22.1.4 - Frictional - behavior - - 摩擦行为

ABAQUS Analysis User's Manual

22.1.4 Frictional behavior 摩擦行为

Products: ABAQUS/Standard ABAQUS/Explicit ABAQUS/CAE

References

? ? ? ? ? ?

“Mechanical contact properties: overview,” Section 22.1.1 “FRIC,” Section 25.2.8 “VFRIC,” Section 25.3.2 *FRICTION

*CHANGE FRICTION

“Creating interaction properties,” Section 15.11.2 of the ABAQUS/CAE User's Manual

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:

当发生接触时，表面通常通过接触面传播剪力和法向力。这两种力之间一般有关系。该关系也叫接触体间的摩擦，它一般表达为物体接触面应力的形式。在ABAQUS中的摩擦模型：

include the classical isotropic Coulomb friction model (see “Coulomb friction,” Section 5.2.3 of the ABAQUS Theory Manual), which in ABAQUS:

? 包括经典的各向同性库仑摩擦模型（见“Coulomb friction,” Section 5.2.3 of the ABAQUS Theory Manual），该模型在ABAQUS中：

?

?

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

? 普通式允许根据滑移率，接触压力，接触点的平均表面温度和场

变量定义摩擦系数；

? provides the option for you to define a static and a kinetic

friction coefficient with a smooth transition zone defined by an exponential curve;

? 提供选项来定义静止和运动学的摩擦系数用由指数曲线定义的平

滑转换区；

?

? ? ? ? ? ?

? ?

? ?

?

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; 允许引入剪应力极限，该应力极限是接触面在开始滑动前所能承受的最大剪应力值；

include an anisotropic extension of the basic Coulomb friction model in ABAQUS/Standard;

包括在ABAQUS/Standard中对基本库仑摩擦模型的各向异性扩展；

include a model that eliminates frictional slip when surfaces are in contact;

包括当表面接触时消除摩擦滑动的模型；

include a “softened” interface model for sticking friction in ABAQUS/Explicit in which the shear stress is a function of elastic slip;

包括在ABAQUS/Explicit中针对粘着摩擦的软接触面模型，在粘着摩擦中剪应力是弹性滑动的函数；

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 可用刚度（罚函数）法，运动学法（ABAQUS/Explicit里）或者拉格朗日乘子法（ABAQUS/Standard里）来实现，摩擦决于使用的算法。 can be defined in user subroutine FRIC (in ABAQUS/Standard) or VFRIC (in ABAQUS/Explicit for the contact pair algorithm only), which allows modeling of very general frictional surface conditions. 可在用户子程序FRIC（ABAQUS/Standard中）或VFRIC（ABAQUS/Explicit中只用于接触对算法），用户子程序容许模拟非常一般的摩擦表面条件。

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 22.1.3, for more information).

在ABAQUS/Standard中能引入切向阻尼力，该力与切向相对速度成比例。在ABAQUS/Explicit中能引入切向阻尼力，该力与接触表面间相对弹性滑移速率成比例（更多信息见“Contact damping,” Section 22.1.3）。

Including friction properties in a contact property definition 在接触属性定义里包含摩擦属性

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. ABAQUS默定接触体间相互作用为无摩擦。你可以在基于面和基于单元的接触属性定义里包含摩擦模型

Input File Usage: Use both of the following options for

surface-based contact:

*SURFACE INTERACTION,

NAME=interaction_property_name *FRICTION

Use 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:

MechanicalTangential Behavior

Element-based contact is not supported in ABAQUS/CAE.

Changing friction properties during an analysis 在分析过程中改变摩擦属性

The methods used to change friction properties during an analysis differ between ABAQUS/Standard and ABAQUS/Explicit.

在ABAQUS/Standard and ABAQUS/Explicit里在分析过程中改变摩擦属性的方法不同。

Changing friction properties during an ABAQUS/Standard analysis 在ABAQUS/Standard分析过程中改变摩擦属性

It is possible to remove, to modify, or to add a friction model 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.

在任何ABAQUS/Standard仿真分析步里可以移除，修改或添加摩擦到接触属性定义里。某些模型，比如收缩配合接触过盈问题，直到第一步完成，才能添加摩擦。在另一些模型，为了表示在物体间引入润滑剂，应该移除或减小摩擦。 You must identify which contact property definition or contact element set is being changed.

你必须确定哪种接触属性定义或接触单元集改变了。

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: MechanicalBehavior

Interaction editor: Contact interaction property: new_interaction_property_name

Element-based contact is not supported in ABAQUS/CAE.

Tangential

Specifying the time variation of the change in friction coefficients 指定改变摩擦系数的时间变化

You can use an amplitude curve (specifying a relative magnitude definition) to define the time variation of the change in friction coefficients throughout the step.

你能使用幅值曲线（指定相对大小的定义）来定义摩擦系数随分析步时间的变化。 If the friction coefficient is dependent on slip rate, contact pressure, average surface temperature at the contact point, or field variables, the current change in the friction coefficient at a material point is defined as the difference between the friction coefficient for the current slip rate, contact pressure, etc. and the friction coefficient at the end of the previous step, multiplied by the amplitude magnitude.

