ProductsAbaqus/StandardAbaqus/CAE Available constraint enforcement methods in Abaqus/StandardThere are three contact constraint enforcement methods available in Abaqus/Standard:
The default constraint enforcement method depends on interaction characteristics, as follows:
You should consider the following factors when choosing the contact enforcement method:
Direct methodThe direct method strictly enforces a given pressureoverclosure behavior for each constraint, without approximation or use of augmentation iterations. Input File Usage Use both of the following options: SURFACE INTERACTION, NAME=interaction_property_name SURFACE BEHAVIOR, DIRECT Abaqus/CAE Usage Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Direct (Standard) Direct method for hard pressureoverclosure behaviorThe direct method can be used to strictly enforce a “hard” pressureoverclosure relationship. Lagrange multipliers are always used in this case. Direct method for softened pressureoverclosure relationshipsThe direct method is the only method that can be used to enforce “softened” pressureoverclosure relationships. The direct method can be used to model softened contact behavior regardless of the type of contact formulation; however, modeling stiff interface behavior with a contact formulation that is prone to overconstraints can be difficult. Lagrange multipliers are used if the slope of the pressureoverclosure curve exceeds 1000 times the underlying element stiffness (as computed by Abaqus/Standard); otherwise, the constraints are enforced without Lagrange multipliers. The usage of Lagrange multipliers, thus, depends on the contact pressure. Softened pressureoverclosure relationships are discussed in more detail in Contact pressureoverclosure relationships. Limitations of the direct methodBecause of its strict interpretation of contact constraints, hard contact simulations utilizing the direct enforcement method are susceptible to overconstraint issues. As a result, directly enforced hard contact is not available for contact pairs defined using threedimensional selfcontact with nodetosurface discretization. In this instance you can use an alternate enforcement method or the direct method with a softened pressureoverclosure relationship. You may experience similar overconstraint problems with symmetric masterslave contact pairs (see Using symmetric masterslave contact pairs to improve contact modeling). Although directly enforced hard contact is the default for these contact pairs, it is recommended that you use an alternate enforcement method or a softened contact relationship. Certain secondorder element faces do not perform well in directly enforced hard contact relationships. See Threedimensional surfaces with secondorder faces and a nodetosurface formulation for details on this issue. Penalty methodThe penalty method approximates hard pressureoverclosure behavior. With this method the contact force is proportional to the penetration distance, so some degree of penetration will occur. Advantages of the penalty method include:
Choosing a penalty methodAbaqus/Standard offers linear and nonlinear variations of the penalty method. With the linear penalty method the socalled penalty stiffness is constant, so the pressureoverclosure relationship is linear. With the nonlinear penalty method the penalty stiffness increases linearly between regions of constant low initial stiffness and constant high final stiffness, resulting in a nonlinear pressureoverclosure relationship. The default penalty method is linear. A comparison of the linear and nonlinear pressureoverclosure relationships with the default settings is shown in Figure 1. Figure 1. Comparison of linear and nonlinear pressureoverclosure relationships
in a general analysis with default settings.
Linear penalty methodWhen the linear penalty method is used, Abaqus/Standard will, by default, set the penalty stiffness to 10 times a representative underlying element stiffness. You can scale or reassign the penalty stiffness, as discussed in Modifying a linear penalty stiffness below. Contact penetrations resulting from the default penalty stiffness will not significantly affect the results in most cases; however, these penetrations can sometimes contribute to some degree of stress inaccuracy (for example, with displacementcontrolled loading and a coarse mesh). The linear penalty method is used by default for the finitesliding, surfacetosurface contact formulation. Input File Usage Use both of the following options to specify the linear penalty method: SURFACE INTERACTION, NAME=interaction_property_name SURFACE BEHAVIOR, PENALTY=LINEAR Abaqus/CAE Usage Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Penalty (Standard), Behavior: Linear Nonlinear penalty methodWith the nonlinear penalty method, the pressureoverclosure curve has four distinct regions shown in Figure 2. Figure 2. Nonlinear penalty pressureoverclosure relationship.
