Contact Formulations in Abaqus/Standard

With traditional node-to-surface discretization the contact conditions are established such that each “secondary” node on one side of a contact interface effectively interacts with a point of projection on the “main” surface on the opposite side of the contact interface (see Figure 1). Thus, each contact condition involves a single secondary node and a group of nearby main nodes from which values are interpolated to the projection point.

Node-to-surface contact discretization.

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

• The secondary nodes are constrained not to penetrate into the main surface; however, the nodes of the main surface can, in principle, penetrate into the secondary surface (for example, see the case on the upper-right of Figure 2).

  Comparison of contact enforcement for different main-secondary surface assignments with node-to-surface and surface-to-surface contact discretizations.
  
  

• The contact direction is based on the normal of the main surface.

• The only information needed for the secondary surface is the location and surface area associated with each node; the direction of the secondary surface normal and secondary surface curvature are not relevant. Thus, the secondary 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 discretization considers the shape of both the secondary and main surfaces in the region of contact constraints. Surface-to-surface discretization has the following key characteristics:

• The surface-to-surface formulation enforces contact conditions in an average sense over regions nearby secondary nodes rather than only at individual secondary nodes. The averaging regions are approximately centered on secondary nodes, so each contact constraint will predominantly consider one secondary node but will also consider adjacent secondary nodes. Some penetration may be observed at individual nodes; however, large, undetected penetrations of main nodes into the secondary surface do not occur with this discretization. Figure 2 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 secondary surface in the region surrounding a secondary node.

• Surface-to-surface discretization is not applicable if a node-based surface is used in the contact pair definition.

In general, surface-to-surface discretization provides more accurate stress and pressure results than node-to-surface discretization if the surface geometry is reasonably well represented by the contact surfaces. Figure 3 shows an example of improved contact pressure accuracy with surface-to-surface contact compared to node-to-surface contact.

Comparison of contact pressure accuracy for node-to-surface and surface-to-surface contact discretizations.

Since node-to-surface discretization simply resists penetrations of secondary nodes into the main surface, forces tend to concentrate at these secondary nodes. This concentration leads to spikes and valleys in the distribution of pressure across the surface. Surface-to-surface discretization resists penetrations in an average sense over finite regions of the secondary surface, which has a smoothing effect. As the mesh is refined, the discrepancies between the discretizations lessen, but for a given mesh refinement the surface-to-surface approach tends to provide more accurate stresses.

Contact using surface-to-surface discretization is also less sensitive to main and secondary surface designations than node-to-surface contact (see Choosing the Main and Secondary Surface Roles in a Two-Surface Contact Pair below). Figure 4 shows a simple model involving two blocks with dissimilar mesh densities.

Test model for comparison of different main and secondary surface designations.

The bottom block is fixed to the ground, and a uniform pressure of 100 Pa is applied to the top face of the top block. Analytically, the top block should exert a uniform pressure of 100 Pa on the bottom block across the entire contact interface. Table 1 compares the Abaqus analysis results for different contact discretizations and secondary surface designations.

If the surface geometry is not well-represented due to the use of a coarse mesh, significant inaccuracies can exist regardless of whether surface-to-surface contact or node-to-surface contact is used. In some cases surface smoothing techniques available for surface-to-surface contact can significantly improve solutions obtained with a coarse mesh. See Smoothing Contact Surfaces in Abaqus/Standard for a discussion of surface smoothing options for surface-to-surface contact.

Surface-to-surface discretization generally involves more nodes per constraint and can, therefore, increase solution cost. In most applications the extra cost is fairly small, but the cost can become significant in some cases. The following factors (especially in combination) can lead to surface-to-surface contact being costly:

• A large fraction of the model is involved in contact.

• The main surface is more refined than the secondary surface.

• Multiple layers of shells are involved in contact, such that the main surface of one contact pair acts as the secondary surface of another contact pair.

The surface-to-surface formulation is primarily intended for common situations in which normal directions of contacting surfaces are approximately opposite. The node-to-surface contact formulation is often preferable for treating contact involving feature edges or corners if the respective secondary and main facet normal directions are not approximately opposite in the active contact region.

