/FAIL/CHANG

Block Format Keyword Describes the Chang failure model.

Format

(1)	(3)	(5)	(7)	(9)
/FAIL/CHANG/`mat_ID`/`unit_ID`
$σ_{1}^{t}$	$σ_{2}^{t}$	${\bar{σ}}_{12}$	$σ_{1}^{c}$	$σ_{2}^{c}$
$β$	$τ_{\max}$	`I`_{fail_sh}

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)
$σ_{1}^{t}$	Longitudinal tensile strength. Default = 10³⁰ (Real)	$[Pa]$
$σ_{2}^{t}$	Transverse tensile strength. Default = 10³⁰ (Real)	$[Pa]$
${\bar{σ}}_{12}$	Shear strength. Default = 10³⁰ (Real)	$[Pa]$
$σ_{1}^{c}$	Longitudinal compressive strength. Default = 10³⁰ (Real)	$[Pa]$
$σ_{2}^{c}$	Transverse compressive strength. Default = 10³⁰ (Real)	$[Pa]$
$β$	Shear scaling factor. Default = 0 (Real)
$τ_{\max}$	Dynamic time relaxation. 7 Default = 10³⁰ (Real)	$[s]$
`I`_{fail_sh}	Shell failure model flag. = 1 (Default) Shell is deleted, if damage is reached for fiber or matrix for one layer. = 2 Shell is deleted, if damage is reached for fiber or matrix for all layers of shell. = 3 Shell is deleted, if damage is reached only for one fiber layer of shell. = 4 Shell is deleted, if damage is reached for all fiber layers of shell. (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: $σ_{11} > 0$ (1)
$e_{f}^{2} = {(\frac{σ_{11}}{σ_{1}^{t}})}^{2} + β {(\frac{σ_{12}}{{\bar{σ}}_{12}})}^{2}$

Compressive fiber mode: $σ_{11} < 0$ (2)
${e_{c}}^{2} = {(\frac{σ_{11}}{σ_{1}^{c}})}^{2}$
For matrix cracking, the failure criteria is:
Tensile matrix mode: $σ_{22} > 0$ (3)
$e_{m}^{2} = {(\frac{σ_{22}}{σ_{2}^{t}})}^{2} + {(\frac{σ_{12}}{{\bar{σ}}_{12}})}^{2}$

Compressive matrix mode: $σ_{22} < 0$ (4)
${e_{d}}^{2} = {(\frac{σ_{22}}{2 {\bar{σ}}_{12}})}^{2} + [{(\frac{σ_{2}^{c}}{2 {\bar{σ}}_{12}})}^{2} - 1] \frac{σ_{22}}{σ_{2}^{c}} + {(\frac{σ_{12}}{{\bar{σ}}_{12}})}^{2}$
If the damage parameter $e_{f}^{2}, e_{c}^{2}, e_{m}^{2}$ , or ${e_{d}}^{2} \geq 1.0$ the stresses are decreased by using an exponential function to avoid numerical instabilities. A relaxation technique is used by decreasing the stress gradually:(5)
$σ (t) = f (t) \cdot σ_{d} (t_{r})$

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

Where,

$t$

Time

$t_{r}$

Start time of relaxation when the damage criteria is assumed

$τ_{max}$

Time of dynamic relaxation

$σ_{d} (t_{r})$

Stress at the beginning of damage
The damage value, D is $0 \leq D \leq 1$ . The status for fracture is:
- Free, if $0 \leq D < 1$
- Failure, if $D = 1$
with $D = M a x (e_{f}^{2}, e_{c}^{2}, e_{m}^{2}, e_{d}^{2})$ . 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 $τ_{\max}$ 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 $τ_{\max} = 1.0 E 30$ results in no element deletion. Therefore, it is recommended to define $τ_{\max}$ 10 times larger than the simulation time step.