/FAIL/PUCK
Block Format Keyword Describes the Puck failure model.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/PUCK/mat_ID/unit_ID  
${\sigma}_{1}^{t}$  ${\sigma}_{2}^{t}$  ${\overline{\sigma}}_{12}$  ${\sigma}_{1}^{c}$  ${\sigma}_{2}^{c}$  
${p}_{12}^{+}$  ${p}_{12}^{}$  ${p}_{22}^{}$  ${\tau}_{\mathrm{max}}$  I_{fail_sh}  I_{fail_so} 
(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) 

${\sigma}_{1}^{t}$  Longitudinal tensile strength Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{t}$  Transverse tensile strength Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${\overline{\sigma}}_{12}$  Shear strength Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{1}^{c}$  Longitudinal compressive
strength Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{c}$  Transverse compressive
strength Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${p}_{12}^{+}$  Failure envelope factor 12 (+) Default = 0 (Real) 

${p}_{12}^{}$  Failure envelope factor 12 () Default = 0 (Real) 

${p}_{22}^{}$  Failure envelope factor 22 () Default = 0 (Real) 

${\tau}_{\mathrm{max}}$  Dynamic time relaxation 5 Default = 10^{30} (Real) 
$\left[\text{s}\right]$ 
I_{fail_sh}  Shell failure model flag
(Integer) 

I_{fail_so}  Solid failure model flag
(Integer) 

fail_ID  Failure criteria
identifier
4 (Integer, maximum 10 digits) 
Example (Composite)
Strength ( ${\sigma}_{1}^{t},{\sigma}_{2}^{t},{\sigma}_{1}^{c},{\sigma}_{2}^{c},{\overline{\sigma}}_{12}$ ) are taken from following tests. m1 is fiber direction.
#RADIOSS STARTER
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/UNIT/1
unit for mat and failure
# MUNIT LUNIT TUNIT
g mm ms
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# 1. MATERIALS:
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/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 P12 P22 Tau_max Ifail_sh Ifail_so
0 0 0 .005 1 0
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#enddata
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Comments
 This failure model is available for Shell and Solid.
 The failure mode criteria is written as:
 Fiber fraction failure:Tensile fiber failure mode: ${\sigma}_{11}>0$
(1) $${e}_{f}=\frac{{\sigma}_{11}}{{\sigma}_{1}^{t}}$$Compressive fiber failure mode: ${\sigma}_{11}<0$(2) $${e}_{f}=\frac{\left{\sigma}_{11}\right}{{\sigma}_{1}^{c}}$$
 Inter fiber failure:Mode A if ${\sigma}_{22}>0$ :
(3) $${e}_{f}=\frac{1}{{\overline{\sigma}}_{12}}\left[\sqrt{{\left(\frac{{\overline{\sigma}}_{12}}{{\sigma}_{2}^{t}}{p}_{12}^{+}\right)}^{2}{\sigma}_{22}{}^{2}+{\sigma}_{12}{}^{2}}+{p}_{12}^{+}{\sigma}_{22}\right]$$Mode C if ${\sigma}_{22}<0$ :(4) $${e}_{f}=\left[{\left(\frac{{\sigma}_{12}}{2(1+{p}_{22}^{}){\overline{\sigma}}_{12}}\right)}^{2}+{\left(\frac{{\sigma}_{22}}{{\sigma}_{2}^{c}}\right)}^{2}\right]\left(\frac{{\sigma}_{2}^{c}}{{\sigma}_{22}}\right)$$Mode B
${e}_{f}=\frac{1}{{\overline{\sigma}}_{12}}\left(\sqrt{{\sigma}_{12}^{2}+{\left({p}_{12}^{}{\sigma}_{{}_{22}}\right)}^{2}}+{p}_{12}^{}{\sigma}_{{}_{22}}\right)$
If the damage parameter is ${e}_{f}\ge 1.0$ , the stresses are decreased by using an exponential function to avoid numerical instabilities. A relaxation technique is used by decreasing the stress gradually:(5) $$\sigma (t)=\mathrm{f}(t)\cdot {\sigma}_{d}({t}_{r})$$With,(6) $$\mathrm{f}(t)=\mathrm{exp}\left(\frac{t{t}_{r}}{{\tau}_{\mathrm{max}}}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}$$and $\text{\hspace{0.17em}}\text{\hspace{0.05em}}t\ge {t}_{r}$
Where, $t$
 Time
 ${t}_{r}$
 Start time of relaxation when the damage criteria is assumed
 ${\tau}_{\text{max}}$
 Time of dynamic relaxation
 ${\sigma}_{d}\left({t}_{r}\right)$
 Stress at the beginning of damage
 Fiber fraction failure:
 The damage value, D is
$0\le D\le 1$
. The status for fracture is:
 Free, if $0\le D<1$
 Failure, if $D=1$
With $D=\mathit{Max}\left({e}_{f}(\mathit{tensile}),{e}_{f}(\mathit{compression}),{e}_{f}(\mathit{ModeA}),{e}_{f}(\mathit{ModeB}),{e}_{f}(\mathit{ModeC})\right)$ . 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 ${\tau}_{\mathrm{max}}$ 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 ${\tau}_{\mathrm{max}}=1.0E30$ results in no element deletion. Therefore, it is recommended to define ${\tau}_{\mathrm{max}}$ 10 times larger than the simulation time step.