/FAIL/ORTHENERG
Block Format Keyword An orthotropic failure criterion based on fracture energy generating a stress softening. Available for solid and shell elements.
Format
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/FAIL/ORTHENERG/mat_ID/unit_ID  
P_thick_{fail}  NMOD  FAILIP 
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${\sigma}_{11}^{T}$  ${G}_{11}^{T}$  Ishape11T  ${\sigma}_{11}^{C}$  ${G}_{11}^{C}$  Ishape11C 
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${\sigma}_{22}^{T}$  ${G}_{22}^{T}$  Ishape22T  ${\sigma}_{22}^{C}$  ${G}_{22}^{C}$  Ishape22C 
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${\sigma}_{33}^{T}$  ${G}_{33}^{T}$  Ishape33T  ${\sigma}_{33}^{C}$  ${G}_{33}^{C}$  Ishape33C 
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${\sigma}_{12}^{T}$  ${G}_{12}^{T}$  Ishape12T  ${\sigma}_{12}^{C}$  ${G}_{12}^{C}$  Ishape12C 
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${\sigma}_{23}^{T}$  ${G}_{23}^{T}$  Ishape23T  ${\sigma}_{23}^{C}$  ${G}_{23}^{C}$  Ishape23C 
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${\sigma}_{31}^{T}$  ${G}_{31}^{T}$  Ishape31T  ${\sigma}_{31}^{C}$  ${G}_{31}^{C}$  Ishape31C 
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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) 

P_thick_{fail} 
(shells only) Default = 1.0 (Real) 

NMOD  Number of failed modes prior to
integration point failure. Default = 1 (Integer) 

FAILIP  Number of failed integration points
prior to solid deletion. (solids only) Default = 1 (Integer) 

${\sigma}_{ij}^{T}$ 
Default = 10^{20} (Real) 
$\left[\text{Pa}\right]$ 
${G}_{ij}^{T}$ 
Default = 10^{20} (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{2}}}\right]$ 
IshapeIJT  Stress softening shape flag for
tension in direction
$ij$
.
(Integer) 

${\sigma}_{ij}^{C}$ 
Default = ${\sigma}_{ij}^{T}$ (Real) 
$\left[\text{Pa}\right]$ 
${G}_{ij}^{C}$ 
Default = ${G}_{ij}^{T}$ (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{2}}}\right]$ 
IshapeIJC  Stress softening shape flag for
compression in direction
$ij$
.
(Integer) 

fail_ID  (Optional) Failure model
identifier. (Integer, maximum 10 digits) 
Comments
 This criterion considers an orthotropic failure, generating a stress
softening effect which is directly linked to the fracture energy in each
direction / shear plane. Each direction or shear plane failure is denoted by
a corresponding mode:
 Mode 1: Tension 11
 Mode 2: Compression 11
 Mode 3: Tension 22
 Mode 4: Compression 22
 Mode 5: Positive shear 12
 Mode 6: Negative shear 12
 Mode 7: Tension 33
 Mode 8: Compression 33
 Mode 9: Positive shear 23
 Mode 10: Negative shear 23
 Mode 11: Positive shear 31
 Mode 12: Positive shear 31
For each mode of number $I$ , a critical stress ${\sigma}_{I}^{crit}$ is defined by you, to trigger the beginning of stress softening. Then, the stress in the corresponding direction/shear plane is decreased to zero so that the elementary fracture energy equals the value you set ${G}_{I}$ . The shape of the stress softening for the corresponding mode is defined by the flag IshapeI: If IshapeI = 1: linear
stress softening (Figure 1). In this case, the damage
variable evolution in the corresponding mode is computed
with:$$\text{\Delta}{D}_{I}=\frac{{L}_{e}\text{\Delta}{\epsilon}_{I}}{{G}_{I}}$$Where,
 ${L}_{e}$
 Initial element characteristic length.
 $\text{\Delta}{\epsilon}_{I}$
 Total strain increment in the corresponding mode.
 If IshapeI = 2: exponential
stress softening (Figure 2). In this case, the
dissipated energy during element failure is explicitly computed
with:$${E}_{I}={\displaystyle \underset{D=0}{\overset{D=1}{\int}}{\sigma}_{I}{L}_{e}\text{\Delta}{\epsilon}_{I}}$$This energy is then used to compute the damage variable evolution:$${D}_{I}=1{e}^{\frac{{E}_{I}}{{G}_{I}}}$$
Then, the stress tensor component of the corresponding mode $I$ is decreased as:
$$\left\{\begin{array}{ccc}{\sigma}_{I}=\left(1{D}_{I}\right){\sigma}_{I}^{eff}& \text{if}& {\sigma}_{I}^{eff}\ge 0\\ {\sigma}_{I}=\left(1{D}_{I}\right){\sigma}_{I}^{eff}& \text{otherwise}& \end{array}\right.$$
 A mode is considered as failed when ${D}_{I}=1$ . The number of failed modes prior to integration points failure can be controlled by the integer value NMOD. By default, this integer is set to 1. Its maximum value is 6 for shells and 12 for solids.
 To trigger shell element failure, the parameter
P_thick_{fail} can be
used. Depending on the property, the rules are:
 P_thick_{fail} > 0: percentage of failed element/ply thickness prior to element/ply failure
 P_thick_{fail} < 0: ratio of failed element/ply thickness integration points prior to element/ply failure
 To trigger solid element failure, the number of failed integration points prior to solid deletion FAILIP can be used.
 /FAIL/ORTHSTRAIN should be only associated to materials compatible with orthotropic shell properties. LAW25 is compatible only if it is used within shell property TYPE51.