/FAIL/INIEVO

Block Format Keyword This criterion allows a two-step failure approach, divided into an initiation phase, in which damage has no effect on the stress computation, and a damage evolution phase, in which a stress softening can be generated. Initiation is based on plastic strain as function of several stress state quantities.

When the initiation criterion is reached, stress softening damage variable evolution is triggered. This evolution can be based on a plastic displacement at the time of failure or on a certain value of fracture energy. In addition, the shape can be chosen between a classic linear stress reduction or an exponential drop of the load-carrying capacity. Multiple pairs of initiation/evolution criterion can be combined in the same input card. This criterion is compatible with both solids and shells and can be used with non-local regularization.

Format

Card 1 - Number of initiation/evolution criterion, shear components effect, element deletion control

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/FAIL/INIEVO/`mat_ID`/`unit_ID`
`NINIEVO`	`ISHEAR`	`ILEN`					`FAILIP`	`PTHICKFAIL`

Card 2 - Read NINIEVO (Number of initiation/evolution couples, at least 1) cards

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`INITYPE`	`EVOTYPE`	`EVOSHAP`	`COMPTYP`

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`TAB_ID`	`SR_REF`		`FSCALE`		`PARAM`

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`TAB_EL`	`EL_REF`		`ELSCAL`

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`DISP`		`ALPHA`		`ENER`

Card 6 - 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)
`NINIEVO`	Number of initiation/evolution criteria. Default = 1 (Integer)
`ISHEAR`	Flag to take transverse shear components into account (shells only). = 0 (Default) Transverse components not considered. = 1 Transverse components considered. (Integer)
`ILEN`	Element characteristic length formulation flag. = 0 (Default) Initial geometric formulation. = 1 Initial critical timestep formulation. = 2 Current geometric formulation (for shells only). (Integer)
`FAILIP`	Number of failed integration point prior to solid element deletion. Default = 1 (Integer)
`PTHICKFAIL`	Percentage of failed layers prior to shell element deletion. 0.0 ≤ `PTHICKFAIL` ≤ 1.0 Default = 0.0 (Real)
`INITYPE`	Damage initiation tabulated criterion type. 2 = 1 (Default) Plastic strain versus stress triaxiality (versus strain rate). = 2 Plastic strain versus shear influence (versus strain rate). = 3 Modified plastic strain versus principal plastic strain rate ratio (versus strain rate) MSFLD. = 4 Plastic strain versus principal plastic strain rate ratio (versus strain rate) FLD. = 5 Plastic strain versus stress state parameter (versus strain rate). (Integer)
`EVOTYPE`	Damage evolution type. = 1 (Default) Plastic displacement at failure based. = 2 Fracture energy based. (Integer)
`EVOSHAP`	Shape of the damage evolution. = 1 (Default) Linear = 2 Exponential (Integer)
`COMPTYP`	Criterion combination type (only if `NINIEVO` > 0). = 1 (Default) Maximum = 2 Multiplication (Integer)
`TAB_ID`	Failure initiation criterion table identifier. (Integer)
`SR_REF`	Reference strain rate for table identifier. Default = 1.0 (Real)	$[\frac{1}{s}]$
`FSCALE`	Scale factor for failure initiation criterion table. Default = 1.0 (Real)
`PARAM`	Parameter for failure initiation criterion. If `INITYPE` = 1 Not used. If `INITYPE` = 2 Pressure dependency parameter. If `INITYPE` = 3 = 0.0 Direct formulation. = 1.0 Incremental formulation If `INITYPE` = 4 Not used = 0.0 Direct formulation. = 1.0 Incremental formulation If `INITYPE` = 5 Triaxiality influence parameter. Default = 0.0 (Real)
`TAB_EL`	Element size scaling for failure initiation criterion. (Integer)
`EL_REF`	Reference element size for size scaling table. Default = 1.0 (Real)	$[m]$
`ELSCAL`	Scale factor for element size scaling function. Default = 1.0 (Real)
`DISP`	Plastic displacement at failure. Default = 0.0 (Real)	$[m]$
`ALPHA`	Exponential shape parameter (not applicable for exponential energy- based evolution). Default = 1.0
`ENER`	Fracture energy. Default = 0.0	$[\frac{J}{m^{2}}]$
`fail_ID`	(Optional) Failure criteria identifier. (Integer, maximum 10 digits)