The low initial penalty stiffness typically results in better convergence of the Newton iterations and better robustness, while the higher final stiffness keeps the overclosure at an acceptable level as the contact pressure builds up. For linear perturbation procedures the default penalty stiffness is constant and equal to 100 times the representative underlying element stiffness, independent of the penalty stiffness used in the base state. Thus, it is equal to the constant final penalty stiffness. Input File Usage Use both of the following options to specify the nonlinear penalty method: SURFACE INTERACTION, NAME=interaction_property_name SURFACE BEHAVIOR, PENALTY=NONLINEAR Abaqus/CAE Usage Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Penalty (Standard), Behavior: Nonlinear Modifying the penalty stiffnessIf you are interested in investigating the effects of modifying the penalty stiffness, it is generally recommended that you consider orderofmagnitude changes. Increasing the penalty stiffness above the threshold value discussed above will, by default, introduce Lagrange multipliers. Modifying a linear penalty stiffnessAs part of the surface behavior definition, you can specify the linear penalty stiffness, shift the pressureoverclosure relationship by specifying the clearance at which the contact pressure is zero, or scale the default or specified penalty stiffness by a factor. Input File Usage To modify the linear penalty behavior in the surface behavior definition: SURFACE BEHAVIOR, PENALTY=LINEAR penalty stiffness, clearance at zero pressure, factor Abaqus/CAE Usage To modify the linear penalty behavior in the surface behavior definition: Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Penalty (Standard), Behavior: Linear, Stiffness value: Specify: penalty stiffness, Stiffness scale factor: factor, Clearance at which contact pressure is zero: clearance at zero pressure Modifying a nonlinear penalty stiffnessAs part of the surface behavior definition, you can specify the final nonlinear penalty stiffness, shift the pressureoverclosure relationship by specifying the clearance at which the contact pressure is zero, or scale the default or specified penalty stiffness by a factor. In addition, you can control directly the ratio of the initial to the final penalty stiffness, the scale factor, and the ratio that determines $d$ and $e$. Input File Usage To modify the nonlinear penalty behavior in the surface behavior definition: SURFACE BEHAVIOR, PENALTY=NONLINEAR final penalty stiffness, clearance at zero pressure, factor, upper quadratic limit scale factor, ratio of initial penalty stiffness over final penalty stiffness, lower quadratic limit ratio Abaqus/CAE Usage To modify the nonlinear penalty behavior in the surface behavior definition: Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Penalty (Standard), Behavior: Nonlinear, Maximum stiffness value: Specify: final penalty stiffness, Stiffness scale factor: factor, Initial/Final stiffness ratio: ratio of initial penalty stiffness over final penalty stiffness, Upper quadratic limit scale factor: upper quadratic limit scale factor, Lower quadratic limit ratio: lower quadratic limit ratio, Clearance at which contact pressure is zero: clearance at zero pressure Scaling the penalty stiffness on a stepbystep basisYou can also scale the penalty stiffness on a stepbystep basis, which will act as an additional multiplier on any scale factor specified as part of the surface behavior definition. Input File Usage To scale the penalty stiffness on a stepbystep basis: CONTACT CONTROLS, STIFFNESS SCALE FACTOR=factor Abaqus/CAE Usage To scale the penalty stiffness on a stepbystep basis: Interaction module: Abaqus/Standard contact controls editor: Augmented Lagrange: Stiffness scale factor: factor Adjusting the penalty stiffness across iterations of the first incrementIt is common to have convergence difficulties in the first increment of an analysis if the contact status changes over a large portion of the contact area upon initial loading. An approach that tends to improve convergence behavior without sacrificing accuracy is to use a reduced penalty stiffness in the early iterations of the first increment and return to the default penalty stiffness for the final iterations of the first increment and all iterations of subsequent increments. Use of a reduced penalty stiffness in early iterations helps to robustly find an approximate contact status distribution, and the goal of later iterations is to then find an accurate solution, which is reported as the converged solution for the first increment. Input File Usage To scale the penalty stiffness within the first increment: CONTACT CONTROLS, STIFFNESS SCALE FACTOR=USER ADAPTIVE Limitations of the penalty methodThe penalty method cannot be used for debonded surfaces. If the penalty method is specified, Lagrange multipliers are always used during analysis steps with the following procedures:
If surface elements have been used to define a contact surface on the exterior of a substructure (see Contact modeling if substructures are present), Abaqus/Standard interprets the underlying element stiffness to be zero. This can lead to difficulty in determining the default penalty stiffness and may cause numerical problems during the analysis. Augmented Lagrange methodThe linear penalty method can be used within an augmentation iteration scheme that drives down the penetration distance. This socalled augmented Lagrange method applies only to hard pressureoverclosure relationships. The following describes the sequence that occurs in each increment with this approach:
