김경종
267 lines
26 KiB
Markdown
267 lines
26 KiB
Markdown
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• Abaqus/Standard assigns default pure master-slave roles for contact involving disconnected bodies within the general contact domain, and contact exclusions are generated by default for the opposite master-slave orientations. Options to override the default pure master-slave assignments with alternative pure master-slave assignments or balanced master-slave assignments are discussed in “Numerical controls for general contact in Abaqus/Standard,” Section 36.2.6.
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• Contact exclusions are generated automatically for portions of surfaces that are severely overclosed in the initial configuration of the model. See “Controlling initial contact status in Abaqus/Standard,” Section 36.2.4, for more information.
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# Examples
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The following input specifies that the contact domain is based on self-contact of an all-inclusive, automatically generated surface but that contact (including self-contact in any overlap regions) should be ignored between the all-inclusive, automatically generated surface and surface\_2:
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```txt
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*CONTACT
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*CONTACT INCLUSIONS, ALL EXTERIOR
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*CONTACT EXCLUSIONS
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, surface_2
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```
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Either of the following methods can be used to exclude self-contact for surface\_1 from the contact domain:
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```txt
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*CONTACT EXCLUSIONS
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surface_1,
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```
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or
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```c
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*CONTACT EXCLUSIONS
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surface_1, surface_1
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```
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# Edge-to-surface contact scenarios
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The general contact algorithm can consider three-dimensional edge-to-surface contact. In addition to modeling contact between segments of beam or truss elements and faceted surfaces, it is more effective at resolving some interactions than the surface-to-surface contact formulation. Figure 36.2.1–2 and Figure 36.2.1–3 show examples in which the edge-to-surface contact formulation is most effective for resolving contact. The edge-to-surface contact formulation is intended to avoid localized penetration of a feature’s edge of one surface into a relatively smooth portion of another surface when the normal directions of the respective surface facets in the active contact region form an oblique angle.
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The contact edges representing beam and truss elements have a circular cross-section, regardless of the actual cross-section of the beam or truss element. The radius of a contact edge representing a truss element is derived from the cross-sectional area specified on the truss section definition (it is equal to the radius of a solid circular section with an equivalent cross-sectional area). For beams with circular crosssections, the radius of the contact edge is equivalent to the section radius. For beams with non-circular cross-sections, the radius of the contact edge is equal to the radius of a circumscribed circle around
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<details>
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<summary>natural_image</summary>
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Three 3D geometric shapes: a cube with orange grid, a gray cube with orange panel, and a gray cube with an orange curved line (no text or symbols)
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</details>
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Figure 36.2.1–3 Edge-to-surface contact examples.
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the section. Edge-to-surface contact for beam or truss elements is activated by including the associated surfaces into the general contact domain. By default, the all-inclusive surface contains surfaces based on beam or truss elements.
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By default, when a surface is used in a general contact interaction, all applicable facets are included in the contact definition along with edges of solid and shell elements with feature angles of at least 45°. See “Feature edges” in “Surface properties for general contact in Abaqus/Standard,” Section 36.2.2, for a discussion of controls related to which feature edges are considered for edge-to-surface contact. Edge-tosurface contact constraints never participate in thermal, electrical, or pore pressure contact properties. For example, in a coupled temperature-displacement analysis, surface-to-surface constraints can influence mechanical and thermal interactions; but, if edge-to-surface constraints are included, they will only help resist penetrations.
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The contact area associated with a feature edge depends on the mesh size; therefore, contact pressures (in units of force per area) associated with edge-to-surface contact are mesh dependent.
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# Edge-to-edge contact scenarios
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The general contact algorithm can optionally consider edge-to-edge contact. Feature edges on solid and shell-like surfaces, shell perimeter edges, and edges representing beams (and trusses) can be included. Figure 36.2.1–4 shows examples in which the edge-to-edge contact formulation is most effective for resolving contact.
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Two edge-to-edge contact formulations are available. One formulation bases the contact normal direction on the cross product between the two respective edges considered for contact, and the other formulation uses a radial direction of one of the beams as the contact direction (similar to what is done for tube-to-tube contact elements, which are discussed in “Tube-to-tube contact elements,” Section 40.3.1). Four of the examples in Figure 36.2.1–4 rely on the formulation with the cross product normal to resist penetrations, and the example on the bottom right of Figure 36.2.1–4 relies on the formulation with the radial normal. The edge-to-edge contact formulation with the radial normal is applicable only to cases with some thickness contributing to the contact calculations.