Finite-sliding contact is the most general tracking approach and allows for arbitrary relative separation, sliding, and rotation of the contacting surfaces. For finite-sliding contact the connectivity of the currently active contact constraints changes upon relative tangential motion of the contacting surfaces. For a detailed description of how Abaqus/Standard calculates finite-sliding contact, see Using the Finite-Sliding Tracking Approach later in this section.

Small-sliding contact assumes that there will be relatively little sliding of one surface along the other and is based on linearized approximations of the main surface per constraint. The groups of nodes involved with individual contact constraints are fixed throughout the analysis for small-sliding contact, although the active/inactive status of these constraints typically can change during the analysis. You should consider using small-sliding contact when the approximations are reasonable, due to computational savings and added robustness. For a detailed description of how Abaqus/Standard calculates small-sliding contact, see Using the Small-Sliding Tracking Approach later in this section.

Most contact formulations will account for the surface thickness of a shell when calculating contact constraints. However, the finite-sliding, node-to-surface formulation will not account for shell thicknesses. These calculations are discussed in more detail in Accounting for Shell and Membrane Thickness.

Self-contact is typically the result of large deformation in a model. It is often difficult to predict which regions will be involved in the contact or how they will move relative to each other. Therefore, self-contact cannot use the small-sliding tracking approach.

Doubled-sided contact surfaces based on shell-like elements are allowed to act as secondary and/or main surfaces for the surface-to-surface contact formulation by default and are allowed to act as the secondary surface for the node-to-surface contact formulation. For a shell-like surface to act as the main surface for the surface-to-surface formulation with the optional state-based tracking algorithm (see Path-Based Versus State-Based Tracking Algorithms below) or for the node-to-surface contact formulation, the surface must be defined as single-sided (see Defining Single-Sided Surfaces and Orientation Considerations for Shell-Like Surfaces for more information).

When using node-to-surface discretization, corners or small protrusions of a jagged main surface are allowed to penetrate the spaces between nodes in the node-based surface. It is sometimes possible for a secondary node sliding along the main surface to snag on these corners. Therefore, Abaqus/Standard automatically smooths the main surface for contact calculations utilizing node-to-surface discretization to minimize this phenomenon. The details are discussed further in Smoothing Main Surfaces for the Finite-Sliding, Node-to-Surface Formulation later in this section.

No surface smoothing occurs by default when using surface-to-surface discretization. Surface-to-surface discretization considers contact conditions in an average sense over a finite region, which tends to alleviate problems associated with small protrusions of the main surface penetrating the secondary surface and introduces some inherent smoothing characteristics at the constraint level. However, this inherent smoothing typically does not significantly mitigate errors associated with poor geometric representations of curved surfaces when a relatively coarse mesh is used. In some cases nondefault circumferential or spherical surface smoothing methods available for surface-to-surface contact can significantly improve solutions obtained with a coarse mesh (see Smoothing Contact Surfaces in Abaqus/Standard).

In many cases Abaqus/Standard strictly enforces the contact constraints discussed previously by default. However, strict enforcement of contact constraints can sometimes lead to overconstraint issues (for example, see Overconstraint Checks) or convergence difficulty. To address these issues and allow for decreased solution cost with typically minimal sacrifice to solution accuracy, Abaqus/Standard also provides penalty-based constraint enforcement methods. The numerical constraint enforcement methods (and defaults) are discussed in detail in Contact Constraint Enforcement Methods in Abaqus/Standard.

Based on Newton's third law of motion, contact forces should be self-equilibrating; that is, the net contact forces acting on the respective surfaces for each active contact constraint should be equal and opposite and effectively act through a common point. Contact constraints based on surface-to-surface contact discretization always exhibit this characteristic. Contact constraints based on node-to-surface discretization always generate zero net force, but under certain circumstances can generate a net moment in the numerical solution. Frictional forces associated with node-to-surface contact constraints will generate net moment if an offset exists between the respective reference surfaces. The following factors can contribute to a normal-direction offset between nodes of respective contact surfaces while contact constraints are active:

• The presence of a softened pressure-versus-overclosure behavior (due to a user-specified, softened pressure-overclosure model or use of a constraint enforcement method, such as the penalty method, that exhibits numerical softening.

