Surface-to-Surface Contact in Abaqus

In this blog post, we’ll explore the most common way structures interact in Abaqus: Surface-to-surface contact.

Check out the picture below—it’s the “Edit Interaction” window that pops up when you’re setting up contact in Abaqus. We’ll break down each part of it so you can understand it easily.

The initial line simply names the contact, emphasizing the significance of organization in Abaqus. Naming is crucial, especially when dealing with multiple contacts in an analysis. In this case, the contact is aptly named “nut_to_washer” to clearly indicate that it involves interaction between a nut and a washer, as evident in the image below.

By the way, the image is extracted from a more extensive model representing a CrossKart’s front suspension assembly. As illustrated below, each area marked in blue and red signifies a distinct contact. The entire assembly comprises 59 contacts, each meticulously named for improved organization and clarity in handling the model.

Beneath the contact’s name, we encounter the contact definition. The default option in Abaqus is Surface-to-Surface contact, and this is the focal point of our discussion in this blog post.

Surface-to-Surface Contact

Surface-to-surface contact interactions entail the interaction between two surfaces—one deformable and the other either deformable or rigid. Abaqus categorizes contact surfaces into four types:

1. Element-based deformable and rigid surfaces.
2. Node-based deformable and rigid surfaces.
3. Analytical rigid surfaces.
4. Eulerian material surfaces for Abaqus/Explicit.

Step

The third line clarifies when this contact becomes active. In this instance, it activates during the initial step. Yet, there are scenarios where we might prefer a contact to become active at a later step in the analysis.

Master and Slave Surfaces

These are the surfaces involved in the contact interaction. Abaqus/Standard enforces the following rules related to the assignment of the master and slave roles for contact surfaces:

• Analytical rigid surfaces and rigid-element-based surfaces must always be the master surface.
• A node-based surface can act only as a slave surface and always uses node-to-surface contact.
• Slave surfaces must always be attached to deformable bodies or deformable bodies defined as rigid.
• Both surfaces in a contact pair cannot be rigid surfaces with the exception of deformable surfaces defined as rigid.

Best practices to define Master and Slave Surfaces

When both surfaces in a contact pair are element-based and attached to either deformable bodies or deformable bodies defined as rigid, you have to choose which surface will be the slave surface and which will be the master surface. This choice is particularly important for node-to-surface contact.

Importance of Surface Size in Master-Slave Relationship

Generally, if a smaller surface contacts a larger surface, it is best to choose the smaller surface as the slave surface.

Considerations for Comparable Stiffness Structures

If that distinction cannot be made, the master surface should be chosen as the surface of the stiffer body or as the surface with the coarser mesh if the two surfaces are on structures with comparable stiffnesses. The stiffness of the structure and not just the material should be considered when choosing the master and slave surface. For example, a thin sheet of metal may be less stiff than a larger block of rubber even though the steel has a larger modulus than the rubber material. If the stiffness and mesh density are the same on both surfaces, the preferred choice is not always obvious.

Master/Slave Formulation in Node-to-Surface Contact Pairs

In master/slave formulation of contact pairs, slave nodes can’t penetrate master surface, but nodes belonging to master surface can penetrate slave surface. That’s why one should select the coarser mesh as the master surface. As you can see in the image below, if the opposite is made, that is, if the slave surface is the one with the coarser mesh, there will be too much penetration.

Impact of Role Assignment in Surface-to-Surface Contact Formulation

The choice of master and slave roles typically has much less effect on the results with a surface-to-surface contact formulation than with a node-to-surface contact formulation. However, the assignment of master and slave roles can have a significant effect on performance with surface-to-surface contact if the two surfaces have dissimilar mesh refinement; the solution can become quite expensive if the slave surface is much coarser than the master surface.

Sliding Formulation

There are two sliding formulation options: finite sliding and small sliding. These options represent tracking approaches, essentially outlining how the algorithm monitors the presence or absence of contact between surfaces.

Finite Sliding

The finite-sliding tracking approach allows for arbitrary separation, sliding, and rotation of the surfaces.

Consider the case shown in the figure below, with surface ASURF acting as the slave surface to surface BSURF in a finite-sliding, node-to-surface contact pair.

In this example slave node 101 may come into contact anywhere along the master surface BSURF. While in contact, it is constrained to slide along BSURF, irrespective of the orientation and deformation of this surface. This behavior is possible because Abaqus/Standard tracks the position of node 101 relative to the master surface BSURF as the bodies deform. The figure below shows the possible evolution of the contact between node 101 and its master surface BSURF.

