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slave surface nodes 103 104 204 b a 203 303 304 102 202 302 c 402 403 503 504 101 201 301 401 501 502 503 504

Figure 35.3.1–5 Searching for the points on an element-based master surface that are closest to nodes $a , b ,$ and c. # Choosing the slave and master surfaces of a surface-based tie constraint The choice of slave and master surfaces can have a significant effect on the accuracy of the solution, in particular if the “node-to-surface” approach is used. The effect is much less (and the accuracy generally better) for the “surface-to-surface” approach. In either case, if both surfaces in a constraint pair are deformable surfaces, the master surface should be chosen as the surface with the coarser mesh for best accuracy. In Abaqus/Standard a rigid surface cannot act as a slave surface in a tie constraint. To comply with this rule, the capability to automatically resolve overconstraints in Abaqus/Standard (see “Overconstraint checks,” Section 35.6.1) will modify tie constraint definitions in the following cases: • Tie constraints between two surfaces of the same rigid body are removed. • Tie constraints between two surfaces of two rigid bodies are replaced by a BEAM-type connector between the respective rigid body reference nodes. • Tie constraints specified with a purely rigid slave surface and a purely deformable master surface are modified to reverse the master and slave assignments unless this is not possible due to other modeling restrictions (in which case an error message is issued). These methods are not applied if the slave surface that you specified is partially rigid and partially deformable; Abaqus/Standard issues an error message in such cases. In acoustic, structural-acoustic, and elastic wave propagation problems care should be exercised when tying meshes of highly dissimilar refinement. If two media have different wave speeds, the optimal meshes for each of the media will have different characteristic element lengths: the faster medium will have larger elements. If surfaces of these meshes are used in a tie constraint, the surface of the finer mesh (of the slower medium) should be designated as the slave. Nevertheless, in the region near the tied surfaces, the physical wave phenomena in both fast and slow media will typically have length scales characteristic of the slower medium; that is, of the shortest length scale in the physical problem. Therefore, if these phenomena are important, the mesh of the faster medium should be refined to the scale of the slower medium in the vicinity of the contact region. # Adjusting the surfaces and considering offsets By default, with the exceptions mentioned below, Abaqus will automatically reposition the slave nodes to be tied in the initial configuration without causing strain to resolve gaps such that the surfaces are just touching, accounting for any shell thickness (unless you have specified that thickness should not be accounted for, as discussed above in the context of the position tolerance criterion) but not accounting for beam or membrane thickness. One exception is that no adjustments are made where tied surfaces are closer together than the combined half-shell thickness. All adjustments are performed such that the slave and master surfaces are never pushed apart; that is, the reference surfaces will only become closer as a result of the adjustments. It is recommended that you allow the automatic adjustments to occur, especially if neither surface has rotations; in this case a constant offset vector is used, so incorrect behavior of the constraint under rigid body rotation can occur when slave nodes are not lying exactly on the master surface. Adjustments are not made if the slave surface belongs to a substructure or when either the slave or master surface is a beam element-based surface; in the latter cases you should locate the beam element nodes with the desired offset from the other surface. Input File Usage: \*TIE, ADJUST=YES or NO Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: toggle Adjust slave node initial position # Criteria for adjustment A slave node is considered for adjustment if both of the following conditions are met: • The slave node satisfies whatever criterion is in effect for generating a constraint (either because it satisfies the position tolerance criterion or belongs to the specified node set of constrained slave nodes, as previously discussed). • The slave node is more than the combined thickness of the slave and master surfaces away from its projection point on the master reference surface, accounting for any offset of the element reference surfaces from the respective element midsurfaces. For an element-based master surface a slave node will be moved toward the closest point on the master surface; for a node-based master surface a slave node will be moved toward the closest master node. The corrected position of an adjusted slave node is determined from the combined effects of shell element thickness and any specified reference surface offset relative to the shell midsurface of either slave or master surfaces. Figure 35.3.1–6 shows the adjusted slave node position in an example with two shell element-based surfaces tied together (in this example one of the element reference surfaces is offset from the element midsurface). It is assumed that the surfaces were farther apart than shown in Figure 35.3.1–6 prior to the adjustment; otherwise, the slave nodes would not have been adjusted. 

