/FAIL/WIERZBICKI

Format

(1)	(3)	(4)	(5)	(7)	(9)
/FAIL/WIERZBICKI/`mat_ID`/`unit_ID`
`C`₁	`C`₂		`C`₃	`C`₄	`m`
`n`	`I`_{fail_sh}	`I`_{fail_so}	`I`_moy

Optional Line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fail_ID`

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`C`₁	1st parameter. (Real)
`C`₂	2nd parameter. (Real)
`C`₃	3rd parameter. (Real)
`C`₄	4th parameter. (Real)
`m`	5th parameter. (Real)
`n`	Hardening exponent. (Real)
`I`_{fail_sh}	Shell failure model flag. = 1 Shell is deleted, if $D = \sum \frac{Δ ε_{p}}{{\bar{ε}}_{f}} \geq 1$ for one integration point or layer. = 2 For each integration point, the stress tensor is set to zero, if $D = \sum \frac{Δ ε_{p}}{{\bar{ε}}_{f}} \geq 1$ and shell is deleted, if $D = \sum \frac{Δ ε_{p}}{{\bar{ε}}_{f}} \geq 1$ for all integration points or layer. (Integer)
`I`_{fail_so}	Brick failure model flag. = 1 Solid element is deleted, if $D = \sum \frac{Δ ε_{p}}{{\bar{ε}}_{f}} \geq 1$ for one integration point. = 2 For each integration point, the deviatoric stress tensor vanishes, if $D = \sum \frac{Δ ε_{p}}{{\bar{ε}}_{f}} \geq 1$ . (Integer)
`I`_moy	Failure 3D model (brick) flag. =0 ${\begin{matrix} \bar{η} = \frac{σ_{m}}{σ_{V M}} \\ \bar{ξ} = \frac{27 J_{3}}{2 σ_{V M}^{3}} \end{matrix}$ =1 ${\begin{matrix} \bar{η} = \frac{\int_{0}^{ε_{p}} \frac{σ_{m}}{σ_{V M}} d ε_{p}}{ε_{p}} \\ \bar{ξ} = \frac{\int_{0}^{ε_{p}} \frac{27 J_{3}}{2 σ_{V M}^{3}} d ε_{p}}{ε_{p}} \end{matrix}$ (Integer)
`fail_ID`	Failure criteria identifier. 2 (Integer, maximum 10 digits)

Example (Metal)

#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
Metal
#              RHO_I
              2.8E-9                   0
#                  E                  Nu
               60000                  .3
#                  a                   b                   n           EPS_p_max            SIG_max0
                 370                 190                  .4                   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/WIERZBICKI/1/1
#                 C1                  C2                  C3                  C4                   m
                0.87                1.77                0.21                0.56                   2
#                  n  Ifail_sh  Ifail_so      Imoy
                 0.2         0         1         0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

For ${\bar{ε}}_{f}$ which is used in failure flag is:
(1)
${\bar{ε}}_{f} = {{\bar{ε}}_{\max}^{n} - [{\bar{ε}}_{\max}^{n} - {\bar{ε}}_{\min}^{n}] {(1 - {\bar{ξ}}^{m})}^{\frac{1}{m}}}^{\frac{1}{n}}$

Figure 1.

Where,

${\bar{ε}}_{\max} = C_{1} e^{- C_{2} \bar{η}}$

${\bar{ε}}_{\min} = C_{3} e^{- C_{4} \bar{η}}$
For Brick:
- If I_moy = 0
- $\bar{η} = \frac{σ_{m}}{σ_{V M}}$ $\bar{ξ} = \frac{27 J_{3}}{2 σ_{V M}^{3}}$
- If I_moy = 1
- $\bar{η} = \frac{\int_{0}^{ε_{p}} \frac{σ_{m}}{σ_{V M}} d ε_{p}}{ε_{p}}$ ; $\bar{ξ} = \frac{\int_{0}^{ε_{p}} \frac{27 J_{3}}{2 σ_{V M}^{3}} d ε_{p}}{ε_{p}}$
For Shell:
- $\bar{η} = \frac{σ_{m}}{σ_{V M}}$ ; $\bar{ξ} = - \frac{27}{2} \bar{η} ({\bar{η}}^{2} - \frac{1}{3})$
Where,

$σ_{m}$

Hydrostatic stress

$σ_{V M}$

von Mises stress

$J_{3}$

Third invariant deviatoric stress
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).