/FAIL/TBUTCHER

Block Format Keyword Describes a Tuler-Butcher failure model.

Format


(1)	(3)	(5)	(7)	(8)	(9)	(10)
/FAIL/TBUTCHER/`mat_ID`/`unit_ID`
$λ$	`K`	$σ_{r}$	`I`_{fail_sh}	`I`_{fail_so}	`I`_duct	`Ixfem`
`a`	`b`		`D`_adv

Optional Line


(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)
$λ$	Exponent. (Positive real)
`K`	Critical damage integral. (Real)	$[P a^{λ} \cdot s]$
$σ_{r}$	Fracture stress. (Real)	$[Pa]$
`I`_{fail_sh}	Shell failure flag. = 1 Shell is deleted or cracked, if `D` ≥ `K` for one integration point or layer. = 2 For each integration point, the stress tensor is set to zero, if `D` ≥ `K`, and shell is deleted or cracked, if `D` ≥ `K` for all integration points or layers. If `Ixfem` =0: failure - element deleted If `Ixfem` =1: failure - element cracked. 2 (Integer)
`I`_{fail_so}	Solid failure flag. = 1 Solid is deleted, if `D` ≥ `K` for one integration point. = 2 For each integration point, the deviatoric stress tensor vanishes, if `D` ≥ `K`. (Integer)
`I`_duct	Ductile-brittle materials flag (Only active if `Ixfem`=1 (shell only)). = 1 (Default) If a ductile material is used. = 2 If a brittle material is used (shell only). (Integer)
`Ixfem`	XFEM flag (for /PROP/SHELL, /PROP/SH_SANDW, and /PROP/TYPE51 properties only). = 0 (Default) Without XFEM. = 1 XFEM formulation. 2 (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)

In this example, use /FAIL/TBUTCHER to simulate ductile failure. Depending on exponent, damage integral could be impulse criteria (

λ = 1.0

), energy (or work) criteria (

λ = 2.0

), or constant stress criteria. This

λ

could get by fitting the experiment data. In this example, use exponent

λ = 2.0

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/PLAS_JOHNS/1/1
Steel + ductile failure model
#              RHO_I
              7.8E-9                   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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

An element fails once the Tuler-Butcher 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:
$D = \int_{0}^{t} \max (0, {(σ - σ_{r})}^{λ}) d t > K$
Where,

$σ_{r}$

Initial fracture stress

$σ$

Maximum principal stress

$λ$

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:
$\dot{D} = \frac{1}{K} {(σ - σ_{r})}^{a}$
$σ_{r} = σ_{0} {(1 - D)}^{b}$
$D = D + \dot{D} Δ t$
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: mono-layer and multi-layer. The XFEM option depends on the property type associated to the failure criteria applied to the material identifier:
1. If /PROP/SHELL (TYPE1) is used, then mono-layer 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.
2. If /PROP/SH_SANDW (TYPE11) is used, then multi-layer 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. Multi-layer XFEM is not compatible with I_{fail_sh}=1. Its value will be automatically set to I_{fail_sh}=2 in this case.
3. If /PROP/TYPE51 is used, then multi-layer 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. Multi-layer XFEM is not compatible with I_{fail_sh}=1. Its value will be automatically set to I_{fail_sh}=2.
Warning: Mono-layer and multi-layer 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 .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.