如果摩擦系数由滑移率，接触压力，接触点的平均表面温度或场变量决定，那么当前在材料点上改变摩擦系数定义为由当前滑移率，接触压力等决定的摩擦系数和上一分析步末的摩擦系数的差，再乘以幅值大小。

If you do not specify an amplitude curve, the change in friction coefficients is applied immediately at the beginning of the step or ramped up linearly over the step, depending on the amplitude variation assigned to the step (see “Procedures: overview,” Section 6.1.1). If the friction coefficients are changed from finite values to rough friction or from rough friction to finite values, the change is always applied immediately at the beginning of the step. Changes in any other friction properties, such as the allowable elastic slip, are also applied instantaneously at the start of the step. Use caution when changing the friction model during an analysis if the surfaces using the model are still in contact and carrying loads. Sudden changes in the frictional model in such cases may lead to convergence problems.

如果你没指定幅值曲线，那么摩擦系数的改变立刻应用在分析步的开始或者在整个分析步直线斜坡上升，取决于指派到分析步的幅度变化（见“Procedures: overview,” Section 6.1.1）。如果摩擦系数从有限数值变为粗糙摩擦或者从粗糙摩擦变为有限值，那么改变总是在分析步的开始立即应用。其它摩擦属性的变化，比如容许的弹性滑移，也在分析步的开始立即应用。如果表面仍接触且承载，那么当在分析过程中改变摩擦模型要小心。

Input File Usage: *CHANGE FRICTION, AMPLITUDE=name

coefficients can be functions of contact pressure, temperature, and field variables.

在默认模型中，静摩擦系数对应零滑移率给出的值，动摩擦系数对应最大滑移率给出的值。静动摩擦系数间的转换定义为给出的中间滑移率的值。在该模型中静动摩擦系数可以定义为接触压力，温度和场变量的函数。

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:

ABAQUS还提供直接指定动静摩擦系数的模型。在该模型中假定摩擦系数从静摩擦系数指数衰减到动摩擦系数，依据的公式：

where is the kinetic friction coefficient, is the static friction coefficient, is a user-defined decay coefficient, and 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.

其中，是动摩擦系数，是静摩擦系数，是用户定义衰减系数，是滑移率（见Oden, J. T. and J. A. C. Martins, 1985）。只有各向同性且不与接触压力，温度和场变量相关的摩擦才能使用该模型。

Providing the static, kinetic, and decay coefficients directly 直接规定静动和衰减系数

You can provide the static friction coefficient, the kinetic friction coefficient, and the decay coefficient directly (see Figure 22.1.4–2). 你能直接规定静动和衰减系数（见图Figure 22.1.4–2）

Input File Usage: *FRICTION, EXPONENTIAL DECAY

, ,

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: Static-Kinetic Exponential Decay: Friction, Definition: Coefficients

Figure 22.1.4–2 Exponential decay friction model.

Using test data to fit the exponential model 使用试验数据拟合指数模型

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 , and the second point, (, ) (shown in Figure 22.1.4–3), corresponds to an experimental measurement taken at a reference slip rate . 同样，你可以提供试验数据点来你和指数模型。最少需要提供两个数据点。第一个点表示指定在的静摩擦系数，第二点（, )（见图Figure 22.1.4–3）对应于在参考滑移率的试验测量值。

Figure 22.1.4–3 Exponential decay friction model specified with test data points.

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, (, ), to model the assumed asymptotic value of the friction coefficient at infinite velocity. In such a case is chosen such that

.

可以指定额外数据点来表征指数衰减。如果省略这些额外的数据点，ABAQUS会自动提供第三数据点(, )来模拟假定的在无限大速度的摩擦系数的渐近线值。这样，选择

使得

。

Input File Usage: *FRICTION, EXPONENTIAL DECAY, TEST DATA

,

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: Static-Kinetic Exponential Decay: Friction, Definition: Test data

Using the optional shear stress limit 使用剪应力极限选项

You can specify an optional equivalent shear stress limit, , so that, regardless of the magnitude of the contact pressure stress, sliding will occur if the magnitude of the equivalent shear stress reaches this value (see Figure 22.1.4–4). A value of zero is not allowed.

你可以指定等效剪应力极限选项，从而使得如果等效剪应力大小达到该值，不管接触压应力多大，都将发生滑移（见图Figure 22.1.4–4）。该值不允许设为零。

Figure 22.1.4–4 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

is

,

where is the Mises yield stress of the material adjacent to the surface; however, empirical data are the best source for . 为了防止当接触压应力可能变得非常大，导致库仑理论产生的接触面上的临界剪应力值超过接触面下材料的屈服应力，通常引入剪应力极限。的一个估计的合理上界是数据是

，其中

是接近表面的材料的Mises屈服应力，然而经验

最好的来源。

Input File Usage: *FRICTION, TAUMAX=

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: Penalty or Lagrange Multiplier: Shear Stress, Shear stress limit: Specify:

Limitations with the shear stress limit 剪应力极限的局限性

In ABAQUS/Explicit a shear stress limit cannot be used when a contact pair uses a node-based surface as one of the surfaces.

在ABAQUS/Explicit中若接触对用基于节点的面作为一个接触面，就不能使用剪应力极限。

Using the anisotropic friction model in ABAQUS/Standard 在ABAQUS/Standard中使用各向异性摩擦模型

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 slip directions defined in “Contact formulation for ABAQUS/Standard contact pairs,” Section 21.2.2; and those for contact elements are described in the sections defining contact modeling with those elements. The orientation of the slip directions cannot be changed.

ABAQUS/Standard中可用的各向异性摩擦模型允许在接触表面两个正交方向有不同的摩擦系数。这些正交方向与滑移方向（“Contact formulation for

ABAQUS/Standard contact pairs,” Section 21.2.2）相符；在定义接触模拟那些单元的截面里描述接触单元里的滑移方向

If you indicate that the anisotropic friction model should be used, you must specify two friction coefficients, where is the coefficient of friction in the first slip direction and is the coefficient of friction in the second slip direction.

如果你需要使用各向异性摩擦模型，你必须指定两个摩擦系数：是第一个滑移方向的摩擦系数，是第二个滑移方向的摩擦系数。

The critical shear stress surface (see Figure 22.1.4–5) is an ellipse in – space with the two extreme points being

and

. The size of this ellipse will change with the change in

contact pressure between the surfaces. The direction of slip, orthogonal to the critical shear stress surface.

, is

边界剪应力面（见图Figure 22.1.4–5）是–空间中以和

为极值点的椭圆。椭圆大小随接触面间接触压力变化而变。滑移方

向

与边界剪应力面正交。

Figure 22.1.4–5 Critical shear stress surface for the anisotropic friction model.

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.

摩擦系数可以决定于滑移率、接触压力、温度和场变量。默认情况下，假定摩擦系数不决定于场变量。

Input File Usage: *FRICTION, ANISOTROPIC, DEPENDENCIES=

,

,

, , ,

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: Penalty: Friction, Directionality: Anisotropic

If necessary, toggle on Use slip-rate-dependent data, Use contact-pressure-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.

Preventing slipping regardless of contact pressure

防止滑移，不管接触压力多大

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. ABAQUS/Standard uses Lagrange multipliers to enforce this constraint; ABAQUS/Explicit uses either a kinematic or penalty method, depending on the contact formulation chosen.

ABAQUS提供指定无穷大的摩擦系数选项（）。这种面相互作用称为“粗”摩擦，且不允许两接触面间有任何相对滑移运动。ABAQUS/Standard用拉格朗日乘子来加强这种约束；ABAQUS/Explicit用运动学或罚函数法，取决于所选接触方程。

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 22.1.2), which prohibits separation of the surfaces once they are closed.

粗摩擦计划供间歇的接触使用； 一旦两表面接触且为粗摩擦，他们应该保持接触状态。在ABAQUS/Standard里，如果一接触的粗摩擦接触面开始分开，尤其是有大剪应力时，可能会导致收敛问题。典型的，在接触面的法向运动上联合使用粗摩擦模型与不分开的接触压力-过盈关系（见“Using the no separation relationship” in “Contact pressure-overclosure relationships,” Section 22.1.2），一旦表面接触，这样做就能阻止它们再分开。

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 “Defining tangential softening in

ABAQUS/Explicit” below), the relative surface motions will be governed by the specified softening behavior.

在ABAQUS/Explicit中，当联合使用粗摩擦和硬接触、运动学接触算法和不分开关系时，接触面就不会出现相对运动。在ABAQUS/Explicit中，使用硬接触、罚函数接触算法时，相对运动将限于弹性滑移和侵彻，相当于不精确的满足应用惩罚力的接触约束要求。当在ABAQUS/Explicit中使用软切向行为时（见下面的“Defining tangential softening in ABAQUS/Explicit），指定的软行为将控制表面间的相对运动。

Input File Usage: *FRICTION, ROUGH

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction formulation: Rough

Shear stress versus elastic slip while sticking 粘着时，剪应力对弹性滑移

In some cases some incremental slip may occur even though the friction model determines that the current frictional state is “sticking.” In other words, the slope of the shear (frictional) stress versus total slip relationship may be finite while in the “sticking” state, as shown in Figure 22.1.4–6.

有时，尽管摩擦模型确定当前接触状态为“粘着”，但也可能会产生一些滑移。换句话说，在“粘着”状态，剪（摩擦）应力对总滑移量关系曲线的斜度可能是有限值，见图Figure 22.1.4–6。

Figure 22.1.4–6 Elastic slip versus shear traction relationship for sticking and slipping friction.

The relationship shown in this figure is analogous to elastic-plastic material behavior without hardening: corresponds to Young's modulus, and corresponds to yield stress; sticking friction corresponds to the elastic regime, and slipping friction corresponds to the plastic regime. A finite value of the sticking stiffness may reflect a user-specified physical behavior or may be characteristic of the constraint enforcement method.

上图显示的关系类似于没有热处理的弹塑性材料行为，相当于杨氏模量，相当于屈服应力；粘着摩擦相当于弹性状态，滑移摩擦相当于塑性状态。一个有限的粘着刚度值可能反映一中用户定义物理行为，也可能是强制约束法的特征。 Frictional constraints are enforced with a stiffness (penalty method) by default in ABAQUS/Standard and for the general contact algorithm in ABAQUS/Explicit; in this case the sticking stiffness will have a finite value. An infinite sticking stiffness, in which case the elastic slip is always zero, can be achieved with the optional Lagrange multiplier method for imposing frictional constraints in ABAQUS/Standard or with the kinematic constraint method (available only for contact pairs) in ABAQUS/Explicit. In ABAQUS/Explicit some tangential contact damping acts on the elastic slip rate by default, as discussed in “Contact damping,” Section 22.1.3. Tangential softening to reflect a physical behavior is available only in ABAQUS/Explicit.

在ABAQUS/Standard和ABAQUS/Explicit的通用接触算法里，默认了一个刚度来强加摩擦约束（罚函数法）；这样粘着刚度就有个有限值。当弹性滑移总是零时，在ABAQUS/Standard里可选择拉格朗日乘子法利用摩擦约束来获得一个有限粘着刚度值；在ABAQUS/Explicit里则用运动学约束法（只限于接触对）获得该值。在ABAQUS/Explicit中，针对弹性滑移率，默认了一些切向接触阻尼，就像“Contact damping,” Section 22.1.3中所讨论的。只在ABAQUS/Explicit里有切向软接触反映物理行为。

Defining tangential softening in ABAQUS/Explicit 在ABAQUS/Explicit里定义切向软接触

To activate softened tangential behavior in ABAQUS/Explicit, specify the slope of the shear stress versus elastic slip relationship ( in Figure 22.1.4–6). User subroutine VFRIC cannot be used in conjunction with softened tangential behavior.

要在ABAQUS/Explicit里实现切向软行为，就要指定剪应力对弹性滑移关系曲线的斜率( Figure 22.1.4–6中的）。用户子程序VFRIC不能与切向软行为共用。 Input File Usage: *FRICTION, SHEAR TRACTION SLOPE=

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: Penalty or Static-Kinetic Exponential Decay: Elastic Slip, Specify:

Stiffness method for imposing frictional constraints 强加摩擦约束的刚度法

The stiffness method used for friction in ABAQUS/Standard, with the general contact algorithm in ABAQUS/Explicit, and optionally with the contact pair method in ABAQUS/Explicit is a penalty method that permits some relative motion of the surfaces (an “elastic slip”) when they should be sticking (similar to the allowable elastic slip defined with softened tangential behavior in ABAQUS/Explicit). While the surfaces are sticking (i.e., ), the magnitude of sliding is limited to this elastic slip. ABAQUS will continually adjust the magnitude of the penalty constraint to enforce this condition.

ABAQUS/Standard、ABAQUS/Explicit的通用接触算法和ABAQUS/Explicit可选的接触对算法中摩擦的刚度法是允许应该粘着的接触面（类似于在

ABAQUS/Explicit里与软切向行为一起定义的许用弹性滑动）发生一点相对运动（“弹性滑移”）的罚函数法。当接触面是粘着的（例如）滑移的大小限于该弹性滑移。ABAQUS会调整罚函数约束的大小以增强该约束条件。

Stiffness method in ABAQUS/Standard ABAQUS/Standard中的刚度法

The stiffness method in ABAQUS/Standard requires the selection of an allowable elastic slip, . Using a large in the simulation makes convergence of the solution more rapid at the expense of solution accuracy (there is greater relative motion of the surfaces when they should be sticking). Behavior in which no slip is permitted in the sticking state is approximated more accurately by allowing only a small . If is chosen very small, convergence problems may occur; in that case, it may be better to use the Lagrange multiplier method to apply the sticking constraint (see “Lagrange multiplier method for imposing frictional constraints in ABAQUS/Standard” later in this section).

ABAQUS/Standard中的刚度法要求选择许用弹性滑移。大的使解在牺牲精度的情况下收敛的更快（接触面本应该粘着的，却有了更大的相对运动）。只容许一个小能更精确的近似那些在粘着状态不能滑动的行为。但如果非常小，就可能收敛困难，那样的话，使用拉格朗日乘子法来施加粘着约束将更好（见后文

的“Lagrange multiplier method for imposing frictional constraints in ABAQUS/Standard）。

The default value of allowable elastic slip used by ABAQUS/Standard generally works very well, providing a conservative balance between efficiency and accuracy. ABAQUS/Standard calculates as a small fraction of the “characteristic contact surface length,” , and scans all of the facets of all the slave surfaces when calculating . ABAQUS/Standard reports the value of used for each contact pair in the data (.dat) file. The allowable elastic slip is given as tolerance; the default value of

is 0.005.

, where

is the slip

在ABAQUS/Standard里许用弹性滑移的默认值通常很凑效，假如是保守的平衡效率和精度。ABAQUS/Standard计算时将它作为“接触面特征长度”的一个小分数，还在计算时扫描从面上所有的小面。ABAQUS/Standard 将接触对中用到的值报告到数据文件（.dat）里。许用弹性滑移为差，默认

值是0.005。

，其中

是滑移公

This method of calculating the allowable elastic slip is used for all analysis procedures in ABAQUS/Standard except steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1), in which the penalty constraint is based on a maximum allowable slip rate, . The maximum slip rate is calculated as

where is the angular spinning rate and is the radius of the rolling structure.

这种计算许用弹性滑移的方法适用于所有ABAQUS/Standard分析，除了稳态传送分析（“Steady-state transport analysis,” Section 6.4.1），在该分析中罚函数约束基于最大许用滑移率。最大滑移率计算式为：

其中是旋转角速率，是旋转结构的半径。

In certain situations the default value for the allowable elastic slip may not be suitable. For instance, slave surfaces defined by node-based surfaces or some contact element types, such as GAPUNI elements, have no

physical dimensions and ABAQUS/Standard cannot estimate a value of . For models containing only node-based surfaces or these types of contact elements, ABAQUS/Standard first tries to use the “characteristic contact surface length” of the other contact pairs in the model. If there are none, it calculates using all of the elements in the model and issues a warning message. If a model contains no elements for which a characteristic length can be determined (for instance, if it contains only substructures), ABAQUS/Standard has no information with which to calculate . As a result, it uses a value of 1.0 and issues a warning message. If the contact surface face dimensions vary greatly, the average value of may be unreasonable for some contact surfaces. The elastic slip should then be specified directly for the surfaces with a much smaller “characteristic face dimension.”

在一些特定情形里默认许用弹性滑移值可能不合适。比如基于节点的面的从面或一些接触单元类型，像GAPUNI单元，就没有物理尺寸，ABAQUS/Standard不能估计一个值。对于包含基于节点面或接触单元的模型， ABAQUS/Standard首先试着用模型里其它接触对的“接触面特征长度”。如果没有，它将用模型里的所有单元来计算并发出警告信息。如果模型没有单元可以确定特征长度（比如，模型只含有子结构），ABAQUS/Standard没有计算的信息。结果，它用1.0这个值并发出警告信息。如果接触面尺寸变化非常大，一些接触面的平均值可能不合理。这时候应该直接用一个小的多的“特征尺寸”为接触面指定弹性滑移。 There are two methods for modifying the allowable elastic slip. One method is to specify directly; the other is to specify the slip tolerance, . 有两种方法来修改许用弹性滑移。一种是直接指定；另一种是指定滑移公差

?

。

You can provide the absolute magnitude of directly. Specify a

reasonable value for the relative displacement that may occur before surfaces actually begin to slip. Typically, the allowable elastic slip is set to a small fraction (10–2–10–4) of a “characteristic contact surface face dimension.” In a steady-state transport analysis you can define the maximum allowable viscous slip rate, .

?

你可以直接规定的绝对大小。为接触面开始滑动前可能发生的相对位移指定一个合理值。典型的，许用弹性滑移设置为“接触面特征尺寸”的一个很小的分数（10–2–10–4）。在稳态传送分析中，你可以定义最大许用粘性滑移率。

The specified allowable elastic slip will be used only for the contact pairs referencing the contact property definition that contains the friction definition. For example, three surfaces ASURF, BSURF, and CSURF form two contact pairs that each refer to their own contact property definition, as shown below. In the DEFAULT contact property definition no value for is specified, so the allowable elastic slip used for the friction interaction between ASURF and BSURF would be the default value

. In the NONDEF

contact property definition a value of 0.1 is specified for , which will be the allowable elastic slip used for the friction interaction between CSURF and BSURF.

指定的许用弹性滑移只用于接触对，参考在接触属性里定义摩擦。例如三表面ASURF，BSURF和CSURF形成两接触对，每个接触对有各自的接触属性定义，如下所示。默认接触属性定义没给赋值，所以用于ASURF和BSURF接触摩擦属性定义的许用弹性滑动为默认值

。在NONDEF接触

属性定义里给赋值0.1，该值将成为CSURF和BSURF间摩擦接触的许用弹性滑移。

Contact Pair Contact Property ASURF, BSURF DEFAULT CSURF, BSURF NONDEF

Input File Usage: *FRICTION, ELASTIC SLIP=

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction formulation: Penalty or Static-Kinetic Exponential Decay: Elastic Slip, Absolute distance:

0.1 Alternatively, you can alter the default value of the slip tolerance, . This method of altering the default elastic slip is convenient if the goal is to increase computational efficiency, in which case a value larger than the default of 0.005 would be given, or if the goal is to increase accuracy, in which case a value smaller than the default would be given.

? 你可以改变滑移公差的默认值。这种改变默认弹性滑移的方法很方便。如果以增加计算效率为目标，该法会赋一个比默认的0.005大的值；如果以增加精度为目标，该法会赋一个比默认小的值。

?

Input File Usage: *FRICTION, SLIP TOLERANCE=

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction formulation: Penalty or Static-Kinetic

Exponential Decay: Elastic Slip, Fraction of characteristic surface dimension:

Stiffness method in ABAQUS/Explicit ABAQUS/Explicit中的刚度法

In ABAQUS/Explicit you can choose to have contact constraints for the contact pair algorithm enforced with the penalty method (see “Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4); the general contact algorithm always uses a penalty method (see “Contact formulation for general contact,” Section 21.3.4).

在ABAQUS/Explicit中，你可以为接触对法选择增强罚函数接触约束（见“Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4）。通用接触算法一般用罚函数法（见“Contact formulation for general contact,” Section 21.3.4）。

The default penalty stiffness for frictional constraints is chosen automatically by ABAQUS/Explicit and is the same as would be used for normal hard contact constraints. Softening in the normal direction does not affect the penalty stiffness used to enforce stick conditions. If tangential softening is specified (see “Defining tangential softening in ABAQUS/Explicit” above), the penalty stiffness will be equal to the value specified for the slope of the shear stress versus elastic slip relationship. You can specify a scale factor to adjust the penalty

stiffness, as discussed in “Contact controls for general contact,” Section 21.3.6, and “Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4.

ABAQUS/Explicit自动选择默认摩擦约束的罚函数刚度，且与用于法向硬接触约束的一样。法向软化不影响用于增强粘着条件的罚函数刚度。如果指定了切向软化（见上面的“Defining tangential softening in ABAQUS/Explicit），罚函数刚度等于指定的剪应力对弹性滑移关系曲线的斜率。你可以指定一个放大系数来调整罚函数刚度，讨论于“Contact controls for general contact,” Section 21.3.6, and “Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4.

Lagrange multiplier method for imposing frictional constraints in ABAQUS/Standard

ABAQUS/Standard强加摩擦约束的拉格朗日乘子法

In ABAQUS/Standard the sticking constraints at an interface between two surfaces can be enforced exactly by using the Lagrange multiplier

implementation. With this method there is no relative motion between two closed surfaces until . However, the Lagrange multipliers

increase the computational cost of the analysis by adding more degrees of freedom to the model and often by increasing the number of iterations required to obtain a converged solution. The Lagrange multiplier

formulation may even prevent convergence of the solution, especially if many points are iterating between sticking and slipping conditions. This effect can occur particularly if locally there is a strong interaction between slipping/sticking conditions and contact stresses.

在ABAQUS/Standard里两接触面的粘着约束可用拉格朗日乘子法正确实现。除非

，使用该法的两接触面间没有相对运动。然而，拉格朗日乘子法增加了

计算成本，它给模型增加了自由度，还经常增加迭代数来获得收敛解。拉格朗日乘子方程可能阻碍解的收敛，尤其是当很多点在粘着和滑移条件间迭代时。特别是当局部有滑移/粘着条件间强相互左右和接触压力时，这种影响可能发生。 Because of the added cost of using the Lagrange friction formulation, it should be used only in problems where the resolution of the stick/slip behavior is of utmost importance, such as modeling fretting between two bodies. In typical metal forming applications or for contact of rubber components, accurate resolution of the stick/slip behavior is not

important enough to justify the added costs of the Lagrange multiplier formulation.

因为使用拉格朗日摩擦方程要增加的成本，该法只用于那些分解粘着/滑移行为及其重要的问题，比如模拟两物体间的侵蚀。在典型的金属成型应用或橡胶组件

接触，精确的分解粘着/滑移行为而带来的拉格朗日乘子方程增加的成本得不偿失。

Input File Usage: *FRICTION, LAGRANGE

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction formulation: Lagrange Multiplier

Kinematic method for imposing frictional constraints in ABAQUS/Explicit 在ABAQUS/Explicit里强加摩擦约束的运动学方法

By default, the contact pair algorithm in ABAQUS/Explicit uses a kinematic method for imposing frictional constraints (see “Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4). The kinematic method applies sticking constraints in a way similar to the optional Lagrange multiplier method in ABAQUS/Standard; however, the algorithm is quite different. The value of the force required to enforce sticking at a node is first calculated using the mass associated with the node; the distance the node has slipped; the time increment; and additionally for softened contact, the current value of the elastic slip and the elastic slip versus shear stress slope. For hard contact this sticking force is that which is required to maintain the node's position on the opposite surface in the predicted configuration. For softened contact this force is consistent with the user-specified value for the slope of the shear stress versus elastic slip relationship. The sticking force for each node is calculated using the mass associated with the node, the distance the node has slipped, the shear traction-elastic slip slope (if softened contact is specified in the tangential direction), and the time increment. If the shear stress at the node calculated using this force is less than , the node is considered to be sticking and this force is applied to each surface in opposing directions. If the shear stress exceeds , the surfaces are slipping and the force corresponding to is applied. In either case the forces result in acceleration corrections tangential to the surface at the slave node and either the nodes of the master surface facet or the points on the analytical rigid surface that it contacts. ABAQUS/Explicit中的接触对算法默认使用运动学方法来强加摩擦约束（见“Contact formulation for ABAQUS/Explicit contact pairs,” Section 21.4.4）。运动学方法应用粘着约束的方法类似于ABAQUS/Standard中可选的拉格朗日乘子法；然而，算法却大不同。加强节点粘着约束所需力的值首先用节点质量、节点滑移距离、时间增量和附加的对软接触而言的当前弹性滑移值和弹性滑移对剪应力曲线斜率来计算。对于硬接触这种粘着力用来保持预测外形的对面

节点位置。对于软接触，这种力与用户定义的剪应力对弹性滑移关系曲线斜率值一致。每个节点的粘着力是用节点质量、节点滑移距离、剪应力-弹性滑移斜率（如果再切向定义了软接触）和时间增量来计算。如果用该力计算的节点剪应力小于，节点为粘着，且该力应用于每个相对方向的面上。如果剪应力超过

，表面为滑动状态，且应用相当于的力。任一情况该力都导致修正从面节点、主面接触节点或解析刚面接触点切向加速。

Defining a friction model in user subroutine FRIC or VFRIC

在用户子程序FRIC或VFRIC中定义摩擦模型

For more complex definitions of the shear stress transmission between contacting surfaces (including cases where solution-dependent state variables are needed in the formulation), ABAQUS/Standard provides user subroutine FRIC (“FRIC,” Section 25.2.8) and ABAQUS/Explicit provides user subroutine VFRIC (“VFRIC,” Section 25.3.2). You define the shear interaction between the contact surfaces in the subroutine.

对于更复杂的剪应力在接触面间传递（包括方程需要依赖解的状态变量的情况）的定义，ABAQUS/Standard提供用户子程序FRIC（“FRIC,” Section 25.2.8），ABAQUS/Explicit提供用户子程序VFRIC（“VFRIC,” Section 25.3.2）。你可以在子程序里定义两接触面间剪切相互作用。

You can indicate the number of solution-dependent state variables that will be defined in FRIC or VFRIC, n.

你可以指出在FRIC或VFRIC里定义的依赖于结果的状态变量的个数n。 You can enter data needed by the user subroutine directly in the friction definition. This method can be useful if the coefficients of friction used by the subroutine differ for various contact pairs in a model or are to be changed from analysis to analysis. They can be given as analysis data rather than incorporated directly into the subroutine, which means that the subroutine is simpler and does not have to be modified each time different coefficients are used.

你可以直接在摩擦定义里输入用户子程序需要的数据。如果模型里子程序用的摩擦系数在不同的接触对里不同或者在各个分析不同，那么此法非常有用。它们可作为分析数据给出而不是直接合并到子程序，这意味着子程序更简单且不用每当用不同摩擦系数时都修改子程序。

User subroutine VFRIC cannot be used in conjunction with softened tangential behavior or with the general contact algorithm.

Solution-dependent state variables defined in VFRIC cannot be output to the output database file (.odb) or to the results file (.fil). 用户子程序VFRIC不能与软切向行为和通用接触算法共用。VFRIC里定义的依赖解的状态变量不能输出到输出数据库文件（.odb）或结果文件（.fil）。 User subroutines FRIC and VFRIC allow for a more complex definition of frictional behavior. See “User-defined interfacial constitutive

behavior,” Section 22.1.5, for information on a more general interface for defining the complete mechanical interaction between surfaces, including the interaction in the normal direction as well as the frictional behavior in the tangential direction.

用户子程序FRIC和VFRIC允许定义更复杂的摩擦行为。见“User-defined

interfacial constitutive behavior,” Section 22.1.5，有更多信息是关于更一般定义表面间完全机械作用的接触面，包括法向和切向摩擦行为。

Input File Usage: *FRICTION, USER, DEPVAR=n, PROPERTIES=p

If p properties are specified, p data items

should be given on the data line.

ABAQUS/CAE Usage: Interaction module: contact property editor:

MechanicalTangential Behavior: Friction

formulation: User-defined, Number of state-dependent variables: n, Friction Properties

Improving ABAQUS/Standard simulations that include friction in the surface interactions

通过在面相互作用中包括摩擦来该进ABAQUS/Standard模拟

Several features of the frictional interaction of surfaces can have a strong influence on the rate of convergence in an ABAQUS/Standard simulation.

表面间摩擦作用的一些特征可以明显影响ABAQUS/Standard模拟的收敛率。 Unsymmetric terms in the system of equations 系统方程的不对称项

Friction constraints produce unsymmetric terms when the surfaces are sliding relative to each other. These terms have a strong effect on the convergence rate if frictional stresses have a substantial influence on the overall displacement field and the magnitude of the frictional stresses is highly solution dependent. ABAQUS/Standard will automatically use the unsymmetric solution scheme if or if is pressure-dependent. If desired, you can turn off the unsymmetric solution scheme; see “Matrix storage and solution scheme in ABAQUS/Standard” in “Procedures: overview,” Section 6.1.1.

当表面相对滑动时，摩擦约束产生不对称项。如果摩擦应力实质的影响总位移场且摩擦应力高度依赖解，那么这些项对收敛率有很强的影响。如果或依赖于压力，ABAQUS/Standard会自动使用不对称解决方案。若需要，你可以关掉不对称解决方案。见“Matrix storage and solution scheme in ABAQUS/Standard” in “Procedures: overview,” Section 6.1.1.

No slip occurs with rough friction; the contribution to the stiffness will be fully symmetric, and ABAQUS/Standard will use the symmetric solution scheme by default.

粗摩擦没有滑移，它对刚度的贡献是完全对称的，ABAQUS/Standard会默认使用对称解决方案。

Application of frictional constraints during changes in contact state 接触状态改变过程中应用摩擦约束

By default, ABAQUS/Standard takes into account the effect of friction at any slave node that is closed at the end of an increment.

默认的，ABAQUS/Standard考虑任一在增量步末发生接触的丛面节点的摩擦影响。

In many situations convergence can be improved if the effects of friction at a node are neglected in any increment during which the contact state changes from open to closed. Errors caused by these assumptions will generally be small; however, if the contact zone changes rapidly as the analysis progresses, these errors can be significant and will sometimes slow or prevent convergence of the solution.

很多情况下，如果在任何接触状态从开到闭的增量步中忽略节点的摩擦影响，将改善收敛性。这些假设引起的错误一般很小，然而，如果接触区迅速改变，这些错误就会显著而且有时会减慢或阻碍解的收敛。

You can force friction at a node to be neglected in increments in which contact is established by delaying the application of friction to the increment; see “Contact controls associated with tangential contact constraints” in “Common difficulties associated with contact modeling in ABAQUS/Standard,” Section 21.2.9. This setting affects all friction models, including rough friction; however, it has no effect on user subroutine FRIC, which is called whenever contact occurs at the end of an increment.

在接触建立的增量步里，你可以延迟应用摩擦到该增量步，以此来强制忽略节点摩擦。见“Contact controls associated with tangential contact

constraints” in “Common difficulties associated with contact modeling in ABAQUS/Standard,” Section 21.2.9。这样设置影响所有摩擦模型，包括粗摩擦，然而，对用户子程序FRIC没用，FRIC是在发生接触的增加步末被调用。

Heat generated by frictional interaction of surfaces 表面摩擦作用生热

In fully coupled temperature-displacement analysis, all dissipated mechanical (frictional) energy is converted to heat and distributed equally between the two surfaces by default. This behavior can be modified; for details about this and other thermal surface interactions, see “Thermal contact properties,” Section 22.2.1.

在完全耦合温度-位移分析中，所有损耗的机械（摩擦）能转化为热并默认均分到两个接触面上。可以修改这种行为。更多细节以及其它热表面相互作用见“Thermal contact properties,” Section 22.2.1。

Temperature and field-variable dependence of friction properties for structural elements

结构单元的依赖温度和场变量的摩擦属性

Temperature and field-variable distributions in beam and shell elements can generally include gradients through the cross-section of the element. Contact between these elements occurs at the reference surface; therefore, temperature and field-variable gradients in the element are not

considered when determining friction properties that depend on these variables.

温度和场变量分布于梁和壳单元能一般的包括单元截面的梯度。这些单元间的接触发生在参考面，因此，当决定摩擦属性依赖这些变量时，不考虑单元中的温度和场变量梯度

Surface interaction variables related to friction 涉及摩擦的面相互作用变量

ABAQUS provides output of the shear stresses at each slave node that uses a surface interaction model containing frictional properties. The shear stresses, CSHEAR1 and CSHEAR2, are given in the two orthogonal slip directions, which are constructed on the master surface (see “Contact formulation for ABAQUS/Standard contact pairs,” Section 21.2.2). There is only one slip direction in two-dimensional problems. Details about how to request contact surface variable output are given in “Defining contact pairs in ABAQUS/Standard,” Section 21.2.1, and “Defining contact pairs in ABAQUS/Explicit,” Section 21.4.1.

Contour plots of these variables can also be plotted in ABAQUS/CAE. ABAQUS提供输出每个包括了接触属性的表面相互作用的从面节点的剪应力。在两个正交滑移方向给出剪应力CSHEAR1和CSHEAR2，这两个方向在主面上构造（见“Contact formulation for ABAQUS/Standard contact pairs,” Section 21.2.2）。在二维问题中只有一个滑移方向。要求输出接触面变量的细节见“Defining contact pairs in ABAQUS/Standard,” Section 21.2.1, and “Defining contact pairs in ABAQUS/Explicit,” Section 21.4.1。 ABAQUS/CAE里可以为这些变量画等高线图。 Additional reference

?

Oden, J. T., and J. A. C. Martins, “Models and Computational Methods for Dynamic Friction Phenomena,” Computer Methods in Applied Mechanics and Engineering, vol. 52, pp. 527–634, 1985.

considered when determining friction properties that depend on these variables.

温度和场变量分布于梁和壳单元能一般的包括单元截面的梯度。这些单元间的接触发生在参考面，因此，当决定摩擦属性依赖这些变量时，不考虑单元中的温度和场变量梯度

Surface interaction variables related to friction 涉及摩擦的面相互作用变量

ABAQUS provides output of the shear stresses at each slave node that uses a surface interaction model containing frictional properties. The shear stresses, CSHEAR1 and CSHEAR2, are given in the two orthogonal slip directions, which are constructed on the master surface (see “Contact formulation for ABAQUS/Standard contact pairs,” Section 21.2.2). There is only one slip direction in two-dimensional problems. Details about how to request contact surface variable output are given in “Defining contact pairs in ABAQUS/Standard,” Section 21.2.1, and “Defining contact pairs in ABAQUS/Explicit,” Section 21.4.1.

Contour plots of these variables can also be plotted in ABAQUS/CAE. ABAQUS提供输出每个包括了接触属性的表面相互作用的从面节点的剪应力。在两个正交滑移方向给出剪应力CSHEAR1和CSHEAR2，这两个方向在主面上构造（见“Contact formulation for ABAQUS/Standard contact pairs,” Section 21.2.2）。在二维问题中只有一个滑移方向。要求输出接触面变量的细节见“Defining contact pairs in ABAQUS/Standard,” Section 21.2.1, and “Defining contact pairs in ABAQUS/Explicit,” Section 21.4.1。 ABAQUS/CAE里可以为这些变量画等高线图。 Additional reference

?

Oden, J. T., and J. A. C. Martins, “Models and Computational Methods for Dynamic Friction Phenomena,” Computer Methods in Applied Mechanics and Engineering, vol. 52, pp. 527–634, 1985.

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