/FAIL/HASHIN
Block Format Keyword Describes the Hashin failure model. This failure model is available for Shell and Solid.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/HASHIN/mat_ID/unit_ID  
I_{form}  I_{fail_sh}  I_{fail_so}  ratio  I_Dam  Imod  I_frwave  ${\dot{\epsilon}}_{min}$  
${\sigma}_{1}^{t}$  ${\sigma}_{2}^{t}$  ${\sigma}_{3}^{t}$  ${\sigma}_{1}^{c}$  ${\sigma}_{2}^{c}$  
${\sigma}_{c}$  ${\sigma}_{12}^{f}$  ${\sigma}_{12}^{m}$  ${\sigma}_{23}^{m}$  ${\sigma}_{13}^{m}$  
$\varphi $  S_{del}  ${\tau}_{\text{max}}$  ${\dot{\epsilon}}_{0}$  T_{cut} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Soft 
(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) 

I_{form}  Formulation flag.
(Integer) 

I_{fail_sh}  Shell failure flag.
(Integer) 

I_{fail_so}  Solid failure flag.
(Integer) 

ratio  For
I_{solid}=2 or
I_{fail_sh}=2: the
element will be deleted, if more than ratio of the layers (or integration points)
have failed. Default = 1.0 (Real) 

I_Dam  Damage calculation flag. 6
(Integer) 

Imod  Relaxation time calculation.
(Integer) 

I_frwave  Failure propagation flag between neighbor elements.
(Integer) 

${\dot{\epsilon}}_{min}$  Low strain rate limit. Default = 0.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\sigma}_{1}^{t}$  Longitudinal tensile strength (in fiber direction). Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{t}$  Transverse tensile strength (perpendicular to the fiber direction). Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{3}^{t}$  Through thickness tensile strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{1}^{c}$  Longitudinal compressive strength (in fiber direction). Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{c}$  Transverse compressive strength (perpendicular to the fiber direction). Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{c}$  Crush strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{12}^{f}$  Fiber shear strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{12}^{m}$  Matrix shear strength 12. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{23}^{m}$  Matrix shear strength 23. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{13}^{m}$  Matrix shear strength 13. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
$\varphi $  Coulomb friction Angle for matrix and
delamination < 90 degrees. Default = 0 (Real) 
$\left[\mathrm{deg}\right]$ 
S_{del}  Delamination criteria scale factor. Default = 1.0 (Real) 

${\tau}_{\text{max}}$  Dynamic time relaxation. 5 Default = 10^{20} (Real) 
$\left[\text{s}\right]$ 
${\dot{\epsilon}}_{0}$  Reference strain rate. Default = 10^{20} (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
T_{cut}  Strain rate cutoff period. Default = ${\tau}_{\text{max}}$ (Real) 
$\left[\text{s}\right]$ 
Soft  Reduction factor applied to failure criteria when
one of neighbor elements has already
failed. Only used if, I_frwave=2. 0.0. ≤ Soft ≤ 1.0 Default = 0.0 (Real) 

