/FAIL/PUCK

Block Format Keyword Describes the Puck failure model.

Format

(1)	(3)	(5)	(7)	(9)	(10)
/FAIL/PUCK/`mat_ID`/`unit_ID`
$σ_{1}^{t}$ $σ_{1}^{t}$	$σ_{2}^{t}$ $σ_{2}^{t}$	${\bar{σ}}_{12}$ ${\bar{σ}}_{12}$	$σ_{1}^{c}$ $σ_{1}^{c}$	$σ_{2}^{c}$ $σ_{2}^{c}$
$p_{12}^{+}$ $p_{12}^{+}$	$p_{12}^{-}$ $p_{12}^{-}$	$p_{22}^{-}$ $p_{22}^{-}$	$τ_{\max}$ $τ_{\max}$	`I`_{fail_sh}	`I`_{fail_so}
`F`_cut

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)
$σ_{1}^{t}$ $σ_{1}^{t}$	Longitudinal tensile strength. Default = 10³⁰ (Real)	$[Pa]$ $[Pa]$
$σ_{2}^{t}$ $σ_{2}^{t}$	Transverse tensile strength. Default = 10³⁰ (Real)	$[Pa]$ $[Pa]$
${\bar{σ}}_{12}$ ${\bar{σ}}_{12}$	Shear strength. Default = 10³⁰ (Real)	$[Pa]$ $[Pa]$
$σ_{1}^{c}$ $σ_{1}^{c}$	Longitudinal compressive strength. Default = 10³⁰ (Real)	$[Pa]$ $[Pa]$
$σ_{2}^{c}$ $σ_{2}^{c}$	Transverse compressive strength. Default = 10³⁰ (Real)	$[Pa]$ $[Pa]$
$p_{12}^{+}$ $p_{12}^{+}$	Failure envelope factor 12 (+). Default = 0 (Real)
$p_{12}^{-}$ $p_{12}^{-}$	Failure envelope factor 12 (-). Default = 0 (Real)
$p_{22}^{-}$ $p_{22}^{-}$	Failure envelope factor 22 (-). Default = 0 (Real)
$τ_{\max}$ $τ_{\max}$	Dynamic time relaxation. 5 Default = 10³⁰ (Real)	$[s]$ $[s]$
`I`_{fail_sh}	Shell failure model flag. = 1 (Default) Shell is deleted, if damage is reached for one layer. = 2 Shell is deleted, if damage is reached for all shell layers. (Integer)
`I`_{fail_so}	Solid failure model flag. = 1 (Default) Solid is deleted, if damage is reached for one integration point of solid. (Integer)
`F`_cut	Stress tensor filtering frequency. Default = 0.0 (Real)	$[\frac{1}{s}]$ $[\frac{1}{s}]$
`fail_ID`	Failure criteria identifier. 4 (Integer, maximum 10 digits)

Example (Composite)

Strength ( $σ_{1}^{t}$ $σ_{1}^{t}$ , $σ_{2}^{t}$ $σ_{2}^{t}$ , $σ_{1}^{c}$ $σ_{1}^{c}$ , $σ_{2}^{c}$ $σ_{2}^{c}$ , ${\bar{σ}}_{12}$ ${\bar{σ}}_{12}$ ) are taken from following tests. m1 is fiber direction.

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSH/1/1
composite example
#              RHO_I
               .0015
#                E11                 E22                NU12     Iform                           E33
              114000                9650                .025         0                             0
#                G12                 G23                 G31              EPS_f1              EPS_f2
                6000                6000                6000                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax
                   0                   0                   0                   0                   0
#              Wpmax               Wpref      Ioff                         ratio
                   0                   0         4                             0
#                  b                   n                fmax
                   0                   0                   0
#            sig_1yt             sig_2yt             sig_1yc             sig_2yc               alpha
                1E30                1E30                1E30                1E30                   0
#           sig_12yc            sig_12yt                c_12          Eps_rate_0       ICC
                1E30                1E30                   0                   0         0
#          GAMMA_ini           GAMMA_max               d3max
                   0                   0                   0
#  Fsmooth                Fcut
         0                   0
/FAIL/PUCK/1/1
#           Sigma1_T            Sigma2_T            Sigma_12            Sigma1_C            Sigma2_C
                1720                55.2                 103                 765                 503
#               P+12                P-12                P-22             Tau_max  Ifail_sh  Ifail_so
                   0                   0                   0                .005         1         0
#               Fcut
                 0.1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This failure model is available for Shell and Solid.
The failure mode criteria is written as:
- Fiber fraction failure:
  Tensile fiber failure mode: $σ_{11} > 0$ $σ_{11} > 0$ (1)
  $e_{f} = \frac{σ_{11}}{σ_{1}^{t}}$ $e_{f} = \frac{σ_{11}}{σ_{1}^{t}}$
  
  Compressive fiber failure mode: $σ_{11} < 0$ $σ_{11} < 0$ (2)
  $e_{f} = \frac{| σ_{11} |}{σ_{1}^{c}}$ $e_{f} = \frac{| σ_{11} |}{σ_{1}^{c}}$
- Inter fiber failure:
  Mode A if $σ_{22} > 0$ $σ_{22} > 0$ :
  
