Abaqus Explicit 接触问题

1. Abaqus/Explicit 中的接触形式

双击Interactions，出现接触形式定义。分为通用接触（General contact）、面面接触（Surface-to-Surface contact）和自接触（Self-contact）。

1. 通用接触General contact

通用接触用于为多组件，并具有复杂拓扑关系的模型建模。

General contact algorithm

?The contact domain spans multiple bodies (both rigid and deformable)

?Default domain is defined automatically via an all-inclusive element-based surface ?The method is geared toward models with multiple components and complex topology。

?Greater ease in defining contact model

2. Surface-to-Surface contact

Contact pair algorithm

?Requires user-specified pairing of individual surfaces

?Often results in more efficient analyses since contact surfaces are limited in scope 3. 自接触（Self-contact）

自接触应用于当部件发生变形时，可能导致自己的某两个或多个面发生接触的情况。如弹簧的压缩变形，橡胶条的压缩。

?容易使用?“自动接触”?节省生成模型的时间?通用接触算法一般比双面接触算法快

机械约束形式

?运动依从Kinematic contact method

（只有接触对形式可用,General contact不可用）

默认的运动接触公式达到的计算精度与接触条件相一致。在多数情况下，它工作得很好。

但是在某些情况下，如抖动接触，使用罚函数接触会更容易得到收敛的解。

不能为刚体-刚体接触建模。

?罚函数（通用接触和接触对均可使用）Penalty contact method 罚函数接触算法中接触约束的严格性低于运动学算法。

罚函数算法可以处理更一般类型的接触；比如，刚体之间的接触。因为罚函数算法在模型中引入附加刚度，该附加刚度将影响稳定时间增量。

Abaqus/Explicit自动计算由与接触力相关的侵彻距离引入的“弹簧”刚度或“罚”刚度。但是必须考虑相关的影响：应该尽量减少对稳定时间增量的影响。在所有的分析中，允许的侵彻不可以太大。

?对于接触对算法：

通过在*CONTACT CONTROLS选项指定SCALE PENALTY参数，用户可

以缩放默认的罚刚度。

?对于通用接触算法：

可以使用*CONTACT CONTROLS ASSIGNMENT, TYPE=SCALE PENAL TY 选项缩放罚刚度。

综上，多数情况下，运动依从算法和罚函数算法将得到几乎一致的结果。然而，在某些情况下，一种方法可能比另一种方法更可取。

如果需要知道kinematic algorithms和 penalty algorithms之间的区别，那就需要啃理论教材了(当然看abaqus 帮助文件也可以).

简略的说：

1）penalty algorithms（罚函数法）

在被abaqus检测到接触距离以内的节点之间定义罚刚度，进而来迭代出接触力。

在每一个时间步先检查各从节点是否穿透主面。如没有穿透则进入下一个时间步；如果穿透，则在该从节点与被穿透主面间定义罚刚度，引入一个较大的界面接触力，其大小与穿透深度、主面的刚度成正比。

2）kinematic algorithms

先在一定时间内检查所有未与主面(master surface)接触的从节点(slave node)，看是否在此时间内穿透了主面。如果存在穿透则缩小时间步，使那些穿透主面的从节点都不贯穿主面，而使其正好到达主面。在计算下一时间步之前，对所有已经与主面接触的从节点都施加约束条件，以保持从节点与主面接触而不贯穿。此外还应检查那些和主面接触的从节点所属单元是否受到拉应力作用。如受到拉应力，则施加释放条件，使从节点脱离主面。

就abaqus接触计算的初级使用来说，如果接触对中有刚体，一般用penalty algorithms；如果接触对是弹性体，有限选Kinematic algorithms. 无刚体的接触，建议直接用Kinematic algorithms试算。

总结：

1）接触面存在刚体，用penalty算法

2）接触面之间的相对运动方向平行于接触面，用penalty算法

3）弹性碰撞分析不可用hard-kinematic 算法。碰撞之中塑性变形控制的接触分析

4）penalty算法一般会减小稳定时间增量

5）接触计算与以下情况耦合时推荐penalty算法：constraint equation, multi-point constraint, tie constraint, embedded element constraint, or kinematic constraint

6）breakable bond model 模拟，必须用hard kinematic contact 。

碰撞应该用罚函数法吧，要是用运动学算法时需要划分较细的网格以避免能量的丢失。

kinematic contact要求更严格，不允许出现穿透，而penalty contact允许。默认的Penalty stiffness为弹性刚度的10%，所以如果是解决塑性变形问题的话，二者算出来的结果相差不大。

penalty对切向的相对位移的接触比较有效。

3. 初始运动学依从关系

Abaqus/Explicit不允许接触表面的初始过盈。

?接触表面的节点将被调整，删除分析之前的初始过盈：

?只移动接触表面的节点。

?对于分析过程第一个分析步定义的接触对，由于调整表面引起的位移不产生初始应变或应力。

?在随后的分析步中：

?对于接触对算法，调整将产生应变。

?对于通用接触算法，忽略初始过盈。

Contact Formulations

接触程式，包括

1. Contact discretization接触离散化

Where is the constraint applied? 接触约束应用在哪？

?Node-to-surface

?Surface-to-surface

2. Constraint enforcement 执行接触

How is the constraint enforced? 接触约束怎么执行？

?Default （Explicit）

?Direct (Lagrange multipliers) Standard

?Penalty method Standard

?Augmented Lagrange (Lagrange multipliers combined with penalty method) Standard

3. Contact tracking (relative sliding) 跟踪接触

How does the constraint evolve? 接触约束怎么发展？

?Finite sliding

?Small sliding

Contact Discretization

Node-to-surface technique: 节点和面接触

?Default method for contact pairs。接触对的默认接触定义方法。

?Not available for general contact。不适用于General contact。

?Nodes on one surface (the slave surface) contact the segments on the other surface (the master surface). 从面上的节点接触主面的面。

?Contact is enforced at discrete points (slave nodes)。在从面节点处执行接触。

从面需要划分较细的单元来提高精度和消除应力振动即消除应力噪声。Use of a “matched mesh” across the contact interface will eliminate this solution noise。Surface-to-surface technique：面面接触

?Only method for general contact，Alternative method for contact pairs

?The method considers the shape of both the master and slave surfaces.

?Contact is enforced in an average sense over the slave surface.

当面面接触用于接触对时，

contact pairs和general contact 区别不大，主要的区别在于使用方便性和性能表

现erformance。

可以看出Node-to-Surface参与接触节点个数较少。而S-to-S较多。

对于面面接触，个别点小的穿透可能会出现，但是不会发生漏检测到的主面穿透

Contact Enforcement

Hard contact:

In Abaqus/Standard, the default contact behavior is “hard” contact.

The behavior is described by a contact property known as the pressure-penetration curve (alternative behavior can be specified; discussed later).

The desired behavior (no penetration) is achieved using an enforcement method.

理想的没有穿透的接触行为可以用三种强化方法来获得。

Three numerical methods are available in Abaqus/Standard to achieve or approximate “hard” contact conditions:

Direct enforcement method:

Strict enforcement of pressure-penetration relationship using the Lagrange multiplier method. 严格压力-穿透关系，用拉格朗日乘法算法。

Pros and cons of direct enforcement：优缺点

Advantages: Accuracy—constraint is satisfied exactly.

Disadvantages:

Adds to equation solver cost. 求解代价高

Additional variable per contact constraint, which enlarges the system of equations to be solved.

Restricts elimination order for sparse solver, which can degrade performance.

Potential convergence difficulties. 潜在的收敛问题。

Abrupt change from zero contact stiffness (while contact is inactive) to infinite contact stiffness (while contact is active). 从0刚度到无穷刚度变化的剧烈。

Difficulties with overconstraints.

Overlap between contact constraints and MPC’s, etc.

