/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
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/FAIL/LAD_DAMA/mat_ID/unit_ID  
K_{1}  K_{2}  K_{3}  ${\gamma}_{1}$  ${\gamma}_{2}$  
${Y}_{0}$  ${Y}_{c}$  k  a  ${\tau}_{\mathrm{max}}$  
I_{fail_sh}  I_{fail_so} 
(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 = 10^{30} (Real) 
$\left[\frac{\text{P}\text{a}}{\text{m}}\right]$ 
K_{2}  Interlaminar stiffness in
direction 2. Default = 10^{30} (Real) 
$\left[\frac{\text{P}\text{a}}{\text{m}}\right]$ 
K_{3}  Interlaminar stiffness in
direction 3. Default = 10^{30} (Real) 
$\left[\frac{\text{P}\text{a}}{\text{m}}\right]$ 
${\gamma}_{1}$  Coupling factor between
delamination Mode I and Mode II. Default = 0 (Real) 

${\gamma}_{2}$  Coupling factor between
delamination Mode I and Mode III. Default = 0 (Real) 

${Y}_{0}$  Yield energy damage for
delamination start. Default = 10^{30} (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) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
a  Crack propagation velocity
multiplier. Default = 10^{30} (Real) 

${\tau}_{\text{max}}$  Dynamic time relaxation.
3 Default = 10^{30} (Real) 
$\left[\text{s}\right]$ 
I_{fail_sh}  Shell failure flag.
(Integer) 

I_{fail_so}  Solid failure flag.
(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
#12345678910
/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 1E20 1E20
# Y0 YC K A Tau_max
40 160 100000 1 .01
# Ifail_sh Ifail_so
1 3
#12345678910
#enddata
#12345678910
Comments
 The Ladeveze failure damage
model for delamination:$${\text{Y}}_{{\text{d}}_{3}}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_{3}}}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{\langle {\sigma}_{33}\rangle}^{2}}{{\text{K}}_{3}{\left(1{\text{d}}_{3}\right)}^{2}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}I$$$${\text{Y}}_{{\text{d}}_{1}}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_{1}}}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{{\sigma}_{31}}^{2}}{{\text{K}}_{1}{\left(1{\text{d}}_{1}\right)}^{2}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}\mathrm{II}$$$${\text{Y}}_{{\text{d}}_{2}}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_{2}}}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{{\sigma}_{32}}^{2}}{{\text{K}}_{2}{\left(1{\text{d}}_{2}\right)}^{2}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}III$$
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.
$Y={Y}_{{d}_{3}}+{\gamma}_{1}{Y}_{{d}_{1}}+{\gamma}_{2}{Y}_{{d}_{2}}$ with ${Y}_{{d}_{i}}{}_{t}=\mathrm{sup}{Y}_{{d}_{i}}{}_{\tau \le t}$
The evolution of the damage parameters is strongly coupled with coupling factor ${\gamma}_{1}$ and ${\gamma}_{2}$ . 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:
$$\dot{d}=\frac{k}{a}\left[1\mathrm{exp}\left(a\langle w\left(Y\right)d\rangle \right)\right]$$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 $\frac{a}{k}$ .
$$\langle x\rangle =\{\begin{array}{c}x\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{if}\text{\hspace{0.17em}}x>0\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{if}\text{\hspace{0.17em}}x<0\end{array}$$The function $w(Y)$ is computed as:
$$w(Y)=\frac{\langle \sqrt{Y}\sqrt{{Y}_{0}}\rangle}{\sqrt{{Y}_{c}}\sqrt{{Y}_{0}}}$$If the damage parameter $d\le 1.0$ , the stresses ${\sigma}_{33}$ , ${\sigma}_{13}$ and ${\sigma}_{23}$ are decreased according to the following function:
A relaxation technique is used by gradually decreasing the stress:
$$\sigma (t)=\mathrm{f}(t)\cdot {\sigma}_{d}({t}_{r})$$With,
$$\mathrm{f}(t)=\mathrm{exp}\left(\frac{t{t}_{r}}{{\tau}_{\mathrm{max}}}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{and}t\ge {t}_{r}$$Where, $t$
 Time
 ${t}_{r}$
 Start time of relaxation when the damage criteria is assumed
 ${\tau}_{\text{max}}$
 Time of dynamic relaxation
 ${\sigma}_{d}\left({t}_{r}\right)$
 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 ${\tau}_{\mathrm{max}}$ 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 ${\tau}_{\mathrm{max}}=1.0E30$ results in no element deletion. Therefore, it is recommended to define ${\tau}_{\mathrm{max}}$ 10 times larger than the simulation time step.