• Contact calculations accounting for shell or membrane thicknesses (which is not allowed with the finite-sliding, node-to-surface formulation).

• User-specified initial contact clearances (see Additional Contact Initialization Options for Small-Sliding Contact in Abaqus/Standard).

• Various usages of special-purpose contact elements, such as tube-to-tube contact elements (see Contact Modeling with Elements and Tube-to-Tube Contact Elements), result in some normal distance between nodes that interact with each other.

While undesirable, the net moment that sometimes occurs with node-to-surface contact constraints is typically not significantly detrimental to the analysis results.

There is no easy way to predict which contact discretization method will result in lower overall solution cost. Basic trends include:

• Node-to-surface contact discretization tends to be less costly per iteration than surface-to-surface contact discretization (because surface-to-surface contact discretization generally involves more nodes per constraint).

• Contact conditions with finite-sliding contact tend to converge in fewer iterations with surface-to-surface contact discretization than with node-to-surface contact discretization (because surface-to-surface contact discretization has more continuous behavior upon sliding).

Consider the case shown in Figure 5, with surface ASURF acting as the secondary surface to surface BSURF in a finite-sliding, node-to-surface contact pair.

Contacting bodies.

In this example secondary node 101 may come into contact anywhere along the main 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 main surface BSURF as the bodies deform. Figure 6 shows the possible evolution of the contact between node 101 and its main surface BSURF.

Trajectory of node 101 in finite-sliding contact.

Node 101 is in contact with the element face with end nodes 201 and 202 at time $t_1$. The load transfer at this time occurs between node 101 and nodes 201 and 202 only. Later on, at time $t_2$, 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.

Brief descriptions of the tracking algorithms available in Abaqus/Standard are provided below so that you can be aware of their characteristics and available options.

The finite-sliding, node-to-surface contact formulation requires that main surfaces have continuous surface normals at all points. Convergence problems can result if main surfaces that do not have continuous surface normals are used in finite-sliding, node-to-surface contact analyses; secondary nodes tend to get “stuck” at points where the main surface normals are discontinuous. Abaqus/Standard automatically smooths the surface normals of element-based main surfaces (see Smoothing Deformable Main Surfaces and Rigid Surfaces Defined with Rigid Elements below) used in finite-sliding, node-to-surface contact simulations, including those modeled with slide lines. You are expected to create smooth analytical rigid surfaces (see Analytical Rigid Surface Definition). No such smoothing of main surface normals is needed with the finite-sliding, surface-to-surface formulation.

Smoothing Deformable Main Surfaces and Rigid Surfaces Defined with Rigid Elements

For finite-sliding, node-to-surface contact simulations with planar or axisymmetric deformable main surfaces, Abaqus/Standard will smooth any discontinuous transitions between two first-order element faces with parabolic curves. Discontinuous transitions between two second-order element faces are smoothed with cubic curves connecting two points located on the element's faces. This smoothing is shown in Figure 7 for first-order elements (linear segments) and in Figure 8 for second-order elements (parabolic segments). For finite-sliding, node-to-surface simulations with three-dimensional deformable main surfaces and rigid main surfaces using rigid elements, Abaqus/Standard will smooth any discontinuous surface normal transitions between the main surface facets.

Smoothing between linear segments.

Smoothing between quadratic segments.

You can control the degree of smoothing of the main surface in node-to-surface contact simulations or in analyses using slide lines and contact elements by specifying a fraction f. The default value of f is 0.2.

For planar or axisymmetric deformable main surfaces, $f=a_1/{\mathrm{\ell }}_1=a_2/{\mathrm{\ell }}_2$ , where ${\mathrm{\ell }}_1$ and ${\mathrm{\ell }}_2$ are the lengths of the element facets that join at the surface node and $f<0.5$ (see Figure 7 and Figure 8). Abaqus/Standard will construct either a parabolic or a cubic segment between two points at distances $a_1$ and $a_2$ from the node at which the discontinuity exists; this smoothed segment will be used in the contact calculations. Thus, the contact surface will differ from the faceted element geometry. Smoothing affects only segments where the normal to the deformable main surface is discontinuous at the node joining two elements: it does not affect the two segments adjacent to the midside nodes on second-order element faces.

