
flag (Only active if Ixfem=1
(shell only)).
(Integer) 

Ixfem  XFEM flag
(for /PROP/SHELL, /PROP/SH_SANDW, and
/PROP/TYPE51 properties only).
(Integer) 

a  Brittle rupture material
parameter (exponent). (Real) 

b  Brittle rupture material
parameter (exponent). (Real) 

D_{adv}  Criterion for the crack
advancement (Only active if Ixfem=1). 4 (Real, between 0 and 1) Default = 0.85 (for backward compatibility) 

fail_ID  Failure criteria identifier. 3 (Integer, maximum 10 digits) 
Example (Steel)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
Mg mm s
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/PLAS_JOHNS/1/1
Steel + ductile failure model
# RHO_I
7.8E9 0
# E Nu
210000 .3
# a b n EPS_p_max SIG_max0
270 450 .6 0 0
# c EPS_DOT_0 ICC Fsmooth F_cut Chard
0 0 0 0 0 0
# m T_melt rhoC_p T_r
0 0 0 0
/FAIL/TBUTCHER/1/1
# LAMDA K SIGMA_R Ifail_sh Ifail_so I_DUCT Ixfem
2 0.3e+8 150 0 1 0 0
# A B Dadv
0 0 0
#12345678910
#enddata
#12345678910
Comments
 An element
fails once the TulerButcher cumulative damage parameter is greater than specified
critical damage value K. The damage parameter accumulation is
calculated differently for ductile and brittle materials
(I_{duct} = 1
or 2). For solids, only the ductile rupture is available,
I_{duct} flag has no effect.
For ductile materials, the cumulative damage parameter is:
$$D={\displaystyle {\int}_{0}^{t}\mathrm{max}\left(0,{\left(\sigma {\sigma}_{r}\right)}^{\lambda}\right)dt}>K$$Where, ${\sigma}_{r}$
 Initial fracture stress
 $\sigma $
 Maximum principal stress
 $\lambda $
 Material constant (positive real value)
 $t$
 Time when the element cracks
 $D$
 Damage integral
 $k$
 Critical value of the damage integral
For brittle materials (shells only), the damage parameter is:
$\dot{D}=\frac{1}{K}{\left(\sigma {\sigma}_{r}\right)}^{a}$
${\sigma}_{r}={\sigma}_{0}{\left(1D\right)}^{b}$
$D=D+\dot{D}\text{\Delta}t$
 XFEM formulation
(Ixfem=1) is only compatible with Belytchko
(I_{shell}=1 or 2), I_{shell}=3 or 4 and QEPH (I_{shell}=24) shell elements. If XFEM flag is
activated (Ixfem=1), the failure criteria will
lead to element cracking instead of element or layer deletion.Two XFEM options are available: monolayer and multilayer. The XFEM option depends on the property type associated to the failure criteria 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 appear in this element. This approach is compatible with all values of the shell flag (I_{fail_sh}=1 or 2). 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 in 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. Its value will be automatically set to I_{fail_sh}=2 in this case.
 If /PROP/TYPE51 is used, then multilayer XFEM will be applied and the separate cracks may appear in each layer and propagate independently from one element to another. Thus, crack directions and patterns will be different in each layer. The failure criterion is calculated separately in each integration point and crack will propagate when all the integration points fail within a layer. Multilayer XFEM is not compatible with I_{fail_sh}=1. Its value will be automatically set to I_{fail_sh}=2.
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 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 .sta file with /STATE/BRICK/FAIL option).
 The failure criteria is
calculated as:
The cumulative damage parameter, D is only rupture criterion used when Ixfem=0.
When Ixfem=1, both D and D_{adv} can be used, respectively for crack initialization and advancement. If an element has no failed neighbors, D is used to initialize a new crack, if satisfied. Otherwise, if an existing crack occurs to a boundary of an element, the crack advancement criterion, D_{adv} will be used, instead of D. Eventually, if a second crack arrives at the same element, it will be deleted.