/FAIL/LAD

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:(1)
$Y_{d_{3}} = {\frac{\partial E_{D}}{\partial d_{3}} |}_{σ = cst} = \frac{1}{2} \frac{{〈 σ_{33} 〉}^{2}}{K_{3} {(1 - d_{3})}^{2}} Mode I$
(2)
$Y_{d_{1}} = {\frac{\partial E_{D}}{\partial d_{1}} |}_{σ = cst} = \frac{1}{2} \frac{{σ_{31}}^{2}}{K_{1} {(1 - d_{1})}^{2}} Mode II$
(3)
$Y_{d_{2}} = {\frac{\partial E_{D}}{\partial d_{2}} |}_{σ = cst} = \frac{1}{2} \frac{{σ_{32}}^{2}}{K_{2} {(1 - d_{2})}^{2}} Mode III$

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:(4)
$\dot{d} = \frac{k}{a} [1 - \exp (- a 〈 w (Y) - d 〉)]$

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 $\frac{a}{k}$ .(5)
$〈 x 〉 = {\begin{matrix} x if x > 0 \\ 0 if x < 0 \end{matrix}$

The function $w (Y)$ is computed as:(6)
$w (Y) = \frac{〈 \sqrt{Y} - \sqrt{Y_{0}} 〉}{\sqrt{Y_{c}} - \sqrt{Y_{0}}}$

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:(7)
$σ (t) = f (t) \cdot σ_{d} (t_{r})$

With,(8)
$f (t) = \exp (- \frac{t - t_{r}}{τ_{\max}}) and t \geq t_{r}$

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.