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The example shown in Figure 36.2.1–5 involves compression of a spring modeled with beam elements. This example relies on the edge-to-edge contact formulation with a radial normal direction to
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<details>
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<summary>natural_image</summary>
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3D geometric shapes including cubes, grids, and rods, rendered in orange, gray, and blue tones (no text or symbols)
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</details>
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Figure 36.2.1–4 Edge-to-edge contact examples.
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resolve contact between adjacent spring coils, and it relies on the edge-to-surface contact formulation to resolve contact between the spring and other surfaces.
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<details>
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<summary>natural_image</summary>
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Three 3D mechanical assembly diagrams showing spring-loaded components with no visible text or symbols
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</details>
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Figure 36.2.1–5 Compressing a spring modeled with beam elements.
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The edge-to-edge contact formulation with a radial normal can involve the “exterior” of beam, shell, and solid feature edges and the “interior” of hollow beams, as shown in the example in Figure 36.2.1–6. This example involves a wire modeled with beam elements being wound onto a cylinder modeled with solid elements. The wire passes through a hollow cylindrical guide before coming onto the cylinder. The “radial” edge-to-edge formulation resolves contact between adjacent coils of the wire and also resolves contact between the wire and the interior of the hollow beam representing the guide. The edge-to-surface contact formulation resolves contact between the wire and the cylinder.
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The edge-to-edge contact formulation with a contact normal direction based on the cross product of the edge directions is applicable only while edges are not nearly parallel. The edge-to-edge contact
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<details>
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<summary>natural_image</summary>
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3D rendered cylindrical object with grid pattern and a small attached component, labeled (A) (no text or symbols on the object itself)
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</details>
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<details>
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<summary>natural_image</summary>
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3D rendered diagram of a cylindrical object with a mesh grid and a connected rod, labeled (B) (no text or symbols on the object itself)
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</details>
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<details>
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<summary>natural_image</summary>
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Close-up of a vertical metallic rod or wire against a grid background (no text or symbols visible)
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</details>
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<details>
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<summary>natural_image</summary>
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3D rendered image of a cylindrical mechanical part with a vertical shaft (no text or symbols)
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</details>
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Figure 36.2.1–6 Winding a wire onto a cylinder.
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formulation with a radial contact normal direction is typically most applicable while contact edges are nearly parallel, but Figure 36.2.1–6 shows an exception. The hollow beam is simultaneously in contact with the two other beams. The cross product version of the edge-to-edge contact formulation resolves contact between the exterior of the hollow beam and the beam that is near the top of Figure 36.2.1–6. The radial version of the edge-to-edge contact formulation resolves contact between the interior of the hollow beam and the spiral-shaped beam, with the contact direction corresponding to the interior radial direction of the hollow beam. The radial version of the edge-to-edge contact formulation is effective in this case because individual segments of the spiral-shaped beam span relatively small arcs of the hollow tube.
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In addition to choosing to activate one or both types of edge-to-edge contact formulations, you must specify a feature angle criterion to activate feature and perimeter edges to participate in edgeto-edge contact. See “Feature edges” in “Surface properties for general contact in Abaqus/Standard,” Section 36.2.2, for a discussion of controls related to which feature edges are considered for edge-to-edge contact. If only beam edges are present, specifying the contact formulation alone is sufficient.
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Beam-to-beam contact cannot be used to model contact between beam-like elements that share nodes with underlying solid or shell elements (for example, beam elements that are used to model stringers).
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<details>
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<summary>natural_image</summary>
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3D rendered mechanical component with green internal channel and blue horizontal bar (no text or symbols)
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</details>
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Figure 36.2.1–7 Edge-to-edge contact example with an internal beam spiral.
