/FAIL/CONNECT

Block Format Keyword Describes the failure model for CONNECTION material with displacement criteria and/or energy criteria.

Format

(1)	(3)	(5)	(7)	(8)	(9)	(10)
/FAIL/CONNECT/`mat_ID`/`unit_ID`
${¯ u}_{max N}$ ${\bar{u}}_{\max N}$	`exp`_N	$α_{N}$ $α_{N}$	`R_fct_ID`_N	`I`_fail	`I`_{fail_so}	`ISYM`
${¯ u}_{max T}$ ${\bar{u}}_{\max T}$	`exp`_T	$α_{T}$ $α_{T}$	`R_fct_ID`_T
`EI`_max	`EN`_max	`ET`_max	`N`_n		`N`_t
`T`_max	`N`_soft	`AREA`_scale

Optional Line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fail_ID`

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier (Integer, maximum 10 digits)
${¯ u}_{max T}$ ${\bar{u}}_{\max T}$	Failure relative displacement in normal direction. Default = 10³⁰ (Real)
`exp`_N	Failure exponent parameter in normal direction. Default = 1.0 (Real)
$α_{N}$ $α_{N}$	Normal direction scale factor. Default = 1.0 (Real)
`R_fct_ID`_N	Identifier for $f_{N} ({˙ ¯ u}_{N})$ $f_{N} ({\dot{\bar{u}}}_{N})$ failure scale factor in normal direction vs displacement rate function. (Integer)
`I`_fail	Failure formulation flag. 2 = 0 (Default) Uni-directional failure (uncoupled failure formulation). = 1 Multi-directional failure (coupled failure formulation). (Integer)
`I`_{fail_so}	Solid failure flag. = 1 (Default) Solid element is deleted, when one integration point reaches the failure criteria. = 2 Solid element is deleted, when all integration points reach the failure criteria. (Integer)
`ISYM`	Rupture deactivation flag for compression. = 0 (Default) Same behavior in tension and compression. = 1 Deactivation of failure in case of compression. (Integer)
${¯ u}_{max T}$ ${\bar{u}}_{\max T}$	Failure relative displacement in tangential plane. Default = 10³⁰ (Real)
`exp`_T	Failure exponent parameter in tangential plane. Default = 1.0 (Real)
$α_{T}$ $α_{T}$	Scale factor in tangential plane. Default = 1.0 (Real)
`R_fct_ID`_T	Identifier for $f_{T} ({˙ ¯ u}_{T})$ $f_{T} ({\dot{\bar{u}}}_{T})$ failure scale factor in tangential plane vs displacement rate function. (Integer)
`EI`_max	Failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{kg}{s^{2}}]$ $[\frac{kg}{s^{2}}]$
`EN`_max	Normal failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{kg}{s^{2}}]$ $[\frac{kg}{s^{2}}]$
`ET`_max	Tangential failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{kg}{s^{2}}]$ $[\frac{kg}{s^{2}}]$
`N`_n	Exponent for normal energy failure criteria. Default = 1.0 (Real)
`N`_t	Exponent for tangential energy failure criteria. Default = 1.0 (Real)
`T`_max	Duration parameter for energy failure criteria. (Real)
`N`_soft	Softening exponent for failure. Default = 1.0 (Real)
`AREA`_scale	Failure scale factor for area increase. 6 Default = 0.0, this option is not used (Real)
`fail_ID`	Failure criteria identifier. 4 (Integer, maximum 10 digits)

Example (Spotweld)

#RADIOSS STARTER
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW59/1/1
spotweld
#              RHO_I
              7.9E-9
#                  E                   G     Imass
               21000               21000         0
# NB_funct   Fsmooth                Fcut
         1         1                   0
# YFun_IDN  YFun_IDT        SR_reference        Fscale_yield
         1         2                   0                   0
/FAIL/CONNECT/1
#          EPS_MAX_N               EXP_N             ALPHA_N R_fct_IDN     Ifail  Ifail_so      ISYM
                   1                   0                   0         0         0         1         0
#          EPS_MAX_T               EXP_T             ALPHA_T R_fct_IDT
                 1.8                   0                   0         0
#              EIMAX               ENMAX               ETMAX                  Nn                  Nt
                   0                   0                   0                   0                   0
#               Tmax               Nsoft           AREAscale
                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
New_function
#                  X                   Y
                   0                 250                                                            
                   1                 350                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
New_function
#                  X                   Y
                   0                 350                                                            
                   1                 350                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This failure model is compatible only with the connection material, /MAT/LAW59 (CONNECT).
Failure criteria:
Solid element failure will occur when displacement values reach the criteria, or when the internal energy reaches the failure internal energy value.
I_fail control coupled or uncoupled failure formulation for are exclusive with each other. Displacement and energy criteria can be used simultaneously. Both energy criteria can be used simultaneously (based on EI_max and energy in both directions separately).
- I_fail =0: Uni-directional formulation (uncoupled failure formulation)
  For displacement criteria:(1)
  ${¯ u}_{i} \cdot f (˙ ¯ u) > {¯ u}_{m a x i}$ ${\bar{u}}_{i} \cdot f (\dot{\bar{u}}) > {\bar{u}}_{m a x i}$
  
  with $i$ $i$ = 33 for normal direction and 13 or 23 for tangent directions.
  
