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19 KiB
Markdown
206 lines
19 KiB
Markdown
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# Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Damage: Evolution tabbed page: Type: Energy: Softening: Linear
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# Exponential damage evolution
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For exponential softening Abaqus uses an evolution of the damage variable, D, that reduces to
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$$
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D = \int_ {\delta_ {m} ^ {o}} ^ {\delta_ {m} ^ {f}} \frac {T _ {\mathrm{eff}} d \delta}{G ^ {C} - G _ {o}}.
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$$
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In the expression above $T _ { \mathrm { e f f } }$ and are the effective traction and separation, respectively. $G _ { o }$ is the elastic energy at damage initiation. In this case the traction might not drop immediately after damage initiation, which is different from what is seen in Figure 37.1.10–5.
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Input File Usage: Use the following option to specify exponential softening:
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\*DAMAGE EVOLUTION, TYPE=ENERGY, $\mathrm { S O F T E N I N G { = } E X P O N E N T I A L }$
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Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Damage: Evolution tabbed page: Type: Energy: Softening: Exponