김경종
174 lines
12 KiB
Markdown
174 lines
12 KiB
Markdown
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fluid flow occurs. Separate controls are provided for the contribution of fluid flow across the interface $( q _ { a c r o s s } )$ and the contribution of fluid flow into the interface $( q _ { g a p } )$ .
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# Input File Usage:
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Use the following option to specify a cutoff distance $( d _ { a c r o s s } )$ for the contribution of fluid flow across the contact interface $\left( q _ { a c r o s s } \right)$ :
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$$
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* \text { CONTACT PERMEABILITY, CUTOFF FLOW ACROSS } = d _ {a c r o s s}
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$$
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Use the following option to specify a cutoff distance $( d _ { g a p } )$ for the contribution of fluid flow into the contact interface $( q _ { g a p } )$ :
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$$
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* \text { CONTACT PERMEABILITY, CUTOFF GAP FILL } = d _ {g a p}
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$$
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# Controlling contact permeability associated with fluid flow across a contact interface
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If you do not specify contact permeability characteristics, the default model ensures continuity of the pore pressures on opposite sides of a contact interface while the contact separation is less than the threshold distance discussed in “Controlling the distance within which pore fluid contact properties are active”:
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$$
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p _ {A} - p _ {B} = 0,
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$$
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where $p _ { A }$ and $p _ { B }$ are pore pressures at points on opposite sides of the interface. This relationship implies that contact permeability across the interface is infinite.
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Alternatively, you can specify a contact permeability, k, such that fluid flow across a contact interface $( q _ { a c r o s s }$ , discussed above in “Including pore fluid properties in a contact property definition”) is proportional to the difference in pore pressure magnitudes across the interface:
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$$
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q _ {a c r o s s} = k (p _ {A} - p _ {B}).
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$$
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When defining k directly, define it as
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$$
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k = k (p _ {c o n t a c t}, \bar {p} _ {p o r e}, \bar {\theta}, \bar {f} _ {\gamma}),
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$$
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where
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Pcontact
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is the contact pressure transmitted across the interface between A and B,
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$$
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\bar {p} _ {p o r e} = \frac {1}{2} (p _ {p o r e A} + p _ {p o r e B})
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$$
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$$
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\bar {\theta} = \frac {1}{2} (\theta_ {A} + \theta_ {B})
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$$
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$$
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\bar {f} _ {\gamma} = \frac {1}{2} \left(f _ {\gamma} ^ {A} + f _ {\gamma} ^ {B}\right)
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$$
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is the average of the pore pressures at A and B,
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is the average of the surface temperatures at A and B, and
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is the average of any predefined field variables at A and B.
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Figure 37.4.1–2 shows an example of k depending on the contact pressure. Use tabular data to specify the value of k at one or more contact pressures as p increases. The value of k remains constant for contact pressures outside of the interval defined by the data points. Once the surfaces have separated, k remains at a constant value until the separation between the surfaces exceeds the specified flow cutoff distance (see “Controlling the distance within which pore fluid contact properties are active”), at which point k drops to zero.
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Figure 37.4.1–2 Contact-pressure-dependent contact permeability.
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Input File Usage: \*CONTACT PERMEABILITY $k , p _ { c o n t a c t } , \bar { p } _ { p o r e } , \bar { \theta }$
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# Defining gap permeability to be a function of predefined field variables
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In addition to the dependencies mentioned previously, the gap permeability can be dependent on any number of predefined field variables, $\bar { f } _ { \gamma }$ . To make the gap permeability depend on field variables, at least two data points are required for each field variable value.
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Input File Usage: $\begin{array} { r l } { { } } & { { \ast \mathrm { C O N T A C T ~ P E R M E A B I L I T Y , D E P E N D E N C I E S } = n } } \\ { { } } & { { k , ~ p _ { c o n t a c t } , ~ \bar { p } _ { p o r e } , ~ \bar { \theta } , ~ \bar { f } _ { \gamma } } } \end{array}$
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# Coupled heat transfer–pore fluid contact properties
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Heat transfer can be considered simultaneously with pore fluid flow, in which case heat flow across the contact interface can occur in conjunction with fluid flow. These various contact property aspects are defined with separate options as part of a single contact property definition that you assign to the contact interaction; see “Thermal contact properties,” Section 37.2.1, for details on defining heat transfer properties.
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# Output
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You can write the contact surface variables associated with the interaction of contact pairs to the Abaqus/Standard data (.dat), results (.fil), and output database (.odb) files. In addition to the surface variables associated with the mechanical contact analysis (shear stresses, contact pressures, etc.) several pore fluid-related variables (such as pore fluid volume flux per unit area) on the contact interface can be reported. A detailed discussion of these output requests can be found in “Surface output
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from Abaqus/Standard” in “Output to the data and results files,” Section 4.1.2, and “Surface output in Abaqus/Standard and Abaqus/Explicit” in “Output to the output database,” Section 4.1.3.