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slave reference surface slave shell midsurface master shell reference and midsurface shell (s) – shell (m) slave shell element has offset = 1/2 (SPOS)

Figure 35.3.1–6 Adjusted slave node position for two shell element-based surfaces tied together. The slave shell element has an offset of 0.5. Adjustments are made only for slave nodes that are included in the user-specified tied node set or that meet the tolerance criteria described above. # Adjustments for overlapping constraints Nodal adjustments for tie constraints are processed sequentially in the order of the constraint definitions at the start of an analysis. If different constraint or contact definitions involve the same nodes, some adjustments may cause lack of compliance for contact or constraint definitions that were previously processed. These conflicts are less likely to occur in Abaqus/Explicit because the adjustments in Abaqus/Explicit are automatically processed in the chaining order discussed in “Overlapping constraints.” These conflicts can be avoided in Abaqus/Standard in some cases by changing the processing order of constraint and contact definitions: nodes in common between different contact or constraint definitions should be processed first as slave nodes and later as master nodes. # Input File Usage: To change the processing order of constraint and contact definitions, change the order of the definitions in the input file. Constraint and contact definitions are processed in the order in which they appear. # Abaqus/CAE Usage: To change the processing order of constraint and contact definitions, change the names of the constraints and interactions in the model. Constraints and interactions are processed alphabetically according to their name. # Accounting for an offset between tied surfaces Abaqus allows a gap to exist between tied surfaces. Such gaps may exist if you prevent nodal adjustments for tied surfaces. A gap between the reference surfaces may remain due to the presence of shell thickness even if nodal adjustments are performed. Figure 35.3.1–7 shows some cases where an offset between the reference surfaces may be desirable for tied surface pairs to account for shell or beam thickness.  Figure 35.3.1–7 Tie constraints being applied between surfaces based on various element types (h = offset between slave and master surfaces). Rigid body motion is properly accounted for when the nodes are separated by a finite distance when at least one of the surfaces is based on shell or beam elements; when the master surface is an analytical rigid surface; $\mathrm { o r } ,$ in the case of node-based surfaces, when the nodes on at least one surface have active rotational degrees of freedom. The nature of the constraint on translational motion between surfaces in Abaqus depends on whether there is an offset between the surfaces and on which surfaces have rotational degrees of freedom, as discussed below. # Neither surface has rotational degrees of freedom If neither surface has rotational degrees of freedom, the global translational degrees of freedom of the slave node and the closest point on the master surface are constrained to be the same. When an offset exists, the behavior of Abaqus/Standard differs from that of Abaqus/Explicit. Abaqus/Explicit enforces the constraint through the fixed offset like a PIN-type MPC when the nodes in the MPC are not coincident. Because the fixed offset does not rotate, the surface-based constraint will not represent rigid body rotation correctly. The constraint represents rigid body motion correctly when the offset is zero. This behavior can be ensured by specifying that all tied slave nodes should be moved onto the master surface. If an offset needs to be maintained, general contact with surface-based cohesive behavior (as explained in “Surface-based cohesive behavior,” Section 37.1.10) that correctly accounts for rigid body rotation of the offset should be used. In general, Abaqus/Standard enforces the constraint such that the surface-based constraint represents rigid body rotation correctly; the enforcement of this constraint will introduce nonlinearity in the model. There are, however, two exceptions in which rigid body rotation between the tied surfaces cannot be enforced: (1) when node-based master surfaces are used and (2) when using tie constraints for cyclic symmetry. # Only one surface has rotational degrees of freedom If the slave surface has rotational degrees of freedom and the master surface does not, the translational motion is constrained at the closest point on the master reference surface. When the reference surfaces are offset, a moment will be applied to each slave node based on the constraint force times the offset distance. Similarly, if the master surface has rotational degrees of freedom and the slave surface does not, the translational motion is constrained at each slave node and a moment will be applied to the relevant nodes on the master surface if an offset exists. In either case the surface-based constraint will behave correctly under rigid body rotation regardless of the amount of offset. # Both surfaces have rotational degrees of freedom If both surfaces have rotational degrees of freedom, are not offset, and the rotations are tied, each slave node is constrained to the master surface like a TIE-type MPC. If an offset exists between the surfaces, the constraint acts like a BEAM-type MPC between the slave node and the closest point on the master reference surface. If the rotations are not tied, Abaqus allows you to choose the location of the translational constraint. It can be enforced at the master reference surface, the slave reference surface, or anywhere in between. The location of the translational constraint enforcement for surfaces where the rotations are not tied will affect the distribution of moment to each of the surfaces. The most physically reasonable choice is to locate the constraint at the point where the actual top or bottom sides of each surface meet. The constraint then models a perfect adhesive between the surfaces, which transfers shear stress to each surface. Abaqus will choose the location of the translational constraint as follows: • If the master surface is shell element-based, the translational constraint is enforced on the top or bottom side of the master surface. • If the slave surface is shell element-based and the master surface is not, the translational constraint is enforced at the top or bottom side of the slave surface. • Otherwise, the translational constraint is enforced at the master reference surface. To override these default locations, you can specify a constraint ratio for the tie constraint equal to the fractional distance between the master reference surface and the slave node at which the translational constraint should act. Figure 35.3.1–8 shows an example of the use of a constraint ratio to prescribe the location of the translational constraint between two shell surfaces that are tied together with no rotational constraints. The distance between the master reference surface and the slave reference surface is b. The prescribed constraint ratio, r, is then used to locate the translational constraint at a distance a from the master reference surface. All distances are measured along the vector between the slave node and its projection point onto the master reference surface. The constraint behavior is then similar to that of two rigid beams pinned together, as shown. Input File Usage: \*TIE, CONSTRAINT RATIO=value Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: Constraint ratio 

