/FAIL/TBUTCHER

Format

Definitions

Example (Steel)

#RADIOSS STARTER
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/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

1. 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:(1)

   $$D={\displaystyle {\int }_0^t\max \left(0,{\left(\sigma -{\sigma }_r\right)}^{\lambda }\right)dt}>K$$
   Where,

   ${\sigma }_r$

   Initial fracture stress

   $\sigma$

   Maximum principal stress

   $\lambda$

   Mmaterial 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:

   $\dot{D}=\frac{1}{K}{\left(\sigma -{\sigma }_r\right)}^a$

   ${\sigma }_r={\sigma }_0{\left(1-D\right)}^b$

   $D=D+\dot{D}\text{Δ}t$

2. 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.
3. 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).
4. 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.