Comments

The INIEVO failure criterion is a two-step failure criterion based on plastic strain and stress state. These two steps consist in the computation of two successive damage variables:
- 1^st step: the damage initiation phase, in which an internal variable evolution denoted is computed. This variable is a purely internal value that has no influence on the stress computation. Once this initiation variable reaches the value 1.0, the second stage of the failure is triggered by the computation of the damage variable evolution denoted $D$ .
- 2^nd step: The damage variable $D$ evolution is computed, generating a stress softening effect until the complete failure of the element and its deletion.
Different types of failure initiation criterion can be used depending on the INITYPE parameter value.
- If INITYPE = 1: A tabulated plastic strain at failure initiation map is given with respect to stress triaxiality and, optionally, with strain rate.
  $\begin{matrix} ε_{p}^{i n i t} = f (η, \dot{ε}) & with & η = - \frac{p}{σ_{V M}} \end{matrix}$
  
  Where,
  
  $p$
  
  Hydrostatic pressure $- Tr (σ) / 3$
  
  $σ_{V M}$
  
  von Mises stress
- If INITYPE = 2: A tabulated plastic strain at failure initiation map is given with respect to a shear influence variable denoted as and, optionally, with strain rate.
  $\begin{matrix} ε_{p}^{i n i t} = f (θ, \dot{ε}) & with & θ = \frac{σ_{V M} + k_{s} p}{τ} \end{matrix}$
  
  Where,
  
  $k_{s}$
  
  Pressure influence parameter
  
  $τ$
  
  Maximum shear stress
  
  $τ = \frac{σ_{major} - σ_{minor}}{2}$
- If INITYPE = 3: A tabulated modified plastic strain at failure initiation map is given with respect to principal strain rate ratio and, optionally, with strain rate. This initiation criterion is also denoted as MSFLD.
  $\begin{matrix} ε_{p}^{i n i t} = f (α, \dot{ε}) & with & α = \frac{{\dot{ε}}_{minor}^{p}}{{\dot{ε}}_{minor}^{p}} \approx \frac{s_{minor}}{s_{major}} \end{matrix}$
  
  Where, $s_{i}$ are the principal deviatoric stress component.
- If INITYPE = 4: A tabulated plastic strain at failure initiation map is given with respect to principal strain rate ratio and, optionally, with strain rate. This initiation criterion is also denoted as FLD.
  $\begin{matrix} ε_{p}^{i n i t} = f (α, \dot{ε}) & with & α = \frac{{\dot{ε}}_{minor}^{p}}{{\dot{ε}}_{minor}^{p}} \approx \frac{s_{minor}}{s_{major}} \end{matrix}$
- If INITYPE = 5: A tabulated plastic strain at failure initiation map is given with respect to a stress state parameter denoted as $β$ and, optionally, with strain rate. This initiation criterion is also denoted as FLD.
  $\begin{matrix} ε_{p}^{i n i t} = f (β, \dot{ε}) & with & β = \end{matrix} \frac{σ_{V M} + k_{d} p}{σ_{major}}$
  Important: The strain rate dependency applied to the failure criterion can only be used with material laws that are strain rate dependent. The strain rate used for the constitutive law (total strain rate, deviatoric strain rate or plastic strain rate), will be the same used for the failure criterion.
The damage initiation variable, $ω_{D}$ is computed incrementally as:(1)
$ω_{D} = \sum_{t = 0}^{\infty} \frac{Δ ε_{p}}{ε_{p}^{i n i t}}$
- If INITYPE = 3 (MSFLD), a modified plastic strain is used, which only evolves when $η > 0$ :(2)
  $ω_{D} = \sum_{t = 0}^{\infty} \frac{Δ ε_{p}}{ε_{p}^{i n i t}}$
- If INITYPE = 3 (MSFLD) and INITYPE = 4 (FLD) criteria, depending on PARAM value, a direct formulation can be used instead of the incremental one:(3)
  $ω_{D} = \frac{ε_{p}}{ε_{p}^{i n i t}}$
To take into account regularization of the element size, a table (TAB_EL) can be defined describing a scale factor for the element size denoted as $f_{s i z e}$ map with respect to initial element size $L_{e}$ and, optionally, the stress state variable used in the failure initiation criterion depending on INITYPE value. For instance, if INITYPE = 2, $f_{s i z e} = f (L_{e}, θ)$ . The element size factor is introduced into the damage initiation variable computation as:(4)
$ω_{D} = \sum_{t = 0}^{\infty} \frac{Δ ε_{p}}{ε_{p}^{i n i t} \cdot f_{s i z e}}$
When the damage initiation variable $ω_{D}$ reaches the value 1, the damage variable evolution $D$ is triggered, generating a stress softening. This evolution can be either based on:
- Plastic displacement at failure (DISP), denoted $u_{p}^{f}$ , if EVOTYPE = 1.
- Dissipated fracture energy (ENER) denoted $G_{f}$ , if EVOTYPE = 2.
EVOSHAP parameter allows to define the shape of the damage evolution. For both evolution type (plastic displacement or fracture energy), a linear and an exponential shape can be chosen.
- If EVOSHAP = 1, the damage evolution is linear:
  - If EVOTYPE = 1: plastic displacement at failure is directly input with DISP:(5)
    $Δ D = \frac{L_{e} Δ ε_{p}}{u_{p}^{f}}$
    
    Where, $L_{e}$ is the initial element length.
    