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Abaqus/Standard provides the following output variables related to the pore fluid interaction of surfaces:
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<table><tr><td>PFL</td><td>Pore volume flux per unit area leaving the slave surface.</td></tr><tr><td>PFLA</td><td>PFL multiplied by the area associated with the slave node.</td></tr><tr><td>PTL</td><td>Time integrated PFL.</td></tr><tr><td>PTLA</td><td>Time integrated PFLA.</td></tr><tr><td>TPFL</td><td>Total pore volume flux leaving the slave surface.</td></tr><tr><td>TPTL</td><td>Time integrated TPFL.</td></tr></table>
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# 38. Contact Formulations and Numerical Methods
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Contact formulations and numerical methods in Abaqus/Standard 38.1
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Contact formulations and numerical methods in Abaqus/Explicit 38.2
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# 38.1 Contact formulations and numerical methods in Abaqus/Standard
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• “Contact formulations in Abaqus/Standard,” Section 38.1.1
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• “Contact constraint enforcement methods in Abaqus/Standard,” Section 38.1.2
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• “Smoothing contact surfaces in Abaqus/Standard,” Section 38.1.3
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# 38.1.1 CONTACT FORMULATIONS IN Abaqus/Standard
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Products: Abaqus/Standard Abaqus/CAE
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# References
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• “Surfaces: overview,” Section 2.3.1
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• “Defining general contact interactions in Abaqus/Standard,” Section 36.2.1
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• “Defining contact pairs in Abaqus/Standard,” Section 36.3.1
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• \*CONTACT
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• \*CONTACT PAIR
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• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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# Overview
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Abaqus/Standard provides several contact fomulations. Each formulation is based on a choice of a contact discretization, a tracking approach, and assignment of “master” and “slave” roles to the contact surfaces. For general contact interactions, the discretization, tracking approach, and surface role assignments are selected automatically by Abaqus/Standard; for contact pairs, you can specify these aspects of the contact formulation using the interface described in “Defining contact pairs in Abaqus/Standard,” Section 36.3.1. The default contact formulation is applicable in most situations, but you may find it desirable to choose another formulation in some cases. This section discusses in detail the formulations that Abaqus/Standard uses in contact simulations.
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Your choice of a tracking approach will have a considerable impact on how contact surfaces interact. 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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• finite sliding, which is the most general and allows any arbitrary motion of the surfaces (see “Finitesliding 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); and
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• small sliding, which assumes that although two bodies may undergo large motions, there will be relatively little sliding of one surface along the other (see “Small-sliding interaction between bodies,” Section 5.1.1 of the Abaqus Theory Guide).
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You can choose between node-to-surface contact discretization and true surface-to-surface contact discretization for each of the above tracking approaches.
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# Formulations for general contact
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General contact in Abaqus/Standard always uses the finite-sliding, surface-to-surface contact formulation. This formulation can also be used for contact pairs, but it is not the default. The discussions in this section of finite-sliding, surface-to-surface contact apply equally to general contact and to contact pairs.
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In a general contact domain the master and slave roles are assigned to surfaces automatically, although it is possible to override these default assignments. The behavior of master surfaces and slave surfaces is consistent across general contact and contact pair interactions. The specification of master and slave surfaces in a general contact domain is covered in detail in “Numerical controls for general contact in Abaqus/Standard,” Section 36.2.6.
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# Discretization of contact pair surfaces
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Abaqus/Standard applies conditional constraints at various locations on interacting surfaces to simulate contact conditions. The locations and conditions of these constraints depend on the contact discretization used in the overall contact formulation. Abaqus/Standard offers two contact discretization options: a traditional “node-to-surface” discretization and a true “surface-to-surface” discretization.
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# Node-to-surface contact discretization
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With traditional node-to-surface discretization the contact conditions are established such that each “slave” node on one side of a contact interface effectively interacts with a point of projection on the “master” surface on the opposite side of the contact interface (see Figure 38.1.1–1). Thus, each contact condition involves a single slave node and a group of nearby master nodes from which values are interpolated to the projection point.
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Traditional node-to-surface discretization has the following characteristics:
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• The slave nodes are constrained not to penetrate into the master surface; however, the nodes of the master surface can, in principle, penetrate into the slave surface (for example, see the case on the upper-right of Figure 38.1.1–2).
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• The contact direction is based on the normal of the master surface.
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• The only information needed for the slave surface is the location and surface area associated with each node; the direction of the slave surface normal and slave surface curvature are not relevant. Thus, the slave surface can be defined as a group of nodes—a node-based surface.
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• Node-to-surface discretization is available even if a node-based surface is not used in a contact pair definition.
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# Surface-to-surface contact discretization
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Surface-to-surface discretization considers the shape of both the slave and master surfaces in the region of contact constraints. Surface-to-surface discretization has the following key characteristics:
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