Node 101 is in contact with the element face with end nodes 201 and 202 at time. The load transfer at this time occurs between node 101 and nodes 201 and 202 only. Later on, at time, node 101 may find itself in contact with the element face with end nodes 501 and 502. Then the load transfer will occur between node 101 and nodes 501 and 502.

Small-sliding tracking approach

For a large class of contact problems, the general tracking of the finite-sliding approach is unnecessary, even though geometric nonlinearity may need to be considered. Abaqus/Standard provides a small-sliding tracking approach for such problems. For geometrically nonlinear analyses this formulation assumes that the surfaces may undergo arbitrarily large rotations but that a slave node will interact with the same local area of the master surface throughout the analysis.

For geometrically linear analyses the small-sliding approach reduces to an infinitesimal-sliding and rotation approach, in which it is assumed that both the relative motion of the surfaces and the absolute motion of the contacting bodies are small.

Since for the small-sliding tracking approach Abaqus/Standard does not have to monitor slave nodes for possible contact along the entire master surface, small-sliding contact is generally less expensive computationally than finite-sliding contact. The cost savings are often most dramatic in three-dimensional contact problems.

Discretization method

Abaqus/Standard applies conditional constraints at various locations on interacting surfaces to simulate contact conditions. The locations and conditions of these constraints depend on the contact discretization used in the overall contact formulation. Abaqus/Standard offers two contact discretization options: a traditional “node-to-surface” discretization and a true “surface-to-surface” discretization.

Node-to-surface contact discretization

With traditional node-to-surface discretization the contact conditions are established such that each “slave” node on one side of a contact interface effectively interacts with a point of projection on the “master” surface on the opposite side of the contact interface (see below). Thus, each contact condition involves a single slave node and a group of nearby master nodes from which values are interpolated to the projection point.

Traditional node-to-surface discretization has the following characteristics:

• The slave nodes are constrained not to penetrate into the master surface; however, the nodes of the master surface can, in principle, penetrate into the slave surface (for example, see the case on the upper-right of the figure below).

• The contact direction is based on the normal of the master surface.
• The only information needed for the slave surface is the location and surface area associated with each node; the direction of the slave surface normal and slave surface curvature are not relevant. Thus, the slave surface can be defined as a group of nodes—a node-based surface.
• Node-to-surface discretization is available even if a node-based surface is not used in a contact pair definition.

Surface-to-surface contact discretization

Surface-to-surface discretization considers the shape of both the slave and master surfaces in the region of contact constraints. It has has the following key characteristics:

• The surface-to-surface formulation enforces contact conditions in an average sense over regions nearby slave nodes rather than only at individual slave nodes. The averaging regions are approximately centered on slave nodes, so each contact constraint will predominantly consider one slave node but will also consider adjacent slave nodes. Some penetration may be observed at individual nodes; however, large, undetected penetrations of master nodes into the slave surface do not occur with this discretization. The last figure shown compares contact enforcement for node-to-surface and surface-to-surface contact for an example with dissimilar mesh refinement on the contacting bodies.
• The contact direction is based on an average normal of the slave surface in the region surrounding a slave node.
• Surface-to-surface discretization is not applicable if a node-based surface is used in the contact pair definition.

Contact Interaction Property

You might have observed that we’ve skipped certain contact options to keep this blog post concise. To ensure efficiency, we’ll concentrate on the most crucial ones. If you’re interested in the ones we’ve skipped, you can explore the Abaqus Analysis User’s Guide for more details.

Moving on, the next aspect to define is the contact interaction property, prompting the appearance of another window when specified.

The initial detail to establish is the name, adhering to the principle mentioned earlier – maintain descriptiveness for clarity in your model.

Once again, there are numerous options available, but for the sake of practicality, we will focus on the most significant ones commonly encountered in structural analyses.

Contact Property Options

There are three dropdown lists labeled Mechanical, Thermal, and Electrical. Let’s summarize what each of these options encompasses:

• Mechanical Contact Properties: This is the most crucial category for structural analysis. Typically, it’s the sole set of properties defined. Within this category, you can specify the friction model, determining the force resisting relative tangential motion between surfaces. Additionally, you can define the normal behavior between surfaces, a topic we’ll explore in more detail shortly.
• Thermal Contact Properties: In this category, you can define thermal conductance to simulate conductive heat transfer between surfaces. Furthermore, you have the capability to consider radiative heat transfer between surfaces when they are separated by a narrow gap.
• Electrical Contact Properties: This category allows you to model electrical conduction between two bodies. However, this property is less frequently used in structural analysis models.

