김경종
289 lines
24 KiB
Markdown
289 lines
24 KiB
Markdown
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<details>
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<summary>text_image</summary>
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master surface
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slave surface
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closest point
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to A
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closest point
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to B
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A
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B
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C
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</details>
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Figure 38.1.1–1 Node-to-surface contact discretization.
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<details>
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<summary>text_image</summary>
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Node-to-Surface Contact
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slave
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master
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</details>
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<details>
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<summary>text_image</summary>
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Node-to-Surface Contact
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master
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slave
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</details>
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<details>
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<summary>text_image</summary>
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Surface-to-Surface Contact
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slave
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master
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</details>
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<details>
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<summary>text_image</summary>
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Surface-to-Surface Contact
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master
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slave
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</details>
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Figure 38.1.1–2 Comparison of contact enforcement for different master-slave assignments with node-to-surface and surface-to-surface contact discretizations.
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• 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. Figure 38.1.1–2 compares contact enforcement for node-to-surface and surface-to-surface contact for an example with dissimilar mesh refinement on the contacting bodies.
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• The contact direction is based on an average normal of the slave surface in the region surrounding a slave node.
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• Surface-to-surface discretization is not applicable if a node-based surface is used in the contact pair definition.
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# Choosing a contact discretization
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In general, surface-to-surface discretization provides more accurate stress and pressure results than nodeto-surface discretization if the surface geometry is reasonably well represented by the contact surfaces. Figure 38.1.1–3 shows an example of improved contact pressure accuracy with surface-to-surface contact compared to node-to-surface contact.
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<details>
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<summary>heatmap</summary>
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| Component | CPRESS_max |
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| ----------------- | -------------- |
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| Node-to-surface | 3.425e+05 |
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| Surface-to-surface| 3.008e+05 |
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</details>
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Figure 38.1.1–3 Comparison of contact pressure accuracy for node-to-surface and surface-to-surface contact discretizations.
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Since node-to-surface discretization simply resists penetrations of slave nodes into the master surface, forces tend to concentrate at these slave nodes. This concentration leads to spikes and valleys in the
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distribution of pressure across the surface. Surface-to-surface discretization resists penetrations in an average sense over finite regions of the slave surface, which has a smoothing effect. As the mesh is refined, the discrepancies between the discretizations lessen, but for a given mesh refinement the surfaceto-surface approach tends to provide more accurate stresses.
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Contact using surface-to-surface discretization is also less sensitive to master and slave surface designations than node-to-surface contact (see “Choosing the master and slave roles in a two-surface contact pair” below). Figure 38.1.1–4 shows a simple model involving two blocks with dissimilar mesh densities.
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<details>
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<summary>text_image</summary>
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uniform pressure
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</details>
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Figure 38.1.1–4 Test model for comparison of different master and slave surface designations.
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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 38.1.1–1 compares the Abaqus analysis results for different contact discretizations and slave surface designations.
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Table 38.1.1–1 Error (from analytical results) for various discretization/slave surface combinations.
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<table><tr><td>Contact discretization</td><td>Slave Surface</td><td>Maximum error in CPRESS</td></tr><tr><td rowspan="2">Node-to-surface</td><td>Top block</td><td>13%</td></tr><tr><td>Bottom block</td><td>31%</td></tr><tr><td rowspan="2">Surface-to-surface</td><td>Top block</td><td>~1%</td></tr><tr><td>Bottom block</td><td>~1%</td></tr></table>
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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
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significantly improve solutions obtained with a coarse mesh. See “Smoothing contact surfaces in Abaqus/Standard,” Section 38.1.3, for a discussion of surface smoothing options for surface-to-surface contact.
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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:
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• A large fraction of the model is involved in contact.
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• The master surface is more refined than the slave surface.
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• Multiple layers of shells are involved in contact, such that the master surface of one contact pair acts as the slave surface of another contact pair.
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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 slave and master facet normal directions are not approximately opposite in the active contact region.
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# Contact tracking approaches
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In Abaqus/Standard there are two tracking approaches to account for the relative motion of two interacting surfaces in mechanical contact simulations.
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# The finite-sliding tracking approach
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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.
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# The small-sliding tracking approach
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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 master 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.
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# Choosing the master and slave roles in a two-surface contact pair
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Abaqus/Standard enforces the following rules related to the assignment of the master and slave roles for contact surfaces:
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• Analytical rigid surfaces and rigid-element-based surfaces must always be the master surface.