For three-dimensional, element-based main surfaces, f is defined as a fraction of the dimension of a facet as shown in Figure 9. The normal vector of a point within the region bounded by the dashed lines is computed to be normal to the facet. Outside this region the normal is smoothed with respect to the adjacent facets, using a generalization of the two-dimensional approach shown in Figure 7 and Figure 8. The physical geometry of a three-dimensional facet is not smoothed; only the surface normal definitions associated with the facet are affected by the smoothing operation. The implementation of the normal-direction smoothing algorithm is slightly different for surfaces based on rigid type elements (see Rigid Elements) than other element types. This difference typically has minimal effect on the convergence behavior or solution results; however, for example, different solution behavior may occasionally be observed between otherwise identical analyses in which a rigid body is modeled with R3D4 elements in one case and S4R elements assigned to a rigid body in another case.

Smoothing of a three-dimensional main surface.

Overriding the Default Smoothing Behavior for Finite-Sliding, Node-to-Surface Contact

To model a main surface with corners in two dimensions (fold lines in three dimensions), break the surface into multiple surfaces. This technique prevents Abaqus/Standard from smoothing out the corners or fold lines and allows Abaqus/Standard to introduce constraints associated with each surface if a secondary node is in contact with an interior corner or fold in the main surface.

To accurately model the main surface with a corner shown in Figure 10, you must define two contact pairs: the first contact pair has ASURF as the secondary surface and BSURFA as the main surface; the second contact pair has ASURF as the secondary surface and BSURFB as the main surface.

main surface with a corner.

Finite-sliding simulations usually include nonlinear geometric effects because such simulations generally involve large deformations and large rotations. However, it is also possible to use the finite-sliding tracking approach in a geometrically linear analysis (see Geometric Nonlinearity). The load transfer paths between the surfaces and the contact direction are updated in finite-sliding, geometrically linear analyses. This capability is useful for analyzing finite sliding between two stiff bodies that do not undergo large rotations.

Normal contact constraints due to node-to-surface discretization produce unsymmetric terms in the system of equations when three-dimensional faceted surfaces come in contact. These terms have a strong effect on the convergence rate in regions on the main surfaces with large differences in surface normals between facets.

Normal contact constraints due to surface-to-surface discretization produce unsymmetric terms in both two- and three-dimensional cases. These terms have a strong effect on the convergence rate in regions where the main and secondary surfaces are not parallel to each other.

In both cases you should use the unsymmetric solution scheme for the step to improve the convergence rate of the simulation (see Matrix Storage and Solution Scheme in Abaqus/Standard).

Contact simulations that involve strong frictional effects can also produce unsymmetric terms. See Unsymmetric Terms in the System of Equations for details.

For node-to-surface contact Abaqus/Standard chooses the anchor point of a secondary node's local tangent plane such that the vector from the anchor point to the secondary node coincides with a smoothly varying normal vector on the main surface. The anchor point is chosen before the analysis starts using the initial configuration of the model.

Modifying the Main Surface Normals

Defining user-specified nodal normals on the main surface (see Normal Definitions at Nodes) will improve the local tangent planes calculated for the small-sliding, node-to-surface formulation in some cases. For example, a default nodal normal corresponding to an average normal among adjacent facets can cause significant deviation from the true surface normal direction at perimeter nodes, as shown in Figure 12. The nodal normal ${\mathbf{N}}_{\mathbf{1}}$ does not point along the symmetry plane, which means that secondary node 100 will never intersect the main surface. In a small-sliding problem if a secondary node fails to intersect the main surface at the start of the analysis, it will be free to penetrate the main surface because no local tangent plane will be formed.

Main surface normal at node 1 in a small-sliding model of concentric cylinders. With the default ${\mathbf{N}}_{\mathbf{1}}$ secondary node 100 will never contact CSURF.

Defining a user-specified normal (1.00E+00, 0.00E+00, 0.00E+00) at node 1 on the main surface CSURF will correct the problem, as shown in Figure 13. This method allows secondary node 100 to see the main surface, and the correct contact normal direction will be used. Main surface normals at perimeter nodes are adjusted automatically to lie along the symmetry plane if boundary conditions are specified at these nodes in symmetry “type” format (XSYMM, YSYMM, or ZSYMM—see Boundary Conditions).