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<table><tr><td>Input File Usage:</td><td>Use the following option to activate both formulations for edge-to-edge contact:*CONTACT FORMULATION, TYPE=EDGE TO EDGE, FORMULATION=BOTHUse the following option to deactivate edge-to-edge contact:*CONTACT FORMULATION, TYPE=EDGE TO EDGE, FORMULATION=NO (default)Use the following option to activate the radial edge-to-edge contact formulation:*CONTACT FORMULATION, TYPE=EDGE TO EDGE, FORMULATION=RADIALUse the following option to activate the formulation based on the cross product of the edge directions for edge-to-edge contact:*CONTACT FORMULATION, TYPE=EDGE TO EDGE, FORMULATION=CROSS</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Modeling edge-to-edge contact is not supported in Abaqus/CAE.</td></tr></table>
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# Vertex-to-surface contact scenarios
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The general contact algorithm can consider vertex-to-surface contact. Figure 36.2.1–8 shows examples in which the vertex-to-surface contact formulation is most effective for resolving contact. The vertexto-surface contact formulation is intended to avoid localized penetration of a node at a convex corner of a solid or shell/membrane surface or at an end point or kink of a beam/truss into a relatively smooth portion of another surface. Most vertex nodes are along feature edges, although, for example, a node at the tip of a cone may satisfy the vertex node criteria. See “Vertex nodes” in “Surface properties for general contact in Abaqus/Standard,” Section 36.2.2, for a discussion of the vertex node criteria. Vertex
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nodes are effectively treated as spherical in the vertex-to-surface formulation. The spherical radius of the contact vertex corresponds to the surface thickness at the node.
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<details>
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<summary>natural_image</summary>
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Five 3D geometric shapes (cube, pyramid, parallelogram, cone) shown in different orientations, no text or symbols present
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</details>
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Figure 36.2.1–8 Vertex-to-surface contact examples.
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# Output
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Output variables associated with contact fall into two categories: nodal variables (sometimes called constraint variables) and whole surface variables. In addition, Abaqus outputs an array of diagnostic information associated with contact interactions, as discussed in “Contact diagnostics in an Abaqus/Standard analysis,” Section 39.1.1, and internal surfaces generated for general contact.
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For more detailed discussions of variables associated with thermal, electrical, and pore fluid analyses, see the sections on the related contact properties in Chapter 37, “Contact Property Models.”
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# General contact domain and component surfaces
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Abaqus/Standard generates the following internal surfaces associated with general contact:
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• General\_Contact\_Faces,
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• General\_Contact\_Edges,
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• General\_Contact\_Vertices,
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• General\_Contact\_Faces\_k,
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• General\_Contact\_Edges\_k, and
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• General\_Contact\_Vertices\_k,
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where k corresponds to an automatically assigned “component number.” The three internal surfaces for general contact without a component number contain all surface faces, all feature edges, and all vertices, respectively, included in the general contact domain.
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Each feature edge component surface, General\_Contact\_Edges\_k, has a subset of face edges (satisfying the feature edge criteria) of the corresponding face component surface, General\_Contact\_Faces\_k. Each vertex component surface, General\_Contact\_Vertices\_k, has a subset of vertices (satisfying the vertex criteria) of the corresponding face component surface, General\_Contact\_Faces\_k. The face component surfaces have no nodes in common with each other. By default, a lowered-numbered face-based component surface will act as a master surface to a higher-numbered face-based component surface for the surface-to-surface formulation. Component numbers do not influence what is considered by the
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edge-to-surface and vertex-to-surface formulations. Component surfaces are referred to in diagnostic messages for both formulation types.
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Internal surfaces can be viewed using display groups in the Visualization module of Abaqus/CAE. Internal surface names generated by Abaqus/Standard should not be used in model definitions.
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# Nodal contact variables
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Nodal contact variables can be contoured on contact surfaces in the Visualization module of Abaqus/CAE. Nodal contact variables include contact pressure and force, frictional shear stress and force, relative tangential motion (slip) of the surfaces during contact, clearance between surfaces, heat or fluid flux per unit area, and fluid pressure. Many of the nodal contact variables written to the output database (.odb) file are often available for all contact nodes, regardless of whether they act as slave or master nodes. Other nodal contact variables are available only at nodes acting as slave nodes. Most contact output to the data (.dat) file, results (.fil) file, and the utility subroutine GETVRMAVGATNODE is associated with individual constraints. For contact output to the output database (.odb) file, some filtering is applied to reduce contact output noise.
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# Contact pressure
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The contact pressure distribution is of key interest in many Abaqus analyses. You can view the contact pressure on all contact surfaces except for analytical rigid surfaces and discrete rigid surfaces based on rigid-type elements (the latter restriction does not apply to general contact). You can view a contour plot of the contact pressure error indicator next to a contour plot of the contact pressure to gain perspective on local accuracy of the contact pressure solution in regions where the contact pressure solution is of interest (see “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2, for further discussion of error indicator output).