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<!-- source-page: 755 -->
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• A node-based surface can act only as a slave surface and always uses node-to-surface contact.
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• Slave surfaces must always be attached to deformable bodies or deformable bodies defined as rigid.
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• Both surfaces in a contact pair cannot be rigid surfaces with the exception of deformable surfaces defined as rigid (see “Rigid body definition,” Section 2.4.1).
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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. Generally, if a smaller surface contacts a larger surface, it is best to choose the smaller surface as the slave surface. 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.
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The choice of master and slave roles typically has much less effect on the results with a surface-tosurface 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.
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# Fundamental choices affecting the contact formulation
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Your choice of contact discretization and tracking approach have considerable impact on an analysis. In addition to the qualities already discussed, certain combinations of discretizations and tracking approaches have their own characteristics and limitations associated with them. These characteristics are summarized in Table 38.1.1–2. You should also consider the solution costs associated with the various contact formulations.
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# Accounting for shell thickness
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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” in “Assigning surface properties for contact pairs in Abaqus/Standard,” Section 36.3.2.
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# Allowing for self-contact
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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, selfcontact cannot use the small-sliding tracking approach.
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Table 38.1.1–2 Comparison of contact formulation characteristics.
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<table><tr><td rowspan="3">Characteristic</td><td colspan="4">Contact formulation</td></tr><tr><td colspan="2">Node-to-surface</td><td colspan="2">Surface-to-surface</td></tr><tr><td>Finite-sliding</td><td>Small-sliding</td><td>Finite-sliding</td><td>Small-sliding</td></tr><tr><td>Account for shell thickness by default</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Allow self-contact</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td></tr><tr><td>Allow double-sided surfaces</td><td>Slave surface only</td><td>Slave surface only</td><td>Yes1</td><td>Yes</td></tr><tr><td>Surface smoothing by default</td><td>Some smoothing of master surface</td><td>Yes for anchor points; each constraint uses flat approximation of master surface</td><td>No</td><td>No for anchor points; each constraint uses flat approximation of master surface</td></tr><tr><td>Default constraint enforcement method</td><td>Augmented Lagrange method for 3D self-contact; otherwise, direct method</td><td>Direct method</td><td>Penalty method</td><td>Direct method</td></tr><tr><td>Ensure moment equilibrium for offset reference surfaces with friction</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td colspan="5">1Double-sided master surfaces are allowed with the finite-sliding, surface-to-surface formulation only if the path-based tracking algorithm is used (see “Path-based versus state-based tracking algorithms”). Double-sided slave surfaces are allowed with both tracking algorithms if the master surface is not user defined.</td></tr></table>
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# Allowing double-sided surfaces
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Doubled-sided contact surfaces based on shell-like elements are allowed to act as slave and/or master surfaces for the surface-to-surface contact formulation by default and are allowed to act as the slave surface for the node-to-surface contact formulation. For a shell-like surface to act as the master 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” in “Element-based surface
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definition,” Section 2.3.2, and “Orientation considerations for shell-like surfaces” in “Defining contact pairs in Abaqus/Standard,” Section 36.3.1, for more information).
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# Surface smoothing
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When using node-to-surface discretization, corners or small protrusions of a jagged master surface are allowed to penetrate the spaces between nodes in the node-based surface. It is sometimes possible for a slave node sliding along the master surface to snag on these corners. Therefore, Abaqus/Standard automatically smooths the master surface for contact calculations utilizing node-to-surface discretization to minimize this phenomenon. The details are discussed further in “Smoothing master surfaces for the finite-sliding, node-to-surface formulation” later in this section.
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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 master surface penetrating the slave 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,” Section 38.1.3).
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# Constraint enforcement methods
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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,” Section 35.6.1) 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,” Section 38.1.2.
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# Moment equilibrium
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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:
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• 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.
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• Contact calculations accounting for shell or membrane thicknesses (which is not allowed with the finite-sliding, node-to-surface formulation).
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• User-specified initial contact clearances (see “Defining a precise initial clearance or overclosure for small-sliding contact” in “Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard contact pairs,” Section 36.3.5).
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• Various usages of special-purpose contact elements, such as tube-to-tube contact elements (see “Contact modeling with elements,” Section 40.1.1, and “Tube-to-tube contact elements,” Section 40.3.1), result in some normal distance between nodes that interact with each other.