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slave reference surface b a pin rigid beams master reference surface constraint ratio, r = a/b

Figure 35.3.1–8 Use of a constraint ratio to prescribe the location of the translational constraint. # Constraining a surface to a three-dimensional beam The master surface for a tie constraint can be based on three-dimensional beam elements. For this case each slave node is projected onto the line formed by the nodes of the beam elements in the undeformed configuration to find the projection point. During the subsequent analysis the motion of each slave node is rigidly constrained to the motion (translation and rotation) of its projection point; i.e., each slave node and its projection point are connected by a rigid beam. Constraining other elements to a beam element-based master surface allows modeling of interactions between the surface of a (complex) beam section and its surroundings, without having to model the beam with continuum and/or shell elements. This feature can be particularly useful for modeling acoustic-structural interactions. The surface-based tie constraint capability can be used in models where the nodal degrees of freedom on both the slave and master surfaces include electrical potential, pore pressure, acoustic pressure, and/or temperature. Except for the type of nodal degree of freedom being constrained, Abaqus uses exactly the same formulation for the tie constraint in nonmechanical simulations as it does for mechanical simulations. In general, degrees of freedom common to both surfaces are tied, and any other degrees of freedom are unconstrained. The case of structural-acoustic constraints is the exception to this rule. Here, appropriate relations between the acoustic pressure on the fluid surface and displacements on the solid surface are formed internally (see “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1). The displacements and/or pressure degrees of freedom on the surfaces are the only ones affected; rotations are ignored by the tie constraint in this case. The internally computed structural-acoustic coupling conditions use surface areas and normal directions associated with the slave surface elements. The slave surface for structural-acoustic tie constraints cannot be a node-based surface. In two-dimensional analyses the out-of-plane thickness of the slave elements is required. Generally, this thickness is the thickness specified on the section definition for the slave surface elements. However, when beam elements form the slave surface in a tie constraint pair with acoustic elements, a unit thickness in the out-of-plane direction is assumed for the beams. In Abaqus/Standard you can define coupling between solid medium and acoustic medium infinite elements along the surfaces that extend to infinity. These surfaces are defined using the edges of the acoustic elements and sides numbered “2” and higher of the solid medium infinite elements. The infinite surfaces of solid medium and acoustic infinite elements can be coupled only through the use of a surfacebased tie constraint. As shown in Figure 35.3.1–9, the acoustic infinite elements must be the slave elements and the edges of the acoustic infinite elements should lie within the specified position tolerance to the solid medium infinite element base facets. 

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position tolerance solid infinite element master surface slave surface acoustic infinite element

Figure 35.3.1–9 Use of a surface-based tie constraint to prescribe the coupling between solid medium and acoustic medium infinite elements. If the base facets of acoustic infinite elements are to be coupled to solid medium finite elements, to solid medium infinite elements, or to structural elements, either a surface-based tie constraint or acousticstructural interaction elements can be used. Surfaces defined on solid medium infinite elements cannot be used in a surface-based tie constraint in Abaqus/Explicit. Table 35.3.1–3 enumerates all possible cases. For other slave-master pairings not listed in this table, an error message will be issued. Table 35.3.1–3 Possible slave-master surface pairings.

Slave Surface	Master Surface	Degrees of Freedom Tied
Acoustic	Acoustic	Acoustic pressure
Acoustic	Stress	Translations
Stress	Acoustic	Acoustic pressure
Stress	Stress	Translations and/or rotations
Heat-Stress	Stress	Translations and/or rotations
Stress	Heat-Stress	Translations and/or rotations
Heat-Stress	Heat-Stress	Temperature, translations and/or rotations
The following surface pairings are available only in Abaqus/Standard:
Heat transfer	Heat transfer	Temperature
Electrical-Heat	Heat transfer	Temperature
Heat transfer	Electrical-Heat	Temperature
Electrical-Heat	Electrical-Heat	Temperature and electric potential
Pore-Stress	Pore-Stress	Pore pressure and translations
Pore-Stress	Stress	Translations
Stress	Pore-Stress	Translations
Pore-Stress	Pore	Pore pressure

