/FAIL/JOHNSON
Block Format Keyword This failure model uses a nonlinear, plastic strainbased, failure criteria with linear damage accumulation. It describes the failure criteria by JohnsonCook failure model.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/JOHNSON/mat_ID/unit_ID  
D_{1}  D_{2}  D_{3}  D_{4}  D_{5}  
${\dot{\epsilon}}_{0}$  I_{fail_sh}  I_{fail_so}  D_{adv}  Ixfem 
(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) 

D_{1}  1st
parameter. (Real) 

D_{2}  2nd
parameter. (Real) 

D_{3}  3rd
parameter. (Real) 

D_{4}  4th
parameter. (Real) 

D_{5}  5th
parameter. (Real) 

${\dot{\epsilon}}_{0}$  Reference strain
rate. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
I_{fail_sh}  Shell failure
flag. (Integer) If Ixfem =0: failure  element deleted. If Ixfem =1: failure  element cracked. 2 = 1: (Default) Shell is deleted or cracked when $D=\sum \frac{\Delta {\epsilon}_{p}}{{\epsilon}_{f}}\ge 1$ for one integration point or layer. = 2: For each integration point, the stress tensor is set to zero when $D=\sum \frac{\Delta {\epsilon}_{p}}{{\epsilon}_{f}}\ge 1$ . The shell is deleted or cracked when $D=\sum \frac{\Delta {\epsilon}_{p}}{{\epsilon}_{f}}\ge 1$ for all integration points or layers. 

I_{fail_so}  Solid failure flag.
(Integer) 

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

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

fail_ID  Failure criteria identifier. 3 (Integer, maximum 10 digits) 
Examples
In these two simple examples, strain rate and temperature are not considered. The stressstrain relationship could be simplified:
Example 1 (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
# 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/JOHNSON/1/1
# D1 D2 D3 D4 D5
0.11 0.08 1.5 0 0
# EPS_0 Ifail_sh Ifail_so Dadv Ixfem
1 1 1 0 0
#12345678910
#enddata
#12345678910
Example 2 (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
# 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/JOHNSON/1/1
# D1 D2 D3 D4 D5
0.11 0.08 1.5 0 0
# EPS_0 Ifail_sh Ifail_so Dadv Ixfem
1 1 1 0.5 1
#12345678910
#enddata
#12345678910
Comments
 The parameters are used in stressstrain
relationship:$${\epsilon}_{f}=\left[{D}_{1}+{D}_{2}\text{exp}\left({D}_{3}{\sigma}^{*}\right)\right]\hspace{0.17em}\left[1+{D}_{4}\mathit{ln}\left({\dot{\epsilon}}^{*}\right)\right]\hspace{0.17em}\left[1+{D}_{5}{T}^{*}\right]$$
Where, ${\sigma}^{*}=\frac{{\sigma}_{m}}{{\sigma}_{VM}}$ ( ${\sigma}^{*}$ is the stress triaxiality).
$${\dot{\epsilon}}^{*}=\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}$$$T*$ is computed for all material laws, as:
$${T}^{*}=\frac{T{T}_{r}}{{T}_{melt}{T}_{r}}$$Where, T_{r}
 Initial temperature
 T_{melt}
 Melting temperature for materials LAW2 and LAW4
When /HEAT/MAT (with I_{form} =1) references this material model, the values of T_{r} and T_{melt} defined in this card will be overwritten by the corresponding T_{0} and T_{melt} defined in /HEAT/MAT.
 XFEM formulation
(Ixfem=1) is only compatible with BT Q4 (I_{shell}=1, 2, 3 or 4), and QEPH (I_{shell}=24) shell elements. If XFEM 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 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 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.
 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).
 Two different failure (rupture or
crack) are introduced in this failure model. The failure criteria is calculated,
as:
 Element rupture (Ixfem=0):
Element rupture (deleted) if D > 1
 Element crack (Ixfem=1):
Element cracked, if:
this element has no failed neighbors and D > 1, then in this case, new crack initialization in element.
this element has failed neighbors and D > D_{adv}, then in this case, crack advanced and D_{adv} is used for crack advancement. D_{adv} will be used if existing crack arrives to a boundary of an element.
Element deleted, if a second crack arrives to the same element.
Where,
$$D=\sum \frac{\text{\Delta}{\epsilon}_{p}}{{\epsilon}_{f}}\ge 1$$
D_{adv} should always be less than 1.
 Element rupture (Ixfem=0):