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37.1.5 FRICTIONAL BEHAVIOR
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
References
• “Mechanical contact properties: overview,” Section 37.1.1
• “FRIC,” Section 1.1.8 of the Abaqus User Subroutines Reference Guide
• “FRIC_COEF,” Section 1.1.9 of the Abaqus User Subroutines Reference Guide
• “VFRIC,” Section 1.2.6 of the Abaqus User Subroutines Reference Guide
• “VFRIC_COEF,” Section 1.2.7 of the Abaqus User Subroutines Reference Guide
• “VFRICTION,” Section 1.2.8 of the Abaqus User Subroutines Reference Guide
• *FRICTION
• *CHANGE FRICTION
• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
Overview
When surfaces are in contact they usually transmit shear as well as normal forces across their interface. There is generally a relationship between these two force components. The relationship, known as the friction between the contacting bodies, is usually expressed in terms of the stresses at the interface of the bodies. The friction models available in Abaqus:
• include the classical isotropic Coulomb friction model (see “Coulomb friction,” Section 5.2.3 of the Abaqus Theory Guide), which in Abaqus:
– in its general form allows the friction coefficient to be defined in terms of slip rate, contact pressure, average surface temperature at the contact point, and field variables; and
provides the option for you to define a static and a kinetic friction coefficient with a smooth transition zone defined by an exponential curve;
• allow the introduction of a shear stress limit, , which is the maximum value of shear stress that can be carried by the interface before the surfaces begin to slide;
• include an anisotropic extension of the basic Coulomb friction model in Abaqus/Standard;
• include a model that eliminates frictional slip when surfaces are in contact;
• include a “softened” interface model for sticking friction in Abaqus/Explicit in which the shear stress is a function of elastic slip;
• can be implemented with a stiffness (penalty) method, a kinematic method (in Abaqus/Explicit), or a Lagrange multiplier method (in Abaqus/Standard), depending on the contact algorithm used; and
• can be defined in user subroutines FRIC or FRIC_COEF (in Abaqus/Standard) or VFRIC, VFRICTION, or VFRIC_COEF (in Abaqus/Explicit).
In Abaqus/Standard tangential damping forces can be introduced proportional to the relative tangential velocity, while in Abaqus/Explicit tangential damping forces can be introduced proportional to the rate of relative elastic slip between the contacting surfaces (see “Contact damping,” Section 37.1.3, for more information).
Including friction properties in a contact property definition
| Abaqus assumes by default that the interaction between contacting bodies is frictionless. You can include a friction model in a contact property definition for both surface-based contact and element-based contact. | |
| Input File Usage: | Use both of the following options for surface-based contact:*SURFACE INTERACTION, NAME=interaction_property_name*FRICTIONUse both of the following options for element-based contact in Abaqus/Standard:*INTERFACE or *GAP, ELSET=name*FRICTION |
| Abaqus/CAE Usage: | Interaction module: contact property editor: Mechanical→Tangential BehaviorElement-based contact is not supported in Abaqus/CAE. |
Changing friction properties during an analysis
The methods used to change friction properties during an analysis differ between Abaqus/Standard and Abaqus/Explicit.
Changing friction properties during an Abaqus/Standard analysis
It is possible to remove, to modify, or to add a friction model that does not involve a user subroutine to a contact property definition in any particular step of an Abaqus/Standard simulation. In some models, such as shrink-fit contact interference problems, friction should not be added until after the first steps have been completed. In other models friction might be removed or lowered to represent the introduction of a lubricant between the bodies.
You must identify which contact property definition or contact element set is being changed.
Input File Usage: Use both of the following options for surface-based contact:
*CHANGE FRICTION, INTERACTION=name
*FRICTION
Use both of the following options for element-based contact:
*CHANGE FRICTION, ELSET=name
*FRICTION
Abaqus/CAE Usage: Define a contact property with a new friction definition. Then change the contact property assigned to an interaction in a particular step.
Interaction module:
Contact property editor: Mechanical→Tangential Behavior
Interaction editor: Contact interaction property:
new_interaction_property_name
Element-based contact is not supported in Abaqus/CAE.
Specifying the time variation of the change in friction properties
You can specify an amplitude curve (see “Amplitude curves,” Section 34.1.2) to define the time variation of changes in friction coefficients and, if applicable, allowable elastic slip (see “Stiffness method for imposing frictional constraints in Abaqus/Standard,” below) throughout the step. If you do not specify an amplitude curve, changes in these friction properties are either applied immediately at the beginning of the step or ramped up linearly over the step, depending on the default amplitude variation assigned to the step (see “Defining an analysis,” Section 6.1.2), with some exceptions as described below. For many step types the default transition type is a linear ramping from old to new values, which helps avoid convergence problems that can occur upon sudden changes in friction properties.
Amplitude curves used to control variations in friction properties are subjected to the following restrictions:
• a tabular or smooth step amplitude definition must be used,
• only amplitudes with monotonically increasing values between 0.0 and 1.0 are accepted, and
• the amplitude must be defined in terms of step time and using relative magnitudes.
The value of a friction coefficient or allowable elastic slip in effect at a given time is typically equal to the value of the property at the start of the step plus the current amplitude value times the anticipated change in property value over the step. Variations in friction properties must consider the following:
• Changes in the type of frictional constraint enforcement method (penalty or Lagrange multiplier methods), changes between a “rough” friction model and a finite friction coefficient, and changes to friction properties other than the friction coefficient or allowable elastic slip always occur at the beginning of a step.
• If a friction coefficient is dependent on slip rate, contact pressure, average surface temperature at the contact point, or field variables, the estimate of the final value of the friction coefficient for the step (which is used in calculating the anticipated change in the friction coefficient over the step) assumes that the current slip rate, contact pressure, etc. will remain in effect at the end of the step.
• If a friction coefficient is changed during the first step of an analysis, its value at the start of the step is equal to zero for this calculation, regardless of the original friction definition in the model.
• Changes in allowable elastic slip always occur at the beginning of a step when an exponential-decay friction model is used or when frictional properties are changed during the first general step or during a steady-state transport step that is preceded by a step type other than steady-state transport.
Input File Usage: *CHANGE FRICTION, AMPLITUDE=name
Abaqus/CAE Usage: Time-dependent changes in friction properties are not supported in Abaqus/CAE.
Resetting the frictional properties to their default values
You can reset the frictional properties of the specified contact property definition or element set to their original values.
Input File Usage: Use either of the following options: *CHANGE FRICTION, RESET, INTERACTION=name *CHANGE FRICTION, RESET, ELSET=name In this case the *FRICTION option is not needed.
Abaqus/CAE Usage: Interaction module: Contact property editor: Mechanical→Tangential Behavior: Friction formulation: Frictionless Interaction editor: Contact interaction property: default_interaction_property_name
Changing friction properties during an Abaqus/Explicit analysis
In Abaqus/Explicit the friction definition is specified as part of the model definition for a general contact analysis and as part of the history definition for a contact pair analysis. See “Assigning contact properties for general contact in Abaqus/Explicit,” Section 36.4.3, and “Assigning contact properties for contact pairs in Abaqus/Explicit,” Section 36.5.3, for information on changing aspects of any contact property definition during an Abaqus/Explicit analysis.
Using the basic Coulomb friction model
The basic concept of the Coulomb friction model is to relate the maximum allowable frictional (shear) stress across an interface to the contact pressure between the contacting bodies. In the basic form of the Coulomb friction model, two contacting surfaces can carry shear stresses up to a certain magnitude across their interface before they start sliding relative to one another; this state is known as sticking. The Coulomb friction model defines this critical shear stress, \tau _ { c r i t } , at which sliding of the surfaces starts as a fraction of the contact pressure, p, between the surfaces ( \tau _ { c r i t } = \mu p ) . The stick/slip calculations determine when a point transitions from sticking to slipping or from slipping to sticking. The fraction, \mu , is known as the coefficient of friction.
For the case when the slave surface consists of a node-based surface, the contact pressure is equal to the normal contact force divided by the cross-sectional area at the contact node. In Abaqus/Standard the default cross-sectional area is 1.0; you can specify a cross-sectional area associated with every node in the node-based surface when the surface is defined or, alternatively, assign the same area to every node through the contact property definition. In Abaqus/Explicit the cross-sectional area is always 1.0, and you cannot change it.