# Tie constraints versus tied contact in Abaqus/Standard There are the following advantages to using a surface-based tie constraint in Abaqus/Standard instead of defining tied contact as discussed in “Defining tied contact in Abaqus/Standard,” Section 36.3.7: • Degrees of freedom of the slave surface nodes will be eliminated. • The tie constraint is more efficient in terms of the size of the fronts of the operator matrix because fewer master surface nodes are associated with each slave node. • Rotational degrees of freedom as well as translational degrees of freedom can be tied. • Tie constraints are much more general since they allow the use of general surfaces. • Surface offsets and shell thickness are taken into account. # Overlapping constraints In a model with multiple tie constraint definitions it is possible that the slave and master surfaces of different tie constraint definitions may intersect. If two tie constraint definitions have part or all of their master surfaces in common or if the surfaces tied are layered (i.e., the master surface of one tie constraint definition acts as the slave surface of a subsequent tie constraint definition), Abaqus will attempt to chain the constraint definitions together. This will reduce the number of degrees of freedom and lower the computational expense, resulting in faster run times. However, in a model with multiple tie constraint definitions if nodes on the slave surface of one tie constraint definition are part of the slave surface of other tie constraint definitions, an overconstraint occurs. In most cases the overconstraint is due to the existence of redundant constraints, and it is safe to eliminate this redundancy. However, the overconstraint may also be due to conflicting constraints, in which case the problem is due to a modeling error that you should correct. Simulation results will vary depending on which constraint is removed to avoid an overconstraint if the overlapping constraints are not identical. It is recommended that, wherever possible, you order the slave and master surfaces of the constraint definitions to avoid intersecting slave surfaces. See “Adjustments for overlapping constraints” for a discussion of initial strain-free adjustments for overlapping constraints. # Overconstrained slave nodes in Abaqus/Standard If an overconstraint occurs, Abaqus/Standard issues an error message unless the constraints are redundant or nearly redundant, as discussed below. As discussed previously, each tie constraint involves a single slave node and a set of master nodes with nonzero tie coefficents. Abaqus/Standard considers tie constraints involving the same slave node to be nearly redundant if at least one node is common among the respective sets of master nodes with nonzero tie coefficients. In such cases, rather than issuing an error message, Abaqus/Standard issues a warning message and only enforces one of the constraints. The surface-based tie constraint is imposed in Abaqus/Standard by eliminating the degrees of freedom on the slave surface; therefore, nodes on the slave surface should not be used to apply boundary conditions, nor should they be used in any subsequent tie, multi-point, equation, or kinematic coupling constraint (see “Overconstraint checks,” Section 35.6.1, for a more complete discussion of overconstraints in Abaqus/Standard). # Overconstrained slave nodes in Abaqus/Explicit In contrast, Abaqus/Explicit treats overconstraints with a penalty method, thus enforcing the constraints in an average sense; the computational cost of the analysis may increase in these cases. In addition, if the slave surface for a tie constraint definition in Abaqus/Explicit is part of a rigid body while the master surface comprises a deformable element- or node-based surface and the master surface acts as the slave surface in a subsequent tie constraint definition, the resolution of the resulting constraints can prove to be computationally intensive. It is recommended that, wherever possible, you order the slave and master surfaces of the constraint definitions to avoid such a situation. # Nullifying the tie constraint on slave nodes due to element deletion in Abaqus/Explicit In Abaqus/Explicit tie constraints are nullified as underlying elements of tied surfaces are deleted due to material point failure. The tie constraint between a slave node and its corresponding master nodes is deleted when either all the elements attached to the slave node are deleted or the master element to which the slave node is tied is deleted. # Limitations The following limitations exist for tie constraints: • Surface-based tie constraints cannot be used to connect gasket elements that model thicknessdirection behavior only. • A rigid surface cannot act as a slave surface in a constraint pair in Abaqus/Standard. • A slave node of a tie constraint cannot act as a slave node of another constraint in Abaqus/Standard. • Tie constraints cannot be used to tie infinite elements to finite elements in Abaqus/Explicit. To couple infinite and finite elements in Abaqus/Explicit, the elements must share nodes. • The axisymmetric solid Fourier elements with nonlinear, asymmetric deformation cannot form element-based surfaces; therefore, such surfaces cannot be used in tie constraints. • In Abaqus/Standard, tie constraints cannot be used to connect nodes included in a node-based surface or nodes included in an element-based surface defined using an element edge identifier if such nodes have more than one temperature degree of freedom.