$\bar{u}_{evol_{1.0}}^{pl} = 0.85$ $\star$ CONNECTOR DAMAGE INITIATION, CRITERION=PLASTIC MOTION $< \bar{u}_{init_{0.0}}^{pl} >, 0.0$ $< \bar{u}_{init_{0.5}}^{pl} >, 0.5$ $< \bar{u}_{init_{1.0}}^{pl} >, 1.0$ $\star$ CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=LINEAR $< \bar{u}_{evol_{0.0}}^{pl} >, 0.0$ $< \bar{u}_{evol_{0.3}}^{pl} >, 0.3$ $< \bar{u}_{evol_{0.5}}^{pl} >, 0.5$ $< \bar{u}_{evol_{1.0}}^{pl} >, 1.0$ The equivalent plastic relative motion on the data lines is defined by the associated coupled plasticity definition illustrated in “Connector plastic behavior,” Section 31.2.6. For the damage evolution the postdamage-initiation equivalent plastic relative motion should be specified. The second column in all the data lines represents the mode-mix ratios as defined in “Connector plastic behavior,” Section 31.2.6. In this particular case the mode-mix ratio is $\scriptstyle ( { \frac { 2 } { \pi } } ) t a n ^ { - 1 } ( F _ { n } / F _ { s } )$ . The data point at 0.0 comes from a pure “shear” experiment, and the data point at 1.0 comes from a pure “normal” experiment. Data for the values in between come from combined “shear-normal” experiments. # Coupled rigid plasticity with force-based damage initiation and motion-based damage evolution Referring to the spot weld in Figure 31.2.7–4 and using the derived components normal and shear defined in “Defining derived components for connector elements” in “Connector functions for coupled behavior,” Section 31.2.4, an alternative way to define damage in the spot weld is to use: *PARAMETER exponent=2 $u_{fail}^{post}=0.85$ $R_n=120.0$ $R_n=115.0$ *CONNECTOR DAMAGE INITIATION, CRITERION=FORCE , 1.0 *CONNECTOR POTENTIAL normal, $$ shear, $$ ** $\sqrt{(\frac{F_n}{R_n})^2+(\frac{F_s}{R_s})^2}$ *CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=EXPONENTIAL $$ , $$ *CONNECTOR POTENTIAL 1 2 3 ** $\bar{u} = \sqrt{u_1^2 + u_2^2 + u_3^2}$ Damage will be initiated when the force magnitude defined by the first connector potential definition exceeds the specified value of 1.0. The scale factors $R _ { n }$ and $R _ { s }$ in the first potential definition are used in this case to define a force magnitude that would be 1.0 at damage initiation. A motion-based exponential decay damage evolution law is chosen. The second connector potential definition is associated with the equivalent post-initiation motion, connector damage evolution definition and defines an equivalent motion, , in the connection. When the $\bar { u } - \bar { u } _ { 0 }$ (where $\bar { u } _ { 0 }$ is at damage initiation), reaches $u _ { f a i l } ^ { p o s t }$ , ultimate failure occurs. All components (1 through 6) are affected in this case since they all ultimately contribute to the first connector potential definition (see “Defining derived components for connector elements” in “Connector functions for coupled behavior,” Section 31.2.4, for the specific definitions associated with the normal and shear derived components). # Elastic-plasticity with four competing damage mechanisms This example illustrates how to specify the contributions of multiple damage mechanisms to the overall damage effect and the components of relative motion affected by the damage evolution law. Most of the data line entries or parameters are not given for conciseness. ** first damage mechanism: force-based damage initiation ** damage variable $d^{F}$ * CONNECTOR DAMAGE INITIATION, COMPONENT=4, CRITERION=FORCE * CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=EXPONENTIAL, DEGRADATION=MAXIMUM, AFFECTED COMPONENTS 4, 6 ** ** second damage mechanism: motion-based damage initiation ** damage variable $d^{M}$ * CONNECTOR DAMAGE INITIATION, COMPONENT=4, CRITERION=MOTION * CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=LINEAR, DEGRADATION=MULTIPLICATIVE, AFFECTED COMPONENTS 1, 2, 6 ** ** third damage mechanism: plastic motion-based damage initiation ** damage variable $d^{P}$ * CONNECTOR DAMAGE INITIATION, COMPONENT=4, CRITERION=PLASTIC