The basic friction model assumes that \mu is the same in all directions (isotropic friction). For a three-dimensional simulation there are two orthogonal components of shear stress, \tau _ { 1 } and \tau _ { 2 } , along the interface between the two bodies. These components act in the local tangent directions for the contact surfaces or contact elements. The local tangent directions for contact surfaces are defined in “Contact
formulations in Abaqus/Standard,” Section 38.1.1, and those for contact elements are defined in the sections describing contact modeling with those elements.
Abaqus combines the two shear stress components into an “equivalent shear stress,” \tau _ { e q } , for the stick/slip calculations, where \tau _ { e q } = \sqrt { \tau _ { 1 } ^ { 2 } + \tau _ { 2 } ^ { 2 } } . In addition, Abaqus combines the two slip velocity components into an equivalent slip rate, \dot { \gamma } _ { e q } = \sqrt { \dot { \gamma } _ { 1 } ^ { 2 } + \dot { \gamma } _ { 2 } ^ { 2 } } . The stick/slip calculations define a surface (see Figure 37.1.5–1 for a two-dimensional representation) in the contact pressure–shear stress space along which a point transitions from sticking to slipping.
text_image
equivalent shear stress critical shear stress in default model stick region μ (constant friction coefficient) contact pressure
Figure 37.1.5–1 Slip regions for the basic Coulomb friction model.
There are two ways to define the basic Coulomb friction model in Abaqus. In the default model the friction coefficient is defined as a function of the equivalent slip rate and contact pressure. Alternatively, you can specify the static and kinetic friction coefficients directly.
Using the default model
In the default model you define the coefficient of friction directly as
\mu = \mu (\dot {\gamma} _ {e q}, p, \bar {\theta}, \bar {f} ^ {\alpha}),
where \dot { \gamma } _ { e q } is the equivalent slip rate, p is the contact pressure, \begin{array} { r } { \overline { { \theta } } = \frac { 1 } { 2 } ( \theta _ { A } + \theta _ { B } ) } \end{array} is the average temperature at the contact point, and \begin{array} { r } { \bar { f } ^ { \alpha } = \frac { 1 } { 2 } ( f _ { A } ^ { \alpha } + f _ { B } ^ { \alpha } ) } \end{array} is the average predefined field variable at the contact point. \theta _ { A } , \theta _ { B } , f _ { A } ^ { \alpha } , and f _ { B } ^ { \alpha } are the temperature and predefined field variables at points A and B on the surfaces. Point A is a node on the slave surface, and point B corresponds to the nearest point on the opposing master surface. The temperature and field variables are interpolated along the surface at location B. If the master surface consists of a rigid body, the temperature and field variable at the reference node are used.
The friction coefficient can depend on slip rate, contact pressure, temperature, and field variables. By default, it is assumed that the friction coefficients do not depend on field variables.
The coefficient of friction can be set to any nonnegative value. A zero friction coefficient means that no shear forces will develop and the contact surfaces are free to slide. You do not need to define a friction model for such a case.
Input File Usage: *FRICTION, DEPENDENCIES=n \mu , \dot { \gamma } _ { e q } , p , \bar { \theta } , \bar { f } ^ { \alpha }
Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Tangential Behavior: Friction formulation: Penalty: Friction
If necessary, toggle on Use slip-rate-dependent data, Use contactpressure-dependent data, and/or Use temperature-dependent data; and/or specify the Number of field variable dependencies in addition to slip rate, contact pressure, and temperature.
Specifying static and kinetic friction coefficients
Experimental data show that the friction coefficient that opposes the initiation of slipping from a sticking condition is different from the friction coefficient that opposes established slipping. The former is typically referred to as the “static” friction coefficient, and the latter is referred to as the “kinetic” friction coefficient. Typically, the static friction coefficient is higher than the kinetic friction coefficient.
In the default model the static friction coefficient corresponds to the value given at zero slip rate, and the kinetic friction coefficient corresponds to the value given at the highest slip rate. The transition between static and kinetic friction is defined by the values given at intermediate slip rates. In this model the static and kinetic friction coefficients can be functions of contact pressure, temperature, and field variables.