The modified main surface normal at node 1 of CSURF now allows secondary node 100 to contact CSURF.

A key difference with the surface-to-surface approach is that more than one secondary node is involved in each contact constraint (except when the secondary surface is based on gasket elements, as discussed below). This is related to the fact that the surface-to-surface formulation enforces contact conditions in an average sense over regions nearby secondary nodes rather than only at individual secondary nodes (see Surface-to-Surface Contact Discretization above). The small-sliding, surface-to-surface contact formulation is a limit case of the finite-sliding, surface-to-surface formulation, using a planar approximation of the main surface per averaging region of the secondary surface. The constraint participation factors for the secondary nodes remain constant for small-sliding contact. The effective center-of-action on the secondary surface per contact constraint may differ slightly from the location of the predominant secondary node associated with the constraint.

A special version of the small-sliding, surface-to-surface formulation is used if the secondary surface is based on gasket elements to avoid a tendency to trigger unstable deformation modes in the gasket elements. This special formulation has only one secondary node per contact constraint and preserves the accuracy advantages of the surface-to-surface formulation, but it is not well-suited for extension to finite-sliding and is otherwise not as generally applicable as the regular small-sliding, surface-to-surface formulation. (The finite-sliding, surface-to-surface formulation always uses multiple secondary nodes per constraint and is not recommended for contact involving gasket elements.)

The small-sliding, surface-to-surface contact formulation determines main anchor points and normal directions in a manner similar to that used by the small-sliding, node-to-surface contact formulation; however, there are some differences. For the surface-to-surface approach the anchor point approximately corresponds to the center of the zone on the main surface where the averaging region of the secondary projects onto the main surface. This projection occurs along the secondary surface normal direction. This method does not make use of smoothed main surface nodal normals. The anchor point location typically does not depend significantly on whether node-to-surface or surface-to-surface discretization is used, unless the surfaces are significantly separated and non-parallel in the initial configuration (in which case small-sliding contact may not be appropriate).

Abaqus/Standard automatically reverts to the node-to-surface approach for individual small-sliding contact constraints in the following circumstances, even if you have specified use of the surface-to-surface approach:

• if the secondary surface is a node-based surface;

• if the projection along the secondary surface normal direction does not intersect the main surface (but an anchor point can be found using the interpolated main surface normal direction algorithm discussed above for the small-sliding, node-to-surface formulation); or

• if single-sided secondary and main surfaces have surface normals in approximately the same direction.

For constraints based on surface-to-surface discretization it is not necessary that the constraint associated with a node on a symmetry plane is parallel to the symmetry plane. Hence, there is usually no need to specify specific normal directions. As in the case of node-to-surface contact, the contact direction points from the anchor point to the secondary node, and the tangent plane is normal to this direction. The contact normal for the small-sliding, surface-to-surface formulation is adjusted automatically to lie along the symmetry plane for each secondary node that has a boundary condition specified in symmetry “type” format (XSYMM, YSYMM, or ZSYMM—see Boundary Conditions).

The local tangent plane is by definition orthogonal to the contact direction. You can override the default contact direction to specify a direction with a spatially varying clearance or overclosure definition (see Specifying the Surface Normal for the Contact Calculations).

Once the contact direction is defined, the orientation of the local tangent plane with respect to the main surface facet remains fixed. Because small-sliding contact considers nonlinear geometric effects, Abaqus/Standard continuously updates the orientation of the local tangent plane to account for the rotation and, assuming that the main surface is deformable, the deformation of the main surface. The position of the anchor point relative to the surrounding nodes on the main surface facet does not change as the main surface deforms.

In a small-sliding analysis each constraint can transfer load only to a limited number of nodes on the main surface. These nodes on the main surface are chosen based on their initial proximity to the anchor point. The magnitude of load transferred to each main surface node is based on proximity in the current, deformed configuration to the center-of-action on the secondary surface (which corresponds to a secondary node for the node-to-surface formulation). For example, in Figure 11 node 103 transmits load to both nodes 2 and 3 on the main surface if node-to-surface discretization is used (if surface-to-surface discretization is used, load may be transmitted to additional nearby main nodes). Thus, if node 103 contacts the local tangent plane, a larger share of the force would be transmitted to the main surface node, 2 or 3, closer to the secondary node.

