/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`

Definitions

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 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)
${e_{m}}^{2} = {(\frac{σ_{22}}{σ_{2}^{t}})}^{2} + β {(\frac{σ_{12}}{{\bar{σ}}_{12}})}^{2}$

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,(6)
$f (t) = \exp (- \frac{t - t_{r}}{τ_{\max}})$

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, no value will 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).
The value of $τ_{\max}$ determines a period of time after failure criterion is reached when the stress in failed element is gradually reduced to zero, then the element is deleted. This is necessary to avoid instability coming from a sudden element deletion and failure "chain reaction" in the neighboring elements. With this value, elements will not be deleted, even if the failure criterion is reached. Normal value of $τ_{\max}$ is 10 times higher than the actual times step should be set in the card directly.