The augmented Lagrange method may require additional iterations in some cases; however, this approach can make the resolution of contact conditions easier and avoid problems with overconstraints, while keeping penetrations small. The augmented Lagrange method is used by default for threedimensional selfcontact using nodetosurface discretization. The default penetration tolerance is onetenth of a percent of the characteristic interface length except in the following cases:
The default penalty stiffness for the augmented Lagrange method is 1000 times the representative underlying element stiffness. Lagrange multipliers are used for the augmented Lagrange method if the penalty stiffness exceeds 1000 times the representative underlying element stiffness computed by Abaqus/Standard; otherwise, no Lagrange multipliers are used. Therefore, Lagrange multipliers are not used for the augmented Lagrange method with the default penalty stiffness. Input File Usage Use both of the following options: SURFACE INTERACTION, NAME=interaction_property_name SURFACE BEHAVIOR, AUGMENTED LAGRANGE Abaqus/CAE Usage Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Augmented Lagrange (Standard) Modifying the penetration tolerance for the augmented Lagrange methodYou can modify the penetration tolerance for the augmented Lagrange method on a stepbystep basis by specifying an absolute or relative penetration tolerance. The relative penetration tolerance is specified with respect to a characteristic length computed by Abaqus/Standard. The default penetration tolerance was discussed above. The default penetration tolerance is increased automatically if you set the penalty stiffness scale factor to a value less than 1.0 (also discussed above); however, Abaqus/Standard will not adjust any directly specified penetration tolerance. Choosing a very small penetration tolerance may result in an excessive number of augmentation iterations. Input File Usage To specify an absolute penetration tolerance: CONTACT CONTROLS, ABSOLUTE PENETRATION TOLERANCE=tolerance To specify a relative penetration tolerance: CONTACT CONTROLS, RELATIVE PENETRATION TOLERANCE=tolerance Abaqus/CAE Usage Interaction module: Abaqus/Standard contact controls editor: Augmented Lagrange: Penetration tolerance: Absolute: tolerance or Relative: tolerance Modifying the penalty stiffness for the augmented Lagrange methodAs with the penalty method, you can specify the penalty stiffness, shift the pressureoverclosure relationship by specifying the clearance at which the contact pressure is zero, or scale the default or specified penalty stiffness by a factor as part of the surface behavior definition. You can also scale the penalty stiffness on a stepbystep basis, which will act as an additional multiplier on any scale factor specified as part of the surface behavior definition. Choosing a very low penalty stiffness may result in an excessive number of augmentation iterations. Input File Usage To modify the penalty behavior in the surface behavior definition: SURFACE BEHAVIOR, AUGMENTED LAGRANGE penalty stiffness, clearance at zero pressure, factor To scale the penalty stiffness on a stepbystep basis: CONTACT CONTROLS, STIFFNESS SCALE FACTOR=factor Abaqus/CAE Usage To modify the penalty behavior in the surface behavior definition: Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Augmented Lagrange (Standard), Stiffness value: Specify: penalty stiffness, Stiffness scale factor: factor, Clearance at which contact pressure is zero: clearance at zero pressure To scale the penalty stiffness on a stepbystep basis: Interaction module: Abaqus/Standard contact controls editor: Augmented Lagrange: Stiffness scale factor: factor Modifying the number of allowed augmentations for the augmented Lagrange methodYou can define the number of allowed augmentations for the augmented Lagrange method. Input File Usage CONTROLS, PARAMETERS=TIME INCREMENTATION , , , , , , , , , , , , ${I}_{A}^{c}$ Abaqus/CAE Usage Defining the number of allowed augmentations for the augmented Lagrange method is not supported in Abaqus/CAE. Limitations of the augmented Lagrange methodThe augmented Lagrange method cannot be used for debonded surfaces. If the augmented Lagrange method is specified, Lagrange multipliers are always used during analysis steps with the following procedures:
If surface elements have been used to define a contact surface on the exterior of a substructure (see Contact modeling if substructures are present), Abaqus/Standard interprets the underlying element stiffness to be zero. This can lead to difficulty in determining the default penalty stiffness and may cause numerical problems during the analysis. Use of Lagrange multiplier degrees of freedom by the various methodsUsing Lagrange multipliers to enforce contact constraints can add significantly to the solution cost, but they also protect against numerical errors related to illconditioning that can occur if a high contact stiffness is in effect. Abaqus/Standard automatically chooses whether the constraint method makes use of Lagrange multipliers, based on a comparison of the contact stiffness to the underlying element stiffness. Table 1 summarizes the use of Lagrange multipliers. Lagrange multipliers are not used for the default contact stiffnesses associated with the penalty and augmented Lagrange approximations of hard contact. Any Lagrange multipliers associated with contact are present only for active contact constraints, so the number of equations may change as the contact status changes.