When the anchor point ${\mathbf{X}}_0$ corresponds to a node on the main surface, as is the case with secondary node 104 and main surface node 3 in Figure 11, the transmitted load for node-to-surface contact is shared by the node at ${\mathbf{X}}_0$ and all of the main surface nodes that share an adjacent surface facet with that node (additional main nodes may take part in the load transfer for surface-to-surface contact). In Figure 11 the three main surface nodes sharing the force transmitted by secondary node 104 are nodes 2, 3, and 4.

As the center-of-action on the secondary surface for a constraint slides along its local tangent plane, Abaqus/Standard updates the distribution among the main surface nodes. However, no additional main surface nodes are ever added to the original list of nodes associated with a given small-sliding constraint. The constraint will continue to transmit load to the original list of main surface nodes, regardless of the sliding distance. Figure 14 shows the potential problem that arises if small sliding is used but the relative tangential motion of the surfaces is not “small.” It shows the possible evolution of contact between secondary node 101 in Figure 5 and its main surface BSURF. Using the unit normal vectors ${\mathbf{N}}_{201}$ and ${\mathbf{N}}_{202}$ , the anchor point ${\mathbf{X}}_0$ is found for secondary node 101; for the purposes of this example, assume that it lies at the midpoint of the 201–202 face. With this location of ${\mathbf{X}}_0$ the local tangent plane for node 101 is parallel with the 201–202 face. The load transfer always occurs between node 101 and nodes 201 and 202, no matter how far node 101 slides along the local tangent plane. Therefore, if node 101 moves as shown in Figure 14, it will continue to transmit load to nodes 201 and 202 when, in fact, it really slid off the mesh forming the main surface BSURF.

Excessive sliding in a small-sliding contact analysis.

A contact pair in a small-sliding contact simulation should not grossly violate any of the assumptions or limitations outlined above. Adhere to the following guidelines:

• Secondary nodes should slide less than an element length from their corresponding anchor point and still be contacting their local tangent plane. If the main surface is highly curved, the secondary nodes should slide only a fraction of an element length. The accumulated slip at a secondary node (CSLIP) can provide a good estimate of how far a secondary node has moved.

• The local tangent planes formed by Abaqus/Standard should be a good approximation of the mesh geometry; if necessary, define a user-specified normal (Normal Definitions at Nodes) to improve the smoothly varying main surface normal, $\mathbf{N}\left(\mathbf{x}\right)$ .

• The rotation and deformation of the main surface should not cause the local tangent planes to become a poor representation of the main surface during the course of the analysis.

The basic guidelines given in About Contact Pairs in Abaqus/Standard should still be followed in a small-sliding simulation—the secondary surface should be the more refined surface or the surface on the more deformable body. However, in a small-sliding simulation more thought must be given when defining the main surface. With small-sliding contact each secondary node views the main surface as a flat surface, which can be significantly different than the true shape of the surface, even in the local region near the anchor point. In some cases the local tangent planes provide a good local approximation to the main surface in the initial configuration, but deformation and rotation of the main surface can reorient the local tangent planes such that they become a poor representation of the main surface. Figure 15 shows an example where distortion of the main surface results in such a situation.

Main surface deformation in a small-sliding contact analysis can cause problems with the local tangent planes.

This problem can be minimized to some extent by using a more refined mesh on the main surface, thus providing more element faces to control the motion of the tangent planes. Excessive mesh refinement should not be necessary since only small sliding should occur.

As was mentioned before, the small-sliding tracking approach reduces to an infinitesimal-sliding tracking approach for geometrically linear analyses. Infinitesimal sliding assumes that both the relative motions of the surfaces and the absolute motions of the model remain small. The orientations of the local tangent planes are not updated, and the load transfer paths and the weightings assigned to each main surface node remain constant during an infinitesimal-sliding simulation.

As in the case of small sliding, you can choose between node-to-surface and surface-to-surface discretizations with the infinitesimal-sliding tracking approach. The same user interface applies, and the default is node-to-surface discretization.