MOTION * CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=TABULAR, DEGRADATION=MULTIPLICATIVE, AFFECTED COMPONENTS 1, 2 ** ** fourth damage mechanism: coupled force-based damage initiation ** damage variable $d^{CF}$ * CONNECTOR DAMAGE INITIATION, CRITERION=FORCE * CONNECTOR POTENTIAL ** using components 1, 2, 3, 4, 5, 6 * CONNECTOR DAMAGE EVOLUTION, TYPE=ENERGY, DEGRADATION=MAXIMUM, AFFECTED COMPONENTS 1, 3, 4, 6 Four damage mechanisms (connector damage initiation/connector damage evolution pairs) are specified: three uncoupled and one coupled. The first line of each damage evolution definition establishes the components that will be damaged by the mechanism. The overall damage in a particular component is determined by contributions from all the mechanisms that affect that component. For example, the overall damage in component 1, $d _ { 1 }$ , is determined by the second, third, and fourth damage mechanisms as follows: $$ 1 - d _ {1} = m i n [ (1 - d ^ {M}) * (1 - d ^ {P}), (1 - d ^ {C F}) ]. $$ $d ^ { M }$ and $d ^ { P }$ use multiplicative degradation; therefore, they are multiplied first: $( 1 - d ^ { M } ) * ( 1 - d ^ { P } )$ . $d ^ { C F }$ uses maximum degradation, so $( 1 - d ^ { C F } )$ is compared to $( 1 - \dot { d } ^ { M } ) * ( 1 - \dot { d } ^ { P } )$ and the minimum value is taken. For example, assume that at a particular time $\scriptstyle t , d ^ { M } = 0 . 5 , d ^ { P } = 0 . 3$ , and $d ^ { C F } { = } 0 . 2$ and at time $t + \Delta t .$ , $d ^ { M } { = } 0 . 6$ (the only one increasing) while $d ^ { P }$ and $d ^ { C F }$ stay the same. The overall damage variable gets closer to the ultimate damage value faster when all three damage mechanisms are used than if we use only the $d ^ { M }$ mechanism: $$ 1 - d _ {1 | _ {t}} = \min [ (1 - 0. 5) * (1 - 0. 3), (1 - 0. 2) ] = 0. 1 5, $$ while $$ 1 - d _ {1 | _ {t + \Delta t}} = \min [ (1 - 0. 6) * (1 - 0. 3), (1 - 0. 2) ] = 0. 1 2. $$ Complete failure occurs when $1 - d _ { 1 }$ reaches 0.0. $F _ { i } = ( 1 - d _ { i } ) * F _ { e f f _ { i } }$ , where i refers to the $i ^ { \mathrm { t h } }$ available component of relative motion. The overall damage variables for the other components are determined as follows (based on the specified affected components for each damage evolution law): $$ \begin{array}{l} 1 - d _ {2} = (1 - d ^ {M}) * (1 - d ^ {P}) \\ 1 - d _ {3} = (1 - d ^ {C F}) \\ 1 - d _ {4} = \min [ (1 - d ^ {F}), (1 - d ^ {C F}) ] \\ 1 - d _ {5} = 1 \quad (\text {not damaged}) \\ 1 - d _ {6} = \min \left[ \left(1 - d ^ {F}\right) * \left(1 - d ^ {M}\right), \left(1 - d ^ {C F}\right) \right] \\ \end{array} $$ # Maximum degradation and choice of element removal in Abaqus/Standard You have control over how Abaqus/Standard treats connector elements with severe damage. By default, the upper bound to the overall damage variable at a material point is $D _ { m a x } = 1 . 0$ . You can reduce this upper bound as discussed in “Controlling element deletion and maximum degradation for materials with damage evolution” in “Section controls,” Section 27.1.4. By default, once the overall damage variable in at least one component reaches $D _ { m a x }$ , the connector elements are removed (deleted). See “Controlling element deletion and maximum degradation for materials with damage evolution” in “Section controls,” Section 27.1.4, for details. Once removed, connector elements offer no resistance to subsequent deformation. Alternatively, you can specify that a connector element should remain in the model even after the overall damage variable reaches $D _ { m a x }$ . In this case, once the overall damage variable reaches $D _ { m a x } .