/FAIL/LAD_DAMA

Block Format Keyword Describes the Ladeveze failure model for delamination (interlaminar fracture).

This failure model is available for orthotropic solids and thick shells. It could also be used with Plyxfem in shell property /PROP/TYPE17 as an interplay material failure model. This failure model is compatible with /MAT/LAW12 (3D_COMP), /MAT/LAW14 (COMPSO) and /MAT/LAW25 (COMPSH) and /MAT/LAW1 (ELAST) (only when used with Plyxfem).

Format


(1)	(2)	(3)	(5)	(7)	(9)
/FAIL/LAD_DAMA/`mat_ID`/`unit_ID`
`K`₁		`K`₂	`K`₃	$γ_{1}$	$γ_{2}$
$Y_{0}$		$Y_{c}$	`k`	`a`	$τ_{\max}$
`I`_{fail_sh}	`I`_{fail_so}

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)
`K`₁	Interlaminar stiffness in direction 1. Default = 10³⁰ (Real)	$[\frac{P a}{m}]$
`K`₂	Interlaminar stiffness in direction 2. Default = 10³⁰ (Real)	$[\frac{P a}{m}]$
`K`₃	Interlaminar stiffness in direction 3. Default = 10³⁰ (Real)	$[\frac{P a}{m}]$
$γ_{1}$	Coupling factor between delamination Mode I and Mode II. Default = 0 (Real)
$γ_{2}$	Coupling factor between delamination Mode I and Mode III. Default = 0 (Real)
$Y_{0}$	Yield energy damage for delamination start. Default = 10³⁰ (Real)
$Y_{c}$	Critical energy damage parameter for full delamination. Default = $2 \sqrt{Y_{0}}$ (Real)
`k`	Crack propagation velocity time constant. Default = 0 (Real)	$[\frac{m}{s}]$
`a`	Crack propagation velocity multiplier. Default = 10³⁰ (Real)
$τ_{max}$	Dynamic time relaxation. 3 Default = 10³⁰ (Real)	$[s]$
`I`_{fail_sh}	Shell failure flag. = 1 (Default) Shell is deleted, if damage criterion is reached for one layer. = 2 Shell is deleted, if damage criterion is reached for all shell layers. (Integer)
`I`_{fail_so}	Solid failure flag. = 1 (Default) Solid is deleted, if damage criterion is reached for one integration point. = 3 Out-of-plane stress is set to zero, if damage is reached for one integration point of solid ( $σ_{33} = σ_{23} = σ_{13} = 0$ ). (Integer)
`fail_ID`	Failure criteria identifier. 2 (Integer, maximum 10 digits)

Example (Composite)

#RADIOSS STARTER
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSH/1/1
composite example
#              RHO_I
             .001506
#                E11                 E22                NU12     Iform                           E33
              144000               10000                 .25         0                         20000
#                G12                 G23                 G31              EPS_f1              EPS_f2
                4200                4200                4200                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax
                   0                   0                   0                   0                   0
#              Wpmax               Wpref      Ioff                         ratio
             1000000                   0         0                             0
#                  b                   n                fmax
                   0                   0             1000000
#            sig_1yt             sig_2yt             sig_1yc             sig_2yc               alpha
               10100               10100               10100               10100                   0
#           sig_12yc            sig_12yt                c_12          Eps_rate_0       ICC
               10068               10068                   0                   0         0
#          GAMMA_ini           GAMMA_max               d3max
                   0                   0                   0
#  Fsmooth                Fcut
         0                   0
/FAIL/LAD_DAMA/1/1
#                 K1                  K2                  K3              Gamma1              Gamma2
                2000                2000                2000               1E-20               1E-20
#                 Y0                  YC                   K                   A             Tau_max
                  40                 160              100000                   1                 .01
# Ifail_sh  Ifail_so                                                                               
         1         3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The Ladeveze failure damage model for delamination:
$Y_{d_{3}} = {\frac{\partial E_{D}}{\partial d_{3}} |}_{σ = cst} = \frac{1}{2} \frac{{〈 σ_{33} 〉}^{2}}{K_{3} {(1 - d_{3})}^{2}} Mode I$
$Y_{d_{1}} = {\frac{\partial E_{D}}{\partial d_{1}} |}_{σ = cst} = \frac{1}{2} \frac{{σ_{31}}^{2}}{K_{1} {(1 - d_{1})}^{2}} Mode II$
$Y_{d_{2}} = {\frac{\partial E_{D}}{\partial d_{2}} |}_{σ = cst} = \frac{1}{2} \frac{{σ_{32}}^{2}}{K_{2} {(1 - d_{2})}^{2}} Mode III$
Figure 1.

^²
For Quad 2D element, only Mode II and Mode III are available.
Where, $d_{i}$ is the internal damage parameters associated with its fracture mode.
The damage evolution law is controlled by equivalent damage energy release rate.
$Y = Y_{d_{3}} + γ_{1} Y_{d_{1}} + γ_{2} Y_{d_{2}}$ with $Y_{d_{i}} |_{t} = \sup Y_{d_{i}} |_{τ \leq t}$
The evolution of the damage parameters is strongly coupled with coupling factor $γ_{1}$ and $γ_{2}$ . These two material parameters come from delamination tests.
For the present failure model, consider that $d_{1} = d_{2} = d_{3} = d$ .
Damage value $d$ increases at certain velocity:
$\dot{d} = \frac{k}{a} [1 - \exp (- a 〈 w (Y) - d 〉)]$
if $d < 1$ .
Otherwise, $d = 1$
While,
$a$ is a measure of the failure ductility, the lower the value the more ductile the failure.
$\frac{a}{k}$ is the minimum failure duration. The duration of the energy between $Y_{0}$ and $Y_{c}$ should be at least equal to $\frac{a}{k}$ .
$〈 x 〉 = {\begin{matrix} x if x > 0 \\ 0 if x < 0 \end{matrix}$
The function $w (Y)$ is computed as:
$w (Y) = \frac{〈 \sqrt{Y} - \sqrt{Y_{0}} 〉}{\sqrt{Y_{c}} - \sqrt{Y_{0}}}$
If the damage parameter $d \leq 1.0$ , the stresses $σ_{33}$ , $σ_{13}$ and $σ_{23}$ are decreased according to the following function:
A relaxation technique is used by gradually decreasing the stress:
$σ (t) = f (t) \cdot σ_{d} (t_{r})$
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 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 $τ_{\max}$ 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.

¹ O. Allix, P. Ladevèze, “Interlaminar interface modeling for the prediction of delamination”, Composite structure 22 (1992) 235-242

² L. Gornet, “Finite Element Damage Prediction of Composite Structures"