    Figure 1. Linear damage evolution with plastic displacement DISP at failure
  - If EVOTYPE = 2: plastic displacement at failure is deduced from the fracture energy input, which is calculated with ENER:
    $\begin{matrix} Δ D = \frac{L_{e} Δ ε_{p}}{u_{p}^{f}} & with & u_{p}^{f} = \frac{2 G_{f}}{σ_{Y}^{0}} \end{matrix}$
    
    Where, $σ_{Y}^{0}$ is the yield stress at damage evolution triggering.
    Note: This expression considers that the plastic behavior is almost perfect at the onset of damage to ensure a dissipated energy equal to $G_{f}$ .
    
    Figure 2. Linear damage evolution with fracture energy input ENER
- If EVOSHAP = 2, the damage evolution is exponential.
  - If EVOTYPE = 1: plastic displacement at failure is directly input with DISP and shape of the exponential can be modified with ALPHA.(6)
    $D = \frac{1 - e^{- α \frac{L_{e} (ε_{p} - ε_{p}^{0})}{u_{p}^{f}}}}{1 - e^{- α}}$
    
    Figure 3. Exponential damage evolution with plastic displacement DISP. at failure with different alpha parameter value
  - If EVOTYPE = 2: the area between the stress – plastic displacement curve of the exponential function corresponds to the failure energy ENER.
    $\begin{matrix} D = 1 - e^{- \frac{E_{d i s}}{G_{f}}} & with & E_{d i s} = \int_{D = 0}^{D = 1} σ_{Y} \cdot L_{e} Δ ε_{p} \end{matrix}$
    
    Figure 4. Exponential damage evolution with fracture energy input ENER
For the same material, several pairs of Initiation/Evolution criteria can be defined in the same input card, setting a value NINIEVO > 1. In this case, another parameter COMPTYP can be used to choose the way the different criteria are combined to create the softening effect.
- If COMPTYP = 1: the damage variable of the criterion concerned, denoted as $D_{i}$ , is compared with the maximum value among all the criteria using COMPTYP = 1.
  $\begin{matrix} D_{M A X} = \max (D_{i}, D_{M A X}) & w i t h & i \in \end{matrix} N_{M A X}$
  
  Where, $N_{M A X}$ is the number of initiation/evolution card using COMPTYP = 1.
- If COMPTYP = 2: the damage variable of the criterion concerned, denoted as $D_{i}$ , is accumulated by a multiplicative formula among all the criteria using COMPTYP = 2.(7)
  $D_{M U L T} = 1 - \prod_{i \in N_{m u l t}} (1 - D_{i})$
  
  Where, $N_{M U L T}$ is the number of initiation/evolution card using COMPTYP = 2.
Finally, the global damage variable used to calculate the damaged stress tensor is defined as the following maximum value:(8)
$\begin{array}{l} D = \max (D_{M A X}, D_{M U L T}) \\ σ = (1 - D) σ_{e f f} \end{array}$

Where,

$σ$

Final damaged stress tensor

$σ_{e f f}$

Effective stress tensor (obtained from the material law after plastic return mapping)
FAILIP is an integer value used only for higher order or fully-integrated solid elements. It defines the number of failed integration points before deletion of the solid element.
The parameter PTHICKFAIL is a real parameter used for shell elements. If PTHICKFAIL is blank or set to 0.0, the value of PTHICKFAIL from the shell property is used. If PTHICKFAIL > 0.0, any PTHICKFAIL value defined in the shell properties are ignored and the value entered in this failure model is used. For values of PTHICKFAIL > 0.0, shell elements fail and are deleted when the ratio of through thickness failed integration points equals or exceeds PTHICKFAIL.
ILEN is a flag parameter for you to choose between two possible formulas for computing the element characteristic length $L_{e}$ .

ILEN=0

Initial geometrical formulation, where the characteristic length corresponds to the square root of the initial area for shells $L_{e} = \sqrt{A_{0}}$ and the cubic root of initial volume for solids $L_{e} = \sqrt[^{3}]{V_{0}}$ .

ILEN = 1

Initial critical timestep formulation where the characteristic length corresponds to the one used to compute the initial element critical timestep. The formula used may vary between the different formulations of shells or solids.

ILEN = 2

Current geometrical formulation, where the characteristic length corresponds to the square root of the current area for shells $L_{e} = \sqrt{A}$ .
If the non-local regularization is used (/NONLOCAL/MAT), the non-local plastic strain is used to compute the damage initiation variable and the damage variable (and the instability variable if used). Also, in this case, the initial element length $L_{e}$ in all formula is replaced by the non-local parameter $L_{M A X}$ .