Penalty method:

Approximate enforcement using penalty stiffness. 用罚刚度近似。

The penalty method is a stiff approximation of hard contact。

罚刚度可以是：

Linear (default): 线性

?Easier convergence. 容易收敛

?Better suited for problemsinvolving firm contact. 较适用于硬面接触。

?Difficult to choose stiffness appropriate for all regimes. 难以选择刚度值适用于所有情况。

Nonlinear: 非线性

?The lower initial stiffness makes it better suited for problems involving chattering. 初始的小刚度值适合于解决包括颤振的接触。

?The higher final stiffness helps reduce penetrations. 高的最终刚度降低穿透?Convergence overall can be more difficult. 收敛较困难。

Default penalty stiffness：默认的刚度值

?Abaqus 折中选择刚度：

刚度小，过度穿透。

刚度大，收敛速度；Lagrange multiplier DOF are needed to avoid ill-conditioning. ?The default penalty stiffness is based on a representative stiffness of the underlying elements.

A scale factor is applied to this representative stiffness to set the default penalty stiffness; its magnitude is higher in Abaqus/Standard than in Abaqus/Explicit.

默认刚度不合适，可以设置比例系数调节。

?Order-of-magnitude changes are recommended. 推荐

?If the scale factor > 100, Abaqus will automatically invoke a variant of the method that uses Lagrange multipliers to avoid ill-conditioning issues. 如果比例系数大于100，自动采用Lagrange multipliers 来避免病态。

罚刚度值：

?Stiff or blocky problems：硬的或短而结实的接触。

默认刚度值产生结果：比的上direct method的精确度。Requires less memory and CPU time。

?Bending-dominated problems：弯曲占主导地位的接触：

默认刚度值会被缩减但是不显著影响精确度。

Scale back two orders of magnitude without any significant loss of accuracy. Scaling back the penalty stiffness for bending-dominated problems sometimes dramatically increases the convergence rate。缩减刚度值还或许会提高收敛率。

可以看出对于Hertz接触，默认的罚刚度值和Direct Lagrange 结果最接近。Advantages:

Significantly improved convergence rates

Better equation solver performance. No Lagrange multiplier DOF unless contact stiffness is very high.

Good treatment of overlapping constraints.

Disadvantages:

Small amount of penetration. Typically insignificant

May need to adjust the penalty stiffness in some cases

使用

Used by default for each of the following: General contact、Contact pairs with the finite-sliding, surface-to-surface formulation。Automatic contact pair detection capability in Abaqus/CAE。

Augmented Lagrange method:

Approximate enforcement using penalty method with augmentation iterations; not discussed further here.

Used by default for: 3D self contact with node-to-surface discretization

Contact tracking (relative sliding)

Finite sliding

Kinematically, finite sliding of deformable bodies against each other allows the most general relative motion between the bodies:

?Arbitrarily large sliding is allowed.

?Arbitrarily large rotations and deformations of the surfaces are allowed.

?任意大的滑动和转动都允许。

接触对和通用接触中均可以使用。

Small sliding

Small sliding assumes that the relative motion per slave node remains small compared to the local curvature of the master surface.

假设从面上每个节点的相对运动相对于主面的接触段的曲率很小。

Advantage: Simplifies the numerical method. Potential for reduced cost per iteration and finding a converged solution in fewer iterations.

优点：简化数值求解过程。收敛性好。

Disadvantage: The results can be non-physical if the relative tangential motion does not remain small.

缺点：当从面节点的相对切线运动不是很小时会产生不合物理规律的错误。

Invoking small-sliding (contact pairs only): 仅在接触对中才能用。

The small sliding formulation cannot be specified with the penalty constraint formulation。不能用于Penalty contact.

如果不想考虑是否满足small-sliding的假设，则选择finite-sliding。

Analytical rigid surfaces

解析刚体面：

Analytical rigid surfaces

?Can only be used with contact pairs 只能用于接触面。

?Surface geometry of limited shape 面形状有限

Preferred method is meshing a body with deformable elements and then applying a rigid body constraint. 用可变形单元划分然后施加刚体约束。本模型中采用的就是推荐的方法。

Friction Enforcement

1. Two friction enforcement methods are implemented in Abaqus:

?Penalty method (default)

?Lagrange multiplier method Standard only

?The most common (and default) combination of model/method is isotropic Coulomb friction using the penalty method.

最常用和默认的就是各向同性库伦摩擦，用罚函数法。

2.