$ the element stiffness remains constant at $\left( 1 - D _ { m a x } \right)$ times the undamaged stiffness. # Viscous regularization in Abaqus/Standard Damage causes a softening response in connector elements, which often leads to convergence difficulties in an implicit code such as Abaqus/Standard. One technique for overcoming convergence difficulties is applying viscous regularization to the constitutive response by introducing a viscous damage variable, $d _ { i } ^ { v }$ , as defined by the evolution equation $$ \dot {d} _ {i} ^ {v} = \frac {1}{\mu} (d _ {i} - d _ {i} ^ {v}), $$ where $d _ { i }$ is the damage variable evaluated in the inviscid backbone model and $\mu$ is the viscosity parameter representing the relaxation time. The damaged response of the viscous material is given as $$ F _ {i} = (1 - d _ {i} ^ {v}) F _ {e f f _ {i}}. $$ As a result of viscous regularization, the damped damage variable does not obey the specified evolution law exactly (only the backbone damage variable does). Input File Usage: \*SECTION CONTROLS, NAME=name, VISCOSITY= $* { \mathrm { C O N N E C T O R ~ S E C T I O N } } , { \mathrm { C O N T R O L S } } { = } { n a m e }$ Abaqus/CAE Usage: Viscous regularization is not supported in Abaqus/CAE. # Defining connector damage behavior in linear perturbation procedures Damage cannot be initiated and damage variables do not evolve during linear perturbation analyses. Consequently, during a linear perturbation step damage is “frozen” in the state attained at the end of the previous general step. # Output The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The following variables are of particular interest when damage is defined in connectors:

CDMG	Connector overall damage variable.
CDIF	Force-based connector damage initiation variable. In addition to the usual six components associated with connector output variables, CDIF includes the scalar CDIFC, which is the damage initiation criterion value associated with a coupled force-based damage initiation criterion.
CDIM	Motion-based connector damage initiation variable. CDIM includes the scalar CDIMC, which is the damage initiation criterion value associated with a coupled motion-based damage initiation criterion.
CDIP	Plastic motion-based connector damage initiation variable. CDIP includes the scalar CDIPC, which is the damage initiation criterion value associated with a coupled plastic motion-based damage initiation criterion.
ALLDMD	Energy dissipated by damage.
ALLCD	Energy dissipated by viscous regularization.

# 31.2.8 CONNECTOR STOPS AND LOCKS Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE # References • “Connectors: overview,” Section 31.1.1 • “Connector behavior,” Section 31.2.1 • \*CONNECTOR BEHAVIOR • \*CONNECTOR LOCK • \*CONNECTOR STOP • “Defining a stop,” Section 15.17.9 of the Abaqus/CAE User’s Guide, in the HTML version of this guide • “Defining a lock,” Section 15.17.10 of the Abaqus/CAE User’s Guide, in the HTML version of this guide # Overview Connector stops and locks can be: • specified in any connector with available components of relative motion; • used to specify contact-enforced stops in individual components of relative motion; and • used to lock in position an available component of relative motion when a certain criterion is met. # Defining connector stops In the physical construction of most connectors the admissible position of one body relative to the other is limited by a certain range. In Abaqus these limits are modeled as built-in inequality constraints. You specify the available components of relative motion for which the connector stops are to be defined and the lower and upper limit values of the connector’s admissible range of positions in the directions of the components of relative motion. Input File Usage: Use the following options to define a connector stop: \*CONNECTOR BEHAVIOR, NAME=name \*CONNECTOR STOP, COMPONENT=component number lower limit, upper limit Abaqus/CAE Usage: Interaction module: connector section editor: Add→Stop: Components: component or components, Lower bound: lower limit, Upper bound: upper limit # Example Since the shock in Figure 31.2.8–1 has finite length, contact with the ends of the shock determines the upper and lower limit values of the distance that node b can be from node a. 