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In some cases you may observe the contact pressure extending beyond the actual contact zone due to the following factors:
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• The contour plots are constructed by interpolating nodal values, which can cause nonzero values to appear within portions of facets outside of the contact region. For example, this effect is often noticeable at corners, such as when two same-sized, aligned blocks are in contact—if the contact surfaces wrap around the corners, the contact pressure contours will extend slightly around the corners.
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To minimize contact stress noise within a region of active contact, Abaqus/Standard computes nodal contact stresses as weighted averages of values associated with active contact constraints in which a node participates. Some filtering is applied to reduce the contact stress values reported for nodes on the fringe of the active contact region (that only weakly participate in contact constraints), but this filtering is not “perfect,” which can result in the contact zone size appearing somewhat exaggerated. Similarly, contact status output will also be affected at nodes that lie on the fringe of the active contact region. In such cases the contact status may be reported as closed at nodes in the exaggerated region even though it is open.
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Due to these factors, trying to infer the contact force distribution from the contact stress distribution can be somewhat misleading. Instead, you can request nodal contact force output, which accurately represents the contact force distribution present in the analysis.
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# Contact stresses due to edge-to-surface, edge-to-edge, and vertex-to-surface interactions
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For edge-to-surface contact and for edge-to-edge contact with the radial formulation where the active contact is along a line, the output variable CLINELOAD can be requested to the output database (.odb) in Abaqus/Standard. This contact load has units of force per length and is mesh independent. Contact stresses (in units of force per area) solely due to edge-to-surface contact (CSTRESSETOS) can be output for visualizing regions where the edge-to-surface constraints are active. The edge-to-surface formulation computes contact stresses in units of force per area by dividing contact force per edge length by a representative surface facet length. Since the contact area depends on the mesh size, edge-to-surface contact stresses are mesh dependent. For edge-to-edge contact using the cross product formulation where the active contact region is idealized as a point, the mesh-independent output variable CPOINTLOAD (with units of force) can be requested.
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For vertex-to-surface contact, the mesh-independent output variable CPOINTLOAD (with units of force) can be requested to the output database (.odb) in Abaqus/Standard.
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Contact stresses (CSTRESS) contain contributions from surface-to-surface, edge-to-surface, edgeto-edge, and vertex-to-surface constraints, if active. While accumulating contributions from edge-tosurface, edge-to-edge, and vertex-to-surface contact constraints, the constraint values are divided by either a representative surface facet length or its squared value to appropriately scale them to have units of force per area.
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Edges and vertices represent a discontinuity in the surface smoothness, and the true contact stress solution near an edge or a vertex is commonly characterized by a strong gradient. Subsequently, error indicator output for contact stresses (CSTRESSERI) are typically quite high and acceptable for regions in which constraints involving edges and vertices are significant.
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# Whole surface variables
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Whole surface variables are only marginally supported for general contact in Abaqus/Standard because these variable are associated with the overall general contact domain by default rather than individual surfaces associated with general contact. The only way to limit whole surface variables to be affected by a portion of the general contact domain is to specify a node set in the output request. Whole surface variables are computed as sums over all nodes (or optionally limited to a particular node set) of general contact while acting as slave nodes. For example, CFN is the total force acting on slave nodes due to contact pressure. CFN and other whole surface variables for general contact are typically of little utility, because contributions to the variable from different interactions within general contact will often cancel one another and the net result will typically depend on internal assignments of master and slave roles.
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# Requesting output
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Certain contact variables must be requested as a group. For example, to output the clearance between surfaces (COPEN), you must request the variable CDISP (contact displacements). CDISP outputs both
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COPEN and CSLIP (tangential motion of the surfaces during contact). A complete listing of available contact variables and identifiers is given in “Abaqus/Standard output variable identifiers,” Section 4.2.1.
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Output requests can be limited by specifying a node set containing a subset of the nodes acting as slave nodes for some general contact interactions. Instructions on forming these output requests are available in the following sections:
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• To request output to the data (.dat) file, see “Surface output from Abaqus/Standard” in “Output to the data and results files,” Section 4.1.2.
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• To request output to the output database (.odb) file, see “Surface output in Abaqus/Standard and Abaqus/Explicit” in “Output to the output database,” Section 4.1.3.