Two-dimensional and standard axisymmetric models have only one local tangent direction, ${\mathbf{t}}_1$. Abaqus/Standard defines the orientation of this direction by the cross product of the vector into the plane of the model (0., 0., 1.0) and the contact normal vector.

Models consisting of generalized axisymmetric bodies have a second local tangent direction, ${\mathbf{t}}_2$ , to account for the component of slip associated with relative differences in circumferential twist between contacting bodies. The first local tangent direction at any point on the surface is always tangent to the main surface in the local r–z plane. The second local tangent direction is orthogonal to this plane in the local circumferential direction. For more information about generalized axisymmetric models, see Generalized Axisymmetric Stress/Displacement Elements with Twist.

By default, Abaqus/Standard determines the initial orientation of the two local tangent directions, ${\mathbf{t}}_1$ and ${\mathbf{t}}_2$, using the following conventions:

Finite-sliding, surface-to-surface formulation

The default initial orientations of the two local tangent directions are based on the secondary surface normal, using the standard convention for calculating surface tangents (see Conventions) with the assumption that the contact normal corresponds to the negative normal to the secondary surface.

Finite-sliding, node-to-surface formulation

For contact involving a secondary surface based on three-dimensional beam-type elements, the first and second local tangent directions are defined along the length of the beam and transverse to the beam, respectively. For contact involving an analytical rigid surface and a secondary surface that is not based on three-dimensional beam-type elements, the first local tangent direction is tangential to the cross-section used to generate the analytical rigid surface, and the second local tangent direction is orthogonal to the plane of the cross-section in which the contact occurs.

In other cases, default initial orientations of the two local tangent directions are calculated by first computing tentative ${\mathbf{t}}_1$ and ${\mathbf{t}}_2$ directions. For element-based secondary surfaces the tentative directions are based on the secondary surface using the standard convention for calculating surface tangents. For node-based secondary surfaces the tentative ${\mathbf{t}}_1$ and ${\mathbf{t}}_2$ directions are set at each node to coincide with the global x- and y-axes, respectively. Abaqus constructs an orthogonal triad of ${\mathbf{t}}_1$ , ${\mathbf{t}}_2$ , and $\mathbf{n}$ (where $\mathbf{n}={\mathbf{t}}_1\times {\mathbf{t}}_2$ ), then rotates this triad such that $\mathbf{n}$ becomes aligned with the main surface normal at the tracked point on the main surface.

Small-sliding, surface-to-surface formulation

The default initial orientations of the two local tangent directions are based on the main surface normal, using the standard convention for calculating surface tangents.

Small-sliding, node-to-surface formulation

The default initial orientations of the two local tangent directions are calculated at each point on the main surface based on the main surface normal, using the standard convention for calculating surface tangents.

If the default local tangent directions are not convenient to prescribe an anisotropic friction model or to view contact output, you can define the local tangent directions for three-dimensional contact pair surfaces. You cannot redefine the local tangent directions for the following types of surfaces:

• Surfaces in a general contact domain

• Analytical rigid surfaces

• Two-dimensional surfaces

You define the local tangent directions by associating an orientation definition (see Orientations) with a contact pair surface. You can assign an orientation only to one surface of a contact pair. The surface on which an orientation can be defined is the same surface on which the default orientation would be calculated (see the conventions given previously). For example, an orientation can be defined only on the secondary surface in deformable versus deformable finite-sliding contact. If a second orientation is also given, an error message is issued. Therefore, it is not possible to redefine the local tangent directions for finite-sliding contact between a deformable secondary surface and an analytical rigid surface.

An orientation that is defined on a secondary surface of a contact pair that is generated from three-dimensional truss-type elements or from a list of nodes without rotational degree of freedoms will not be rotated if the secondary surface undergoes finite motion. In this case a warning message is issued during input processing.

For geometrically nonlinear analyses the local tangent directions rotate with the surface on which these directions were initially calculated or redefined using an orientation definition as described above with the exception that the local tangent direction rotates with the main surface for the small-sliding, surface-to-surface formulation. These rotated local tangent directions are further rotated to ensure that the normal vector, computed using the cross product of the rotated local tangent directions, corresponds to the normal vector on the main surface when the secondary node comes into contact.