Now, let’s delve into more details about the Mechanical Contact Properties. Clicking on this dropdown list reveals the following options.

We will now delve into more detailed discussions about the first two options: Tangential and Normal Behaviors. While the other options are important, they are less commonly utilized. If you are interested in exploring the less frequently used options, refer to the Abaqus Analysis User’s Guide for further information.

Tangential Behavior

Upon selecting Tangential Behavior from the dropdown menu, the following options become available:

The initial option is the Friction Formulation, with the available choices illustrated in the image below:

Frictionless

By default, Abaqus assumes that contact between surfaces is frictionless. In other words, if you don’t define any tangential behavior, Abaqus will consider that there’s no friction at all, leading to the absence of tangential forces.

Rough

The contrasting option to frictionless is “Rough,” which is the fourth option in the list. Abaqus provides this choice to specify an infinite coefficient of friction. This type of surface interaction effectively prevents all relative sliding motion between two contacting surfaces.

Penalty and Lagrange Multiplier

You can incorporate a friction model as part of a surface interaction definition, recognizing that surfaces in contact typically transmit both shear and normal forces across their interface. The relationship between these force components, known as friction between the contacting bodies, is typically expressed in terms of stresses at the interface.

As depicted in the image above, the static friction coefficient is set at 0.2, a standard value for friction between two steel surfaces. This coefficient implies that the maximum tangential force can reach 20% of the normal force before slipping occurs.

When defining a static friction coefficient, there are two contact formulations available: Penalty and Lagrange Multiplier.

• The Penalty method allows for some relative motion of the surfaces (an “elastic slip”) when they should be sticking. While the surfaces are sticking (i.e., when shear stress is less than the maximum allowed shear stress, calculated as normal stress multiplied by the coefficient of friction), the sliding magnitude is restricted to this elastic slip. Abaqus continuously adjusts the penalty constraint magnitude to enforce this condition.

• In Abaqus/Standard, sticking constraints at the interface between two surfaces can be precisely enforced using the Lagrange multiplier implementation. With this method, there is no relative motion between two closed surfaces until the shear stress equals the maximum allowed shear stress. However, the use of Lagrange multipliers increases the computational cost of the analysis by introducing more degrees of freedom to the model and often requiring more iterations to achieve a converged solution.

Static-Kinetic Exponential Decay

The Static-Kinetic Exponential Decay model operates by having the friction coefficient start at its highest value during the initial phase (static friction) and then gradually decrease as motion occurs, reaching a lower value (kinetic friction). This model allows for the specification of distinct static and kinetic friction coefficients with a smooth transition zone defined by an exponential curve.

User-defined friction model

You can define the shear stress between contacting surfaces through a user subroutine when the friction behavior provided by Abaqus is not sufficient. The shear stress can be defined as a function of a number of variables such as slip, slip rate, temperature, and field variables. You can also introduce a number of solution-dependent state variables that you can update and use within the friction user subroutines. You can declare a number of properties or constants associated with your friction model and use these values in the user subroutine.

Normal Behavior

When the normal behavior is selected in the contact property options, the “Edit Contact Property” window appears as depicted in the image below:

Pressure-Overclosure

The initial option that appears is Pressure-Overclosure. Clicking on the dropdown menu reveals the following options:

Let’s discuss below about each one of these options:

“Hard” Contact Relationship

The most common contact pressure-overclosure relationship is shown in the figure below, although the zero-penetration condition may or may not be strictly enforced depending on the constraint enforcement method used (the constraint enforcement methods later). When surfaces are in contact, any contact pressure can be transmitted between them. The surfaces separate if the contact pressure reduces to zero. Separated surfaces come into contact when the clearance between them reduces to zero.

“Softened” Contact Relationship

Three types of “softened” contact relationships are available in Abaqus. The pressure-overclosure relationship can be prescribed by using a linear law, a tabular piecewise-linear law, or an exponential law (in Abaqus/Explicit available only with the contact pair algorithm).