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extensible range 7.5


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node 12 b 1 (local orientation) a 2 node 11

Figure 31.2.8–1 Simplified connector model of a shock absorber. Assume that the maximum length of the shock is 15.0 units and that the minimum length is 7.5 units. Modify the input file presented in “Connectors: overview,” Section 31.1.1, that is associated with the example in Figure 31.2.8–1 to include the following lines: ```txt * CONNECTOR BEHAVIOR, NAME=sbehavior ... * CONNECTOR STOP, COMPONENT=1 7.5, 15.0 ``` # Defining connector locks Connector mechanisms may have devices designed to lock the connector in place once a desired configuration is achieved. For example, a revolute connection might have a falling-pin mechanism that locks the rotational motion after achieving a desired angle. A user-defined connector locking criterion can be defined for connector elements that contain available components of relative motion. You can select the component of relative motion for which the locking criterion is defined. Connector locks can be used to specify connector behavior for constrained as well as available components of relative motion. Limit values for force or moment can be specified for all components of relative motion involved in the connection. The force/moment used in evaluating the criterion is as computed in the output variable CTF. In addition, limit values can be specified for relative position corresponding to the available components of relative motion. If no other behavior is specified for an available component of relative motion, a force locking criterion will not be useful because CTF is zero. In Abaqus/Explicit you can also specify the limiting values of velocity in the available components as a criterion for locking. Velocity-dependent locking criteria are useful in modeling seatbelt systems in automobiles (see “Seat belt analysis of a simplified crash dummy,” Section 3.3.1 of the Abaqus Example Problems Guide). Moreover, the limiting values can be dependent on temperature and field variables. Field variable dependencies can be used to model time-dependent locks. If the locking criterion specified for the selected component of relative motion is met, either all components lock or a single available component locks in place. By default, all components of relative motion are locked in place upon meeting the locking criterion. In this case the connector element will be completely kinematically locked from that point on. In dynamic analyses this locking may introduce high accelerations. You can specify if only a selected component of relative motion is locked. Input File Usage: Use the following options to define a connector lock: \*CONNECTOR BEHAVIOR, NAME=name \*CONNECTOR LOCK, COMPONENT=component number, LOCK=ALL or component number Abaqus/CAE Usage: Interaction module: connector section editor: Add→Lock: Components: component or components, Lock: All or Specify component # Example In the example in Figure 31.2.8–1 assume that relative rotations about the shock will lock if the force in the local 3-direction exceeds 500.0 units of force. \*CONNECTOR BEHAVIOR, NAME=sbehavior \*CONNECTOR LOCK, COMPONENT=3, LOCK=4 , , -500.0, 500.0 # Defining connector stops and locks in linear perturbation procedures The status of connector locks or stops cannot change during a linear perturbation analysis; all connector stop and connector lock definitions remain in the same status as in the base state. # Output The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The following output variables are of particular interest when defining stops and locks in connectors: CSLST Flags for connector stops and locks. CRF Connector reaction forces/moments. At a given time and for a particular component of relative motion i, the output variable CSLSTi is 1 if the connector is actually stopped or locked in that component (stop or lock criteria are met). In that case, the correspondent CRF output variable will most likely be nonzero and equal to the actual force/moment required to enforce the stop or lock constraint. Since CRF is included in the calculation of CTF, the latter will change as well when the lock or stop is active. If the stop or lock criteria are not met at a given time for a particular component i, the output variable CSLSTi is 0 and in most cases the corespondent reaction force CRF is zero (the only possible exception is when a connector motion is also applied in that component).