/FAIL/PUCK

Format

Definition

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
#---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

1. This failure model is available for Shell and Solid.
2. 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 ${\sigma }_{22}>0$ :

     
     
     Figure 1.

     (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 ${\sigma }_{22}<0$ :

     
     
     Figure 2.

     (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

     
     
     Figure 3.

   $e_f=\frac{1}{{\overline{\sigma }}_{12}}\left(\sqrt{{\sigma }_{12}^2+{\left(p_{12}^{-}{\sigma }_{{}_{22}}\right)}^2}+p_{12}^{-}{\sigma }_{{}_{22}}\right)$

   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)

   $$\mathrm{f}(t)=\exp \left(-\frac{t-t_r}{{\tau }_{\max }}\right)$$

   and $t\ge t_r$

   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

3. 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.

4. 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).
5. After the failure criterion is reached, the ${\tau }_{\max }$ 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 ${\tau }_{\max }=1.0E30$ results in no element deletion. Therefore, it is recommended to define ${\tau }_{\max }$ 10 times larger than the simulation time step.
6. 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)
   $${\sigma }_{n+1}^{filt}=\alpha {\sigma }_{n+1}+\left(1-\alpha \right){\sigma }_n^{filt}$$
   With(8)

   $$\alpha =\frac{2\pi \cdot F_{cut}\cdot \text{Δ}t}{2\pi \cdot F_{cut}\cdot \text{Δ}t+1}$$

   Where, $\text{Δ}t$ is the current timestep.

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