• Linear: a “softened” contact relationship in which the contact pressure is a linear function of the clearance between the surfaces.
• Exponential: a “softened” contact relationship in which the contact pressure is an exponential function of the clearance between the surfaces (in Abaqus/Explicit this relationship is available only for the contact pair algorithm);
• Tabular: a “softened” contact relationship in which a tabular pressure-overclosure curve is constructed by progressively scaling the default penalty stiffness (available only for general contact in Abaqus/Explicit);
• Scale Factor: An alternative piecewise linear tabular pressure-overclosure relationship can be constructed by geometrically scaling the default contact stiffness. This model provides a simple interface to increase the default contact stiffness when a critical penetration is exceeded.

Constraint enforcement method

There are three contact constraint enforcement methods available in Abaqus/Standard:

• The direct method attempts to strictly enforce a given pressure-overclosure behavior per constraint, without approximation or use of augmentation iterations.
• The penalty method is a stiff approximation of hard contact.
• The augmented Lagrange method uses the same kind of stiff approximation as the penalty method, but also uses augmentation iterations to improve the accuracy of the approximation.

The default constraint enforcement method depends on interaction characteristics, as follows:

• The penalty method is used by default for finite-sliding, surface-to-surface contact (including general contact) if a “hard” pressure-overclosure relationship is in effect.
• The augmented Lagrange method is used by default for three-dimensional self-contact with node-to-surface discretization if a “hard” pressure-overclosure relationship is in effect.
• The direct method is the default in all other cases.

You should consider the following factors when choosing the contact enforcement method:

• The direct method must be used for contact pairs with a “softened” pressure-overclosure relationship.
• The direct method strictly enforces the specified pressure-overclosure behavior consistent with the constraint formulation.
• The penalty or augmented Lagrange constraint enforcement methods sometimes provide more efficient solutions (generally due to reduced calculation costs per iteration and a lower number of overall iterations per analysis) at some (typically small) sacrifice in solution accuracy.
• Over constraints due to overlapping contact definitions or the combination of contact and other constraint types should be avoided for directly enforced hard contact.

Direct Method

The direct method strictly enforces a given pressure-overclosure behavior for each constraint, without approximation or use of augmentation iterations.

Because of its strict interpretation of contact constraints, hard contact simulations utilizing the direct enforcement method are susceptible to over constraint issues. As a result, directly enforced hard contact is not available for contact pairs defined using three-dimensional self-contact with node-to-surface discretization. In this instance you can use an alternate enforcement method or the direct method with a softened pressure-overclosure relationship.

Penalty Method

The penalty method approximates hard pressure-overclosure 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:

• Numerical softening associated with the penalty method can mitigate overconstraint issues and reduce the number of iterations required in an analysis.
• The penalty method can be implemented such that no Lagrange multipliers are used, which allows for improved solver efficiency.

Augmented Lagrange method

The linear penalty method can be used within an augmentation iteration scheme that drives down the penetration distance. This so-called augmented Lagrange method applies only to hard pressure-overclosure relationships. The following describes the sequence that occurs in each increment with this approach:

1. Abaqus/Standard finds a converged solution with the penalty method.

• If a slave node penetrates the master surface by more than a specified penetration tolerance, the contact pressure is “augmented” and another series of iterations is executed until convergence is once again achieved.

• Abaqus/Standard continues to augment the contact pressure and find the corresponding converged solution until the actual penetration is less than the penetration tolerance.

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 over constraints, while keeping penetrations small.

Conclusion

In summary, this blog post explores key aspects of surface-to-surface contact in Abaqus, emphasizing the importance of organized contact naming and providing insights into master-slave roles, sliding formulations, and discretization methods. The discussion covers the complexities of master-slave surface selection, with considerations for size, stiffness, and mesh density.

The post delves into mechanical contact properties, detailing options for tangential behavior (friction models) and normal behavior (contact relationships). Constraint enforcement methods—direct, penalty, and augmented Lagrange—are introduced, with considerations for their use based on specific scenarios.

The blog also briefly touches on contact interaction properties, focusing on mechanical properties and mentioning thermal and electrical considerations. The comprehensive coverage, accompanied by practical examples and visual aids, equips readers with a solid understanding of surface-to-surface contact in Abaqus for effective use in structural analyses.

SIMULIA – How-to Tutorial for Abaqus | Modeling Contact using Contact Pairs

Dassault Systèmes Simulia offers an outstanding tutorial on the intricacies of contact in their YouTube channel. The comprehensive video can be found below:

Learn More

Understanding constraints in a model is crucial, and Surface-Based Coupling Constraints in Abaqus are key. Explore more in our blog post. Click here to read.

Explore advanced topics not covered in this post by visiting the Abaqus Analysis User’s Manual. Enhance your knowledge further.