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While undesirable, the net moment that sometimes occurs with node-to-surface contact constraints is typically not significantly detrimental to the analysis results.
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# Effect of the contact discretization method on solution cost
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There is no easy way to predict which contact discretization method will result in lower overall solution cost. Basic trends include:
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• 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).
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• Contact conditions with finite-sliding contact tend to converge in fewer iterations with surface-tosurface contact discretization than with node-to-surface contact discretization (because surface-tosurface contact discretization has more continuous behavior upon sliding).
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# Using the finite-sliding tracking approach
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The finite-sliding tracking approach allows for arbitrary separation, sliding, and rotation of the surfaces. Abaqus/Standard contact pairs use a finite-sliding, node-to-surface contact formulation by default. General contact in Abaqus/Standard always uses a finite-sliding, surface-to-surface contact formulation.
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# Example
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Consider the case shown in Figure 38.1.1–5, with surface ASURF acting as the slave surface to surface BSURF in a finite-sliding, node-to-surface contact pair.
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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. Figure 38.1.1–6 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 $t _ { 1 }$ . 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.
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<details>
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<summary>text_image</summary>
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ESETB
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201
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202
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501
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502
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BSURF
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</details>
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<details>
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<summary>text_image</summary>
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ESETA
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101 102 103
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ASURF
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</details>
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Figure 38.1.1–5 Contacting bodies.
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<details>
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<summary>line</summary>
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| Point | Value |
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|-------|-------|
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| t = t₁ | 201 |
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| t = t₂ | 502 |
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| t = 0 | 101 |
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| t = t₁ | 202 |
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| t = t₂ | 501 |
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</details>
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Figure 38.1.1–6 Trajectory of node 101 in finite-sliding contact.
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# Path-based versus state-based tracking algorithms
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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.
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# Path-based tracking algorithm
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The “path-based” tracking algorithm carefully considers the relative paths of points on the slave surface with respect to the master surface within each increment and allows for double-sided shell and membrane master surfaces. The path-based tracking algorithm is available only for finite-sliding, surface-to-surface contact interactions involving element-based master surfaces and is the default for those interactions. The path-based algorithm is sometimes more effective than the state-based algorithm for analyses involving self-contact or large incremental relative motion.
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Input File Usage: Use the following option to specify use of the path-based tracking algorithm: \*CONTACT PAIR, INTERACTION=interaction\_property\_name, TYPE=SURFACE TO SURFACE, TRACKING=PATH
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Abaqus/CAE Usage: Interaction module: surface-to-surface contact or self-contact interaction editor: Discretization method: Surface to surface, Contact tracking: Two configurations (path)
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# State-based tracking algorithm
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The “state-based” tracking algorithm updates the tracking state based on the tracking state associated with the beginning of the increment together with geometric information associated with the predicted configuration. This algorithm is well-suited for most finite-sliding analyses but requires the use of singlesided surfaces and occasionally has difficulty tracking large incremental motion. State-based tracking may miss detecting contact if the incremental relative motion exceeds the dimensions of the master surface or if the incremental motion cuts across corners of the master surface; specifying an upper bound for the increment size helps avoid these problems. The state-based tracking algorithm is:
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• the only tracking algorithm available for finite-sliding, node-to-surface contact pairs;
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• the only tracking algorithm available for finite-sliding contact interactions involving an analytical rigid master surface;
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• a non-default option for finite-sliding, surface-to-surface contact pairs involving an element-based master surface.
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Input File Usage: Use the following option to specify use of the state-based tracking algorithm: \*CONTACT PAIR, INTERACTION=interaction\_property\_name, TYPE=SURFACE TO SURFACE, TRACKING=STATE
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Abaqus/CAE Usage: Interaction module: surface-to-surface contact or self-contact interaction editor: Discretization method: Surface to surface, Contact tracking: Single configuration (state)
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# Smoothing master surfaces for the finite-sliding, node-to-surface formulation
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The finite-sliding, node-to-surface contact formulation requires that master surfaces have continuous surface normals at all points. Convergence problems can result if master surfaces that do not have continuous surface normals are used in finite-sliding, node-to-surface contact analyses; slave nodes tend to get “stuck” at points where the master surface normals are discontinuous. Abaqus/Standard automatically smooths the surface normals of element-based master surfaces (see “Smoothing deformable master 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,” Section 2.3.4). No such smoothing of master surface normals is needed with the finite-sliding, surface-to-surface formulation.
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