fail_ID  (Optional) Failure criteria identifer. 4 (Integer, maximum 10 digits) 
Example (Composite)
#RADIOSS STARTER
/UNIT/1
unit for mat and failure
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
/MAT/COMPSH/1/1
composite material
# RHO_I
1.5E6
# E11 E22 NU12 Iform E33
42 40 .05 1 .5
# G12 G23 G31 EPS_f1 EPS_f2
3.4 3 3 0 0
# EPS_t1 EPS_m1 EPS_t2 EPS_m2 dmax
0 0 0 0 .9999
# Wpmax Wpref Ioff IFLAWP ratio
0 0 5 0 0
# c EPS_rate_0 alpha ICC_global
0 2E4 0 1
# sig_1yt b_1t n_1t sig_1maxt c_1t
.1 25 .1 0 0
# EPS_1t1 EPS_2t1 SIGMA_rst1 Wpmax_t1
0 0 0 0
# sig_2yt b_2t n_2t sig_2maxt c_2t
.1 20 .1 0 0
# EPS_1t2 EPS_2t2 sig_rst2 Wpmax_t2
0 0 0 0
# sig_1yc b_1c n_1c sig_1maxc c_1c
.005 800 .5 0 0
# EPS_1c1 EPS_2c1 sig_rsc1 Wpmax_c1
.08 .15 .1 0
# sig_2yc b_2c n_2c sig_2maxc c_2c
.005 2000 .5 0 0
# EPS_1c2 EPS_2c2 sig_rsc2 Wpmax_c2
0 0 0 0
# sig_12yt b_12t n_12t sig_12maxt c_12t
.004 83 .31 0 0
# EPS_1t12 EPS_2t12 sig_rst12 Wpmax_t12
.075 .085 .05 0
# GAMMA_ini GAMMA_max d3max
1E31 1E31 .9999
# Fsmooth Fcut
0 0
#12345678910
/FAIL/HASHIN/1/1
# Iform Ifail_sh Ifail_so Ratio I_Dam Imod Ifrwave EPS_DOT_MIN
2 1 0 0 1
# Sigma1_T Sigma2_T Sigma3_T Sigma1_C Sigma2_C
2 .525 1E30 1.7 1.7
# Sigma_C SigmaF_12 SigmaM_12 SigmaM_23 SigmaM_13
1E30 1E30 .075 1E30 1E30
# Phi Sdelam Tau_max EPS_DOT_0 Tcut
0 1 .01
#12345678910
#enddata
#12345678910
Comments
 Example of ratio: if ratio=0.5, and I_{fail_sh}=2 (or I_{fail_so}=2), the element will be deleted, if more than half of the layers (or integration points) failed.
 The 3D material failure model:
 Unidirectional lamina model:
Tensile/shear fiber mode:
$${F}_{1}={\left(\frac{\langle {\sigma}_{11}\rangle}{{\sigma}_{1}^{t}}\right)}^{2}+\left(\frac{{\sigma}_{12}^{2}+{\sigma}_{13}^{2}}{{\sigma}_{12}^{f}{}^{2}}\right)$$Compression fiber mode:
$${F}_{2}={\left(\frac{\langle {\sigma}_{a}\rangle}{{\sigma}_{1}^{c}}\right)}^{2}\text{\hspace{0.17em}}$$with, $\text{\hspace{0.17em}}{\sigma}_{a}={\sigma}_{11}+\text{}\langle \frac{{\sigma}_{22}+{\sigma}_{33}}{2}\rangle $
Crush mode:
$${F}_{3}={\left(\frac{\langle p\rangle}{{\sigma}_{c}}\right)}^{2}$$with, $\text{\hspace{0.17em}}p=\frac{{\sigma}_{11}+{\sigma}_{22}+{\sigma}_{33}}{3}$
Failure matrix mode:
$${F}_{4}={\left(\frac{\langle {\sigma}_{22}\rangle}{{\sigma}_{2}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{23}}{{S}_{23}}\right)}^{2}+{\left(\frac{{\sigma}_{12}}{{S}_{12}}\right)}^{2}$$Delamination mode:
$${F}_{5}={S}_{del}^{2}\left[{\left(\frac{\langle {\sigma}_{33}\rangle}{{\sigma}_{2}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{23}}{{\tilde{S}}_{23}}\right)}^{2}+{\left(\frac{{\sigma}_{13}}{{S}_{13}}\right)}^{2}\right]$$Where,
$\begin{array}{c}{S}_{12}={\sigma}_{12}^{m}+\langle {\sigma}_{22}\rangle \mathrm{tan}\varphi \\ {S}_{23}={\sigma}_{23}^{m}+\langle {\sigma}_{22}\rangle \mathrm{tan}\varphi \\ {S}_{13}={\sigma}_{13}^{m}+\langle {\sigma}_{33}\rangle \mathrm{tan}\varphi \\ {\tilde{S}}_{23}={\sigma}_{23}^{m}+\langle {\sigma}_{33}\rangle \mathrm{tan}\varphi \end{array}$