  Figure 1.
  (3)
  $e_{f} = \frac{1}{{\bar{σ}}_{12}} [\sqrt{{(\frac{{\bar{σ}}_{12}}{σ_{2}^{t}} - p_{12}^{+})}^{2} σ_{22}^{2} + σ_{12}^{2}} + p_{12}^{+} σ_{22}]$ $e_{f} = \frac{1}{{\bar{σ}}_{12}} [\sqrt{{(\frac{{\bar{σ}}_{12}}{σ_{2}^{t}} - p_{12}^{+})}^{2} σ_{22}^{2} + σ_{12}^{2}} + p_{12}^{+} σ_{22}]$
  
  Mode C if $σ_{22} < 0$ $σ_{22} < 0$ :
  
  Figure 2.
  (4)
  $e_{f} = [{(\frac{σ_{12}}{2 (1 + p_{22}^{-}) {\bar{σ}}_{12}})}^{2} + {(\frac{σ_{22}}{σ_{2}^{c}})}^{2}] (\frac{σ_{2}^{c}}{- σ_{22}})$ $e_{f} = [{(\frac{σ_{12}}{2 (1 + p_{22}^{-}) {\bar{σ}}_{12}})}^{2} + {(\frac{σ_{22}}{σ_{2}^{c}})}^{2}] (\frac{σ_{2}^{c}}{- σ_{22}})$
  
  Mode B
  
  Figure 3.
$e_{f} = \frac{1}{{\bar{σ}}_{12}} (\sqrt{σ_{12}^{2} + {(p_{12}^{-} σ_{_{22}})}^{2}} + p_{12}^{-} σ_{_{22}})$ $e_{f} = \frac{1}{{\bar{σ}}_{12}} (\sqrt{σ_{12}^{2} + {(p_{12}^{-} σ_{_{22}})}^{2}} + p_{12}^{-} σ_{_{22}})$

If the damage parameter is $e_{f} \geq 1.0$ $e_{f} \geq 1.0$ , the stresses are decreased by using an exponential function to avoid numerical instabilities. A relaxation technique is used by decreasing the stress gradually:(5)
$σ (t) = f (t) \cdot σ_{d} (t_{r})$ $σ (t) = f (t) \cdot σ_{d} (t_{r})$

With,(6)
$f (t) = \exp (- \frac{t - t_{r}}{τ_{\max}})$ $f (t) = \exp (- \frac{t - t_{r}}{τ_{\max}})$

and $t \geq t_{r}$ $t \geq t_{r}$

Where,

$t$ $t$

Time

$t_{r}$ $t_{r}$

Start time of relaxation when the damage criteria is assumed

$τ_{max}$ $τ_{max}$

Time of dynamic relaxation

$σ_{d} (t_{r})$ $σ_{d} (t_{r})$

Stress at the beginning of damage
The damage value, D is $0 \leq D \leq 1$ $0 \leq D \leq 1$ . The status for fracture is:
- Free, if $0 \leq D < 1$ $0 \leq D < 1$
- Failure, if $D = 1$ $D = 1$
With $D = Max (e_{f} (tensile), e_{f} (compression), e_{f} (ModeA), e_{f} (ModeB), e_{f} (ModeC))$ $D = Max (e_{f} (tensile), e_{f} (compression), e_{f} (ModeA), e_{f} (ModeB), e_{f} (ModeC))$ . This damage value shows with /ANIM/BRICK/DAMA or /ANIM/SHELL/DAMA.
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).
After the failure criterion is reached, the $τ_{\max}$ $τ_{\max}$ value determines a period of time when the stress in the failed element is gradually reduced to zero. When the stress reaches 1% of stress value at the start of failure, the element is deleted. This is necessary to avoid instabilities coming from a sudden element deletion and a failure “chain reaction” in the neighboring elements. Even if the failure criterion is reached, the default value of $τ_{\max} = 1.0 E 30$ $τ_{\max} = 1.0 E 30$ results in no element deletion. Therefore, it is recommended to define $τ_{\max}$ $τ_{\max}$ 10 times larger than the simulation time step.
To avoid a “chain reaction” when deleting elements, you can also define a stress tensor filtering frequency F_cut. Thus, the stress tensor used to calculate the PUCK criterion is first be filtered according to the formula below:(7)
$σ_{n + 1}^{f i l t} = α σ_{n + 1} + (1 - α) σ_{n}^{f i l t}$ $σ_{n + 1}^{f i l t} = α σ_{n + 1} + (1 - α) σ_{n}^{f i l t}$

With(8)
$α = \frac{2 π \cdot F_{c u t} \cdot Δ t}{2 π \cdot F_{c u t} \cdot Δ t + 1}$ $α = \frac{2 π \cdot F_{c u t} \cdot Δ t}{2 π \cdot F_{c u t} \cdot Δ t + 1}$

Where, $Δ t$ $Δ t$ is the current timestep.

If no filtering frequency is defined (F_cut = 0.0), the filtering effect is deactivated.