/FAIL/ORTHENERG

Block Format Keyword An orthotropic failure criterion based on fracture energy generating a stress softening. Available for solid and shell elements.

Format


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/FAIL/ORTHENERG/`mat_ID`/`unit_ID`
`P_thick`_fail								`NMOD`	`FAILIP`

Card 2 - Direction 11


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{11}^{T}$		$G_{11}^{T}$		`Ishape11T`	$σ_{11}^{C}$		$G_{11}^{C}$		`Ishape11C`

Card 3 - Direction 22


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{22}^{T}$		$G_{22}^{T}$		`Ishape22T`	$σ_{22}^{C}$		$G_{22}^{C}$		`Ishape22C`

Card 4 - Direction 33 (solids only, leave blank for shells)


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{33}^{T}$		$G_{33}^{T}$		`Ishape33T`	$σ_{33}^{C}$		$G_{33}^{C}$		`Ishape33C`

Card 5 – Shear Plane 12


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{12}^{T}$		$G_{12}^{T}$		`Ishape12T`	$σ_{12}^{C}$		$G_{12}^{C}$		`Ishape12C`

Card 6 - Shear Plane 23 (solids only, leave blank for shells)


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{23}^{T}$		$G_{23}^{T}$		`Ishape23T`	$σ_{23}^{C}$		$G_{23}^{C}$		`Ishape23C`

Card 7 - Shear Plane 31 (solids only, leave blank for shells)


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$σ_{31}^{T}$		$G_{31}^{T}$		`Ishape31T`	$σ_{31}^{C}$		$G_{31}^{C}$		`Ishape31C`

Card 8 – Failure model ID (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)
`P_thick`_fail	> 0 Percentage of failed thickness/layer/ply prior to element/layer/ply failure. < 0 Ratio of failed integration points/layers prior to element or ply/layer failure. (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)
$σ_{i j}^{T}$	If $i = j$ Critical stress for tension in direction $i$ , If $i \neq j$ Critical stress for positive shear in plane $i j$ . Default = 10²⁰ (Real)	$[Pa]$
$G_{i j}^{T}$	If $i = j$ Fracture energy for tension in direction $i$ . If $i \neq j$ Fracture energy for positive shear in plane $i j$ . Default = 10²⁰ (Real)	$[\frac{J}{m^{2}}]$
`IshapeIJT`	Stress softening shape flag for tension in direction $i j$ . =1 (Default) Linear stress softening. = 2 Exponential stress softening. (Integer)
$σ_{i j}^{C}$	If $i = j$ Critical stress for compression in direction $i$ . If $i \neq j$ Critical stress for negative shear in plane $i j$ . Default = $σ_{i j}^{T}$ (Real)	$[Pa]$
$G_{i j}^{C}$	If $i = j$ Fracture energy for compression in direction $i$ . If $i \neq j$ Fracture energy for negative shear in plane $i j$ . Default = $G_{i j}^{T}$ (Real)	$[\frac{J}{m^{2}}]$
`IshapeIJC`	Stress softening shape flag for compression in direction $i j$ . =1 (Default) Linear stress softening. = 2 Exponential stress softening. (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 $σ_{I}^{c r i t}$ 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:
  $Δ D_{I} = \frac{L_{e} Δ ε_{I}}{G_{I}}$
  Where,
  
  $L_{e}$
  
  Initial element characteristic length.
  
  $Δ ε_{I}$
  
  Total strain increment in the corresponding mode.
  
  Figure 1. Example of linear stress softening with $σ_{I}^{c r i t} = 450 M P a$ and $G_{I} = 50 \times 10^{- 3} J / m m^{2}$
- If IshapeI = 2: exponential stress softening (Figure 2). In this case, the dissipated energy during element failure is explicitly computed with:
  $E_{I} = \int_{D = 0}^{D = 1} σ_{I} L_{e} Δ ε_{I}$
  This energy is then used to compute the damage variable evolution:
  $D_{I} = 1 - e^{- \frac{E_{I}}{G_{I}}}$
  Figure 2. Example of linear stress softening with $σ_{I}^{c r i t} = 450 M P a$ and $G_{I} = 50 \times 10^{- 3} J / m m^{2}$
  
  Then, the stress tensor component of the corresponding mode $I$ is decreased as:
  $\{\begin{matrix} σ_{I} = (1 - D_{I}) σ_{I}^{e f f} & if & σ_{I}^{e f f} \geq 0 \\ σ_{I} = (1 - D_{I}) σ_{I}^{e f f} & otherwise \end{matrix}$
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.