/FAIL/MAXSTRAIN

Block Format Keyword Maximum strain failure criterion for modeling the failure of composite materials. This criterion is available for solids and shells.

Format

(1)	(3)	(5)	(9)	(10)
/FAIL/MAXSTRAIN/`mat_ID`/`unit_ID`
$ε_{1}^{M A X}$ $ε_{1}^{M A X}$	$ε_{2}^{M A X}$ $ε_{2}^{M A X}$	$γ_{12}^{M A X}$ $γ_{12}^{M A X}$	`I`_{fail_sh}	`I`_{fail_so}
$τ_{max}$ $τ_{\max}$	`F`_cut

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`	(Optional) Unit identifier. (Integer, maximum 10 digits)
$ε_{1}^{M A X}$ $ε_{1}^{M A X}$	Longitudinal critical strain. Default = 10²⁰ (Real)
$ε_{2}^{M A X}$ $ε_{2}^{M A X}$	Transverse critical strain. Default = 10²⁰ (Real)
$γ_{12}^{M A X}$ $γ_{12}^{M A X}$	Shear critical engineering strain. Default = 10²⁰ (Real)
`I`_{fail_sh}	Shell failure model flag. = 0 (Default) Shell is never deleted and no stress softening. = 1 Shell is deleted, if damage is reached for one layer. = 2 Shell is deleted, if damage is reached for all shell layers. (Integer)
`I`_{fail_so}	Solid failure model flag. = 0 Solid is never deleted and no stress softening. = 1 (Default) Solid is deleted, if damage is reached for one integration point of solid. = 2 Solid is deleted, if damage is reached for all integration points. (Integer)
$τ_{max}$ $τ_{\max}$	Dynamic time relaxation. 5 Default = 10²⁰ (Real)	$[s]$ $[s]$
`F`_cut	Stress tensor filtering frequency. Default = 0.0 (Real)	$[\frac{1}{s}]$ $[\frac{1}{s}]$
`fail_ID`	(Optional) Failure criteria identifier.4 (Integer, maximum 10 digits)

▸Example

/UNIT/1
                  Mg                  mm                   s
/FAIL/MAXSTRN/1/1
#          EPS1_MAX             EPS2_MAX           GAM12_MAX                        IFAIL_SH  IFAIL_SO 
               0.052                0.045              0.0157                                1          1
#            TAU_MAX                 FCUT
              1.0E-4                100.0ZZ

Comments

This failure model is available for shells and solids. It considers a composite ply with the fibers oriented in the direction 1 (also denoted as m1) and the matrix oriented in transverse direction 2 (and 3 for solids). Each direction considers a critical strength value valid for both tension and compression:

Figure 1.

Where, $ε_{1}^{M A X}$ $ε_{1}^{M A X}$ , $ε_{2}^{M A X}$ $ε_{2}^{M A X}$ , $γ_{12}^{M A X}$ $γ_{12}^{M A X}$ are respectively the critical strain in direction 1, critical strain in direction 2 and critical engineering strain in shear.
Note: $γ_{12} = 2 ε_{12}$ $γ_{12} = 2 ε_{12}$
Where, $ε_{12}$ $ε_{12}$ is the shear strain.
The failure criterion for shells is written as:(1)
$F = max (\frac{| ε_{1} |}{ε_{1}^{M A X}}; \frac{| ε_{2} |}{ε_{2}^{M A X}}; \frac{| γ_{12} |}{γ_{12}^{M A X}}) \leq 1$ $F = \max (\frac{|ε_{1}|}{ε_{1}^{M A X}}; \frac{|ε_{2}|}{ε_{2}^{M A X}}; \frac{|γ_{12}|}{γ_{12}^{M A X}}) \leq 1$

For solids the criterion becomes:(2)
$F = max (\frac{| ε_{1} |}{ε_{1}^{M A X}}; \frac{| ε_{2} |}{ε_{2}^{M A X}}; \frac{| ε_{3} |}{ε_{2}^{M A X}}; \frac{| γ_{12} |}{γ_{12}^{M A X}}; \frac{| γ_{31} |}{γ_{12}^{M A X}}) \leq 1$ $F = \max (\frac{|ε_{1}|}{ε_{1}^{M A X}}; \frac{|ε_{2}|}{ε_{2}^{M A X}}; \frac{|ε_{3}|}{ε_{2}^{M A X}}; \frac{|γ_{12}|}{γ_{12}^{M A X}}; \frac{|γ_{31}|}{γ_{12}^{M A X}}) \leq 1$

The criterion is considered to be reached when $F = 1$ $F = 1$ . The damage variable corresponds to the criterion itself $D = F$ $D = F$ .
Once the criterion is reached $D = F = 1$ $D = F = 1$ , two behaviors can be set up:
- If I_{fail_sh} = 0 or I_{fail_so} = 0, there is no stress softening and elements are never deleted. In this case, the failure criterion is purely visual using the output of the damage variable.
- If I_{fail_sh} ≠ 0 or I_{fail_so} ≠ 0, a stress relaxation is generated to decrease the load carrying capacity of the element.(3)
  $σ (t) = f (t) \cdot σ_{d} (t_{r})$
  
  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 tensor when the criterion is reached.
  
  When the stresses reach 1% of the stress value at the beginning of the failure, the element is deleted. This is necessary to avoid instabilities coming from a sudden deletion of an element and a failure “chain reaction” in the neighboring elements. Even if the failure criterion is reached, there will be no element deletion with the default value of $τ_{\max} = 1.0 E 20$ . Therefore, it is recommended to define a value for $τ_{\max}$ 10 times larger than the simulation time step.
To avoid “chain reaction” when deleting elements, you can also define a stress tensor filtering frequency F_cut. Thus, the stress tensor used to calculate the MAXSTRAIN criterion is first to be filtered according to:(4)
$ε_{n + 1}^{f i l t} = α ε_{n + 1} + (1 - α) ε_{n}^{f i l t}$

With $α = \frac{2 π \cdot F_{c u t} \cdot Δ t}{2 π \cdot F_{c u t} \cdot Δ t + 1}$

Where, $Δ t$ is the current timestep.

If a filtering frequency is not defined (F_cut= 0.0), the filtering effect is deactivated.
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).