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# Output of tangential results
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Abaqus reports the values of tangential variables (frictional shear stress, viscous shear stress, and relative tangential motion) with respect to the local tangent directions defined on the surfaces. The local tangent directions CTANDIR1 and CTANDIR2 can be output by requesting the generic output variable CTANDIR. The definition of local tangent directions is explained in “Local tangent directions on a surface” in “Contact formulations in Abaqus/Standard,” Section 38.1.1. These directions do not always correspond to the global coordinate system, and they rotate with the contact pair in a geometrically nonlinear analysis.
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Abaqus/Standard calculates tangential results at each constraint point by taking the scalar product of the variable’s vector and a local tangent direction, or , associated with the constraint point. The number at the end of a variable’s name indicates whether the variable corresponds to the first or second local tangent direction. For example, CSHEAR1 is the frictional shear stress component in the first local tangent direction, while CSHEAR2 is the frictional shear stress component in the second local tangent direction.
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# Definition of accumulated incremental relative motion (slip)
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Abaqus/Standard defines the incremental relative motion (also known as slip) as the scalar product of the incremental relative nodal displacement vector and a local tangent direction. The incremental relative nodal displacement vector measures the motion of a slave node relative to the motion of the master surface. The incremental slip is accumulated only when the slave node is contacting the master surface. The sums of all such incremental slips during the analysis are reported as CSLIP1 and CSLIP2. Details about the calculation of this quantity can be found in “Small-sliding interaction between bodies,” Section 5.1.1 of the Abaqus Theory Guide; “Finite-sliding interaction between deformable bodies,” Section 5.1.2 of the Abaqus Theory Guide; and “Finite-sliding interaction between a deformable and a rigid body,” Section 5.1.3 of the Abaqus Theory Guide.
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# Extending the range for which contact opening output is provided for gaps
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To reduce computational costs, detailed computations to monitor potential points of interaction are avoided by default where surfaces are separated by a distance greater than the minimum gap distance at which contact forces (or thermal fluxes, etc.) may be transmitted. Therefore, contact opening (COPEN) output is typically not provided where surfaces are opened by more than a small amount compared
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to surface facet dimensions. You can extend the range for which Abaqus/Standard provides contact opening output; COPEN will be provided up to gap distances equal to a specified “tracking thickness.” Using this control may increase computational cost due to extra contact tracking computations, especially if you specify a large tracking thickness value.
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Input File Usage: \*SURFACE INTERACTION, TRACKING THICKNESS=value
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Abaqus/CAE Usage: You cannot adjust the default tracking thickness in Abaqus/CAE.
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# Whole model contact-related energy variables
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The contact-related energy variables, shown in Table 36.2.1–1, are available in Abaqus/Standard (see “Abaqus/Standard output variable identifiers,” Section 4.2.1). An example of using the contact-related energies is provided in “Energy computations in a contact analysis,” Section 1.1.25 of the Abaqus Example Problems Guide.
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Table 36.2.1–1 Contact-related energy output variables.
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<table><tr><td colspan="2">Description</td><td>Output variable</td></tr><tr><td colspan="2">Frictional dissipation</td><td>ALLFD</td></tr><tr><td rowspan="3">Elastic contact energy</td><td>Energy stored among all penalty springs and “softened” contact constraints associated with normal contact constraints</td><td>ALLCCEN</td></tr><tr><td>Energy stored among all penalty springs associated with tangential contact constraints</td><td>ALLCCET</td></tr><tr><td>Energy stored among all penalty springs and “softened” contact constraints associated with normal and tangential contact constraints (equal to the sum of ALLCCEN and ALLCCET)</td><td>ALLCCE</td></tr><tr><td rowspan="3">Energy dissipation associated with contact stabilization and contact damping</td><td>Normal contact direction for the whole model</td><td>ALLCCSDN</td></tr><tr><td>Tangential contact direction for the whole model</td><td>ALLCCSDT</td></tr><tr><td>Whole model (equal to the sum of ALLCCSDN and ALLCCSDT)</td><td>ALLCCSD</td></tr><tr><td>Energy associated with contact constraint “discontinuity work”</td><td>Accounts for the portion of the work done by contact forces when contact conditions change that is not accounted for by other contact energy variables</td><td>ALLCCDW</td></tr></table>
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The output variables ALLSD and ALLVD also account for dissipative energies associated with contact stabilization and contact damping.
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