Abaqus also provides a model to specify a static and a kinetic friction coefficient directly. In this model it is assumed that the friction coefficient decays exponentially from the static value to the kinetic value according to the formula:
\mu = \mu_ {k} + (\mu_ {s} - \mu_ {k}) e ^ {- d _ {c} \dot {\gamma} _ {e q}},
where \mu _ { k } is the kinetic friction coefficient, \mu _ { s } is the static friction coefficient, d _ { c } is a user-defined decay coefficient, and \dot { \gamma } _ { e q } is the slip rate (see Oden, J. T. and J. A. C. Martins, 1985). This model can be used only with isotropic friction and does not allow dependence on contact pressure, temperature, or field variables. There are two ways of defining this model.
Providing the static, kinetic, and decay coefficients directly
You can provide the static friction coefficient, the kinetic friction coefficient, and the decay coefficient directly (see Figure 37.1.5–2).
line
| γ̇_eq | μ |
|---|---|
| 0 | μ_s |
| >0 | μ_k |
Figure 37.1.5–2 Exponential decay friction model.
Input File Usage: *FRICTION, EXPONENTIAL DECAY \mu _ { s } , \ \mu _ { k } , \ d _ { c }
Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Tangential Behavior: Friction formulation: Static-Kinetic Exponential Decay: Friction, Definition: Coefficients
Using test data to fit the exponential model
Alternatively, you can provide test data points to fit the exponential model. At least two data points must be provided. The first point represents the static coefficient of friction specified at \dot { \gamma } _ { e q } = 0 . 0 , and the second point, ( \dot { \gamma } _ { 2 } , \mu _ { 2 } ) (shown in Figure 37.1.5–3), corresponds to an experimental measurement taken at a reference slip rate \dot { \gamma } _ { 2 } . An additional data point can be specified to characterize the exponential decay. If this additional data point is omitted, Abaqus will automatically provide a third data point, ( \dot { \gamma } _ { \infty } , \mu _ { \infty } ) , to model the assumed asymptotic value of the friction coefficient at infinite velocity. In such a case \mu _ { \infty } is chosen such that ( \mu _ { 2 } - \mu _ { \infty } ) / ( \mu _ { 1 } - \mu _ { \infty } ) = 0 . 0 5 .
Input File Usage: *FRICTION, EXPONENTIAL DECAY, TEST DATA
\begin{array}{l} \mu_ {1} \\ \mu_ {2}, \dot {\gamma} _ {2} \\ \mu_ {\infty} \\ \end{array}
Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Tangential Behavior: Friction formulation: Static-Kinetic Exponential Decay: Friction, Definition: Test data
line
| γ̇eq | μ |
|---|---|
| 0.0 | μ₁ (γ̇₁ = 0, μ₁ = μₛ) |
| γ̇₂ | (γ̇₂, μ₂) |
| γ̇₃ | (γ̇₃ = γ̇∞, μ₃ = μ∞ = μₖ) |
Figure 37.1.5–3 Exponential decay friction model specified with test data points.
Using the optional shear stress limit
You can specify an optional equivalent shear stress limit, \tau _ { m a x } , so that, regardless of the magnitude of the contact pressure stress, sliding will occur if the magnitude of the equivalent shear stress, \tau _ { e q } , reaches this value (see Figure 37.1.5–4). A value of zero is not allowed.
text_image
equivalent shear stress τ_max critical shear stress in model with τ_max limit μ (constant friction coefficient) stick region contact pressure
Figure 37.1.5–4 Slip regions for the friction model with a limit on the critical shear stress.
This shear stress limit is typically introduced in cases when the contact pressure stress may become very large (as can happen in some manufacturing processes), causing the Coulomb theory to provide a critical shear stress at the interface that exceeds the yield stress in the material beneath the contact surface. A reasonable upper bound estimate for \tau _ { m a x } is \sigma _ { y } / \sqrt { 3 } . , where \sigma _ { y } is the Mises yield stress of the material adjacent to the surface; however, empirical data are the best source for \tau _ { m a x } .
Input File Usage: *FRICTION, TAUMAX=
Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Tangential Behavior: Friction formulation: Penalty or Lagrange Multiplier: Shear Stress, Shear stress limit: Specify: \tau _ { m a x }
Limitations with the shear stress limit
In Abaqus/Explicit a shear stress limit cannot be used when a contact pair uses a node-based surface as one of the surfaces.
