/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`

Definition

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 versus 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 versus displacement rate function. (Integer)
`EI`_max	Failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{k g}{s^{2}}]$ $[\frac{k g}{s^{2}}]$
`EN`_max	Normal failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{k g}{s^{2}}]$ $[\frac{k g}{s^{2}}]$
`ET`_max	Tangential failure internal energy, per surface unit. Default = 10³⁰ (Real)	$[\frac{k g}{s^{2}}]$ $[\frac{k g}{s^{2}}]$
`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)	$[s]$ $[s]$
`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_fct   Fsmooth                Fcut
         1         1                   0
# YFun_IDN  YFun_IDT              SR_ref          Fscale_yld
         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:
From relative displacement:
- I_fail=0: Uni-directional formulation (uncoupled failure formulation)(1)
  $C s (t) = max ({∣ ∣ ∣ \frac{{¯ u}_{N}}{{¯ u}_{max N}} \cdot α_{N} \cdot f_{N} ({˙ ¯ u}_{N}) ∣ ∣ ∣}_{N}^{{exp}_{N}}, {∣ ∣ ∣ \frac{{¯ u}_{T}}{{¯ u}_{max T}} \cdot α_{T} \cdot f_{T} ({˙ ¯ u}_{T}) ∣ ∣ ∣}_{T}^{{exp}_{T}}) > 1$ $C s (t) = \max ({| \frac{{\bar{u}}_{N}}{{\bar{u}}_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{\bar{u}}}_{N}) |}^{\exp_{N}}, {| \frac{{\bar{u}}_{T}}{{\bar{u}}_{\max T}} \cdot α_{T} \cdot f_{T} ({\dot{\bar{u}}}_{T}) |}^{\exp_{T}}) > 1$
- I_fail=1: Multi-directional formulation (coupled failure formulation)(2)
  $C s (t) = {∣ ∣ ∣ \frac{{¯ u}_{N}}{{¯ u}_{max N}} \cdot α_{N} \cdot f_{N} ({˙ ¯ u}_{N}) ∣ ∣ ∣}_{N}^{{exp}_{N}} + {∣ ∣ ∣ \frac{{¯ u}_{T}}{{¯ u}_{max T}} \cdot α_{T} \cdot f_{T} ({˙ ¯ u}_{T}) ∣ ∣ ∣}_{T}^{{exp}_{T}} > 1$ $C s (t) = {| \frac{{\bar{u}}_{N}}{{\bar{u}}_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{\bar{u}}}_{N}) |}^{\exp_{N}} + {| \frac{{\bar{u}}_{T}}{{\bar{u}}_{\max T}} \cdot α_{T} \cdot f_{T} ({\dot{\bar{u}}}_{T}) |}^{\exp_{T}} > 1$
From energy:(3)
$C e (t) = max [{(\frac{E n}{E N_{max}})}_{n}^{N_{n}} + {(\frac{E t}{E T_{max}})}_{t}^{N_{t}}, \frac{E I}{E I_{m a x}}] > 1$ $C e (t) = \max [{(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}}, \frac{E I}{E I_{m a x}}] > 1$

Where,

$E I$ $E I$

Internal energy per connection element area.

$E n$ $E n$

Internal energy in the normal direction per connection element area.

$E t$ $E t$

Internal energy in the shear direction per connection element area.
A damage variable, $D$ $D$ is defined as maximum of the cumulative damage generated by relative displacement or energy:(4)
$D_{max} = max [\int_{0}^{t} ({C s (t) |}_{C s (t) > 1}) d t, \int_{0}^{t} ({C e (t) |}_{C e (t) > 1}) d t]$ $D_{\max} = \max [\int_{0}^{t} ({C s (t) |}_{C s (t) > 1}) d t, \int_{0}^{t} ({C e (t) |}_{C e (t) > 1}) d t]$

The element is deleted (or stress in local integration point is set to zero), if:(5)
$D_{max} \geq T_{max}$ $D_{\max} \geq T_{\max}$

If $T_{max}$ $T_{\max}$ is equal to default value, failure is immediate.

Otherwise, when $T_{max} > D_{max} > 0$ $T_{\max} > D_{\max} > 0$ , softening is applied (for all directions) as:(6)
$σ = σ {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$
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.