  For energy criteria:(2)
  $E_{n} > E N_{m a x}$ $E_{n} > E N_{m a x}$
  
  or, for each direction:(3)
  $E_{t} > E T_{m a x}$ $E_{t} > E T_{m a x}$
  
  or, for total energy:(4)
  $E (t) > E I_{m a x}$ $E (t) > E I_{m a x}$
- I_fail=1: Multi-directional formulation (coupled failure formulation)
  For displacement criteria:(5)
  ${∣ ∣ ∣ \frac{{¯ u}_{N}}{{¯ u}_{max N}} \cdot α_{N} \cdot f_{N} ({˙ ¯ u}_{N}) ∣ ∣ ∣}_{N}^{{exp}_{N}} + {∣ ∣ ∣ \frac{{¯ u}_{T}}{{¯ u}_{{max}_{T}}} \cdot α_{T} \cdot f_{T} ({˙ ¯ u}_{T}) ∣ ∣ ∣}_{T}^{{exp}_{T}} > 1$ ${| \frac{{\bar{u}}_{N}}{{\bar{u}}_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{\bar{u}}}_{N}) |}^{\exp_{N}} + {| \frac{{\bar{u}}_{T}}{{\bar{u}}_{\max_{T}}} \cdot α_{T} \cdot f_{T} ({\dot{\bar{u}}}_{T}) |}^{\exp_{T}} > 1$
  
  For energy criteria:(6)
  ${(\frac{E n}{E N_{max}})}_{n}^{N_{n}} + {(\frac{E t}{E T_{max}})}_{t}^{N_{t}} > 1$ ${(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}} > 1$
  
  With $E N$ $E N$ and $E T$ $E T$ being the energy in the normal and the tangential direction, respectively.
A damage variable is defined, as:(7)
$D_{1} = \int_{0}^{t} ⟨ {\frac{E (t)}{E I_{max}} ∣ ∣ ∣}_{E (t) \geq E I_{max}} ⟩ d t$ $D_{1} = \int_{0}^{t} 〈 {\frac{E (t)}{E I_{\max}} |}_{E (t) \geq E I_{\max}} 〉 d t$
(8)
$D_{2} = \int_{0}^{t} 〈 {C (t) |}_{C (t) \geq 1} 〉 d t$
(9)
$D_{\max} = m a x (D_{1}, D_{2})$

The element is deleted (or stress in local integration point is set to zero), if:(10)
$D_{\max} \geq T_{\max}$

(if $T_{\max}$ is equal to default value, failure is immediate).

Otherwise, when $T_{\max} > D_{\max} > 0$ , softening is applied as follows (for all directions):(11)
$σ = σ {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$

The energy failure parameter will be activated as of input version 120 in /BEGIN.
fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL. There is no default value. If the line is blank, no value is output for the failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL option).

The following animation (/ANIM/BRICK) and time history (/TH/BRICK) outputs are available using USR (maximum value over integration points):

	`EI`_max (only)	`EN`_max or `ET`_max (only)	`EI`_max and (`EN`_max or `ET`_max)
USR1	$\frac{E I}{E I_{\max}}$		$\max [{(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}}, \frac{E I}{E I_{\max}}]$
USR2		${(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}}$	${(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}}$

Where,

EI: Internal energy per connection element area
En: Internal energy in the normal direction per connection element area
Et: Internal energy in the shear direction per connection element area

	`I`_fail=0	`I`_fail=1
USR3	$\max [f_{N} ({\dot{ε}}_{N}) \cdot \frac{ε_{N}}{ε_{\max N}}, f_{T} ({\dot{ε}}_{T}) \cdot \frac{ε_{T}}{ε_{\max T}}]$	$f_{N} ({\dot{ε}}_{N}) \cdot \frac{ε_{N}}{ε_{\max N}}$
USR4	$f_{T} ({\dot{ε}}_{T}) \cdot \frac{ε_{T}}{ε_{\max T}}$	$c 4 = f_{T} ({\dot{ε}}_{T}) \cdot \frac{ε_{T}}{ε_{\max T}}$
USR5		${\| \frac{ε_{N}}{ε_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{ε}}_{N}) \|}^{\exp_{N}} + {\| \frac{ε_{T}}{ε_{\max_{T}}} \cdot α_{T} \cdot f_{T} ({\dot{ε}}_{T}) \|}^{\exp_{T}} > 1$
USR6	$S O F T = {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$	$S O F T = {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$

The area is calculated as the mean value of the upper and lower surface of the solid element. If the actual area reaches the value of initial area multiplied by AREA_scale factor, the whole element will be deleted. If the elements attached to the connect elements fail, this option can be used to prevent shooting nodes due to large deformation of the connect elements.