Using the anisotropic friction model in Abaqus/Standard
The anisotropic friction model available in Abaqus/Standard allows for different friction coefficients in the two orthogonal directions on the contact surface. These orthogonal directions coincide with the local tangent directions defined in “Contact formulations in Abaqus/Standard,” Section 38.1.1; and those for contact elements are described in the sections defining contact modeling with those elements. The orientation of the local tangent directions cannot be changed.
If you indicate that the anisotropic friction model should be used, you must specify two friction coefficients, where \mu _ { 1 } is the coefficient of friction in the first local tangent direction and \mu _ { 2 } is the coefficient of friction in the second local tangent direction.
The critical shear stress surface (see Figure 37.1.5–5) is an ellipse in \tau _ { 1 } - \tau _ { 2 } space with the two extreme points being \tau _ { 1 } ^ { c r i t } = \mu _ { 1 } p and \tau _ { 2 } ^ { c r i t } = \mu _ { 2 } p . The size of this ellipse will change with the change in contact pressure between the surfaces. The direction of slip, d \gamma _ { \alpha } , is orthogonal to the critical shear stress surface.
The optional equivalent shear stress limit, \tau _ { m a x } . is applied to the scaled equivalent shear stress, \bar { \tau } _ { e q } , for anisotropic friction. See “Anisotropic friction” in “Coulomb friction,” Section 5.2.3 of the Abaqus Theory Guide, for the definition and discussion of \overline { { \tau } } _ { e q } .
The friction coefficients can depend on slip rate, contact pressure, temperature, and field variables. By default, it is assumed that the friction coefficients do not depend on field variables.
Input File Usage: *FRICTION, ANISOTROPIC, DEPENDENCIES=n
\mu_ {1}, \mu_ {2}, \dot {\gamma} _ {e q}, \pmb {p}, \bar {\theta}, \bar {f} ^ {\alpha}
Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Tangential Behavior: Friction formulation: Penalty: Friction, Directionality: Anisotropic
If necessary, toggle on Use slip-rate-dependent data, Use contactpressure-dependent data, and/or Use temperature-dependent data;
text_image
|τ₂| τ₂ᶜʳⁱᵗ = μ₂ P direction of slip dγₐ stick region τ₁ᶜʳⁱᵗ = μ₁ P |τ₁|
Figure 37.1.5–5 Critical shear stress surface for the anisotropic friction model.
and/or specify the Number of field variable dependencies in addition to slip rate, contact pressure, and temperature.
Preventing slipping regardless of contact pressure
Abaqus offers the option of specifying an infinite coefficient of friction ( ). This type of surface interaction is called “rough” friction, and with it all relative sliding motion between two contacting surfaces is prevented (except for the possibility of “elastic slip” associated with penalty enforcement) as long as the corresponding normal-direction contact constraints are active. In most cases Abaqus/Standard uses a penalty method to enforce these tangential constraints; however, a Lagrange multiplier method is used during general (non-perturbation) analysis steps if the corresponding normal-direction constraints have directly enforced “hard contact” or exponential pressure-overclosure behavior. Abaqus/Explicit uses either a kinematic or penalty method, depending on the contact formulation chosen.
Rough friction is intended for nonintermittent contact; once surfaces close and undergo rough friction, they should remain closed. Convergence difficulties may arise in Abaqus/Standard if a closed contact interface with rough friction opens, especially if large shear stresses have developed. The rough friction model is typically used in conjunction with the no separation contact pressure-overclosure relationship for motions normal to the surfaces (see “Using the no separation relationship” in “Contact pressure-overclosure relationships,” Section 37.1.2), which prohibits separation of the surfaces once they are closed.
When rough friction is used with the no separation relationship for hard contact in Abaqus/Explicit specified with the kinematic contact method, no relative motions of the surfaces will occur. For hard contact in Abaqus/Explicit specified with the penalty contact method, relative motions will be limited to the elastic slip and penetration corresponding to the inexact satisfaction of the contact constraints by the applied penalty forces. When softened tangential behavior is specified in Abaqus/Explicit (see