/FAIL/CHANG
Block Format Keyword Describes the Chang failure model.
Format
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/FAIL/CHANG/mat_ID/unit_ID  
${\sigma}_{1}^{t}$  ${\sigma}_{2}^{t}$  ${\overline{\sigma}}_{12}$  ${\sigma}_{1}^{c}$  ${\sigma}_{2}^{c}$  
$\beta $  ${\tau}_{\mathrm{max}}$  I_{fail_sh}  FAILIP 
(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) 

${\sigma}_{1}^{t}$  Longitudinal tensile
strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{t}$  Transverse tensile
strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\overline{\sigma}}_{12}$  Shear strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{1}^{c}$  Longitudinal compressive
strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2}^{c}$  Transverse compressive
strength. Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
$\beta $  Shear scaling
factor. Default = 0 (Real) 

${\tau}_{\mathrm{max}}$  Dynamic time relaxation.
7 Default = 10^{20} (Real) 
$\left[\text{s}\right]$ 
I_{fail_sh}  Shell failure model flag.
(Integer) 

FAILIP  Number of failed
integration points prior to solid deletion. Default = 1 (Integer) 

fail_ID  Failure criteria identifier. 6 (Integer, maximum 10 digits) 
Comments
 This failure model is available for shell only.
 Where direction one is the fiber
direction. The failure criteria for fiber breakage is written as:Tensile fiber mode: ${\sigma}_{11}>0$
 For shells:$${e}_{f}{}^{2}={\left(\frac{{\sigma}_{11}}{{\sigma}_{1}^{t}}\right)}^{2}+\beta {\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
 For solids:$${e}_{f}{}^{2}={\left(\frac{{\sigma}_{11}}{{\sigma}_{1}^{t}}\right)}^{2}+\beta {\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}+{\left(\frac{{\sigma}_{13}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
Compressive fiber mode: ${\sigma}_{11}<0$
$${{e}_{c}}^{2}={\left(\frac{{\sigma}_{11}}{{\sigma}_{1}^{c}}\right)}^{2}$$  For shells:
 For matrix cracking, the failure criterion
is:Tensile matrix mode: ${\sigma}_{22}>0$
 For shells:$${e}_{m}{}^{2}={\left(\frac{{\sigma}_{22}}{{\sigma}_{2}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
 For solids:$${e}_{m1}{}^{2}={\left(\frac{{\sigma}_{22}}{{\sigma}_{2}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}$$$${e}_{m2}{}^{2}={\left(\frac{\sigma 33}{{\sigma}_{2}^{t}}\right)}^{2}+{\left(\frac{{\sigma}_{13}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
Compressive matrix mode: ${\sigma}_{22}<0$ For shells:$${{e}_{d}}^{2}={\left(\frac{{\sigma}_{22}}{2{\overline{\sigma}}_{12}}\right)}^{2}+\left[{\left(\frac{{\sigma}_{2}^{c}}{2{\overline{\sigma}}_{12}}\right)}^{2}1\right]\frac{{\sigma}_{22}}{{\sigma}_{2}^{c}}+{\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
 For solids:$${{e}_{d1}}^{2}={\left(\frac{{\sigma}_{22}}{2{\overline{\sigma}}_{12}}\right)}^{2}+[{\left(\frac{{\sigma}_{2}^{c}}{2{\overline{\sigma}}_{12}}\right)}^{2}1]\frac{{\sigma}_{22}}{{\sigma}_{2}^{c}}+{\left(\frac{{\sigma}_{12}}{{\overline{\sigma}}_{12}}\right)}^{2}$$$${{e}_{d2}}^{2}={\left(\frac{\sigma 33}{2{\overline{\sigma}}_{12}}\right)}^{2}+[{\left(\frac{{\sigma}_{2}^{c}}{2{\overline{\sigma}}_{12}}\right)}^{2}1]\frac{\sigma 33}{{\sigma}_{2}^{c}}+{\left(\frac{{\sigma}_{13}}{{\overline{\sigma}}_{12}}\right)}^{2}$$
 For shells:
 If the damage parameter
${e}_{f}{}^{2},{e}_{c}{}^{2},{e}_{m}{}^{2}$
, or
${{e}_{d}}^{2}\ge 1.0$
the stresses are decreased by using an
exponential function to avoid numerical instabilities. A relaxation technique is
used by decreasing the stress gradually:$$\sigma (t)=\mathrm{f}(t)\cdot {\sigma}_{d}({t}_{r})$$
With, $\mathrm{f}(t)=\mathrm{exp}\left(\frac{t{t}_{r}}{{\tau}_{\mathrm{max}}}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}$ and $t\ge {t}_{r}$ .
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
 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 $D=Max\left({e}_{f}{}^{2},{e}_{c}{}^{2},{e}_{m}{}^{2},{e}_{d}{}^{2}\right)$ . This damage value shows with /ANIM/SHELL/DAMA.
 The fail_ID is used with /STATE/SHELL/FAIL and /INISHE/FAIL for shell. There is no default value. If the line is blank, a value will not be output for failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL for brick and with /STATE/SHELL/FAIL for shell).
 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.