Note:$$\langle a\rangle =\{\begin{array}{c}a\text{\hspace{0.17em}}\text{\hspace{0.17em}}if\text{\hspace{0.17em}}a>0\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}if\text{\hspace{0.17em}}a<0\end{array}$$  Fabric lamina model:
Tensile/shear fiber mode:
$${F}_{1}={\left(\frac{\langle {\sigma}_{11}\rangle}{{\sigma}_{1}^{t}}\right)}^{2}+\left(\frac{{\sigma}_{12}^{2}+{\sigma}_{13}^{2}}{{\sigma}_{a}^{f}{}^{2}}\right)$$$${F}_{2}={\left(\frac{\langle {\sigma}_{22}\rangle}{{\sigma}_{2}^{t}}\right)}^{2}+\left(\frac{{\sigma}_{12}^{2}+{\sigma}_{23}^{2}}{{\sigma}_{b}^{f}{}^{2}}\right)$$With ${\sigma}_{a}^{f}={\sigma}_{12}^{f}\text{}\text{\hspace{0.17em}},\text{\hspace{0.05em}}\text{\hspace{1em}}\text{}{\sigma}_{b}^{f}={\sigma}_{12}^{f}\frac{{\sigma}_{2}^{t}}{{\sigma}_{1}^{t}}$
Compression fiber mode:
$${F}_{3}={\left(\frac{\langle {\sigma}_{a}\rangle}{{\sigma}_{1}^{c}}\right)}^{2}$$with, ${\sigma}_{a}={\sigma}_{11}+\text{}\langle {\sigma}_{33}\rangle $
$${F}_{4}={\left(\frac{\langle {\sigma}_{b}\rangle}{{\sigma}_{2}^{c}}\right)}^{2}$$with, ${\sigma}_{b}={\sigma}_{22}+\text{}\langle {\sigma}_{33}\rangle $
Crush mode:
$${F}_{5}={\left(\frac{\langle p\rangle}{{\sigma}_{c}}\right)}^{2}$$with, $p=\frac{{\sigma}_{11}+{\sigma}_{22}+{\sigma}_{33}}{3}$
Shear failure matrix mode:
$${F}_{6}={\left(\frac{{\sigma}_{12}}{{\sigma}_{12}^{m}}\right)}^{2}$$Matrix failure mode:
$${F}_{7}={S}_{del}^{2}\left[{\left(\frac{\langle {\sigma}_{33}\rangle}{{\sigma}_{3}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{23}}{{S}_{23}}\right)}^{2}+{\left(\frac{{\sigma}_{13}}{{S}_{13}}\right)}^{2}\right]$$Where,
$\begin{array}{c}{S}_{13}={\sigma}_{13}^{m}+\langle {\sigma}_{33}\rangle \mathrm{tan}\varphi \\ {S}_{23}={\sigma}_{23}^{m}+\langle {\sigma}_{33}\rangle \mathrm{tan}\varphi \end{array}$
If the damage parameter is F_{i} ≥ 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:
$$\sigma (t)=\mathrm{f}(t)\cdot {\sigma}_{d}({t}_{r})$$With,
$$\mathrm{f}(t)=\mathrm{exp}\left(\frac{t{t}_{r}}{{\tau}_{\mathrm{max}}}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}$$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
 Unidirectional lamina model:
 The damage value, D is 0 ≤ D ≤ 1. The
status for fracture is:
 Free, if 0 ≤ D < 1
 Failure, if D = 1
with $D=Max\left({F}_{1},{F}_{2},{F}_{3},{F}_{4},{F}_{5}\right)$ for unidirectional lamina model and $D=Max\left({F}_{1},{F}_{2},{F}_{3},{F}_{4},{F}_{5},{F}_{6},{F}_{7}\right)$ for fabric lamina model. 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 the 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.
 The I_Dam option
improves damage calculation and stability calculating damage.Important: The failure model /FAIL/CHANG with Beta=1 should be used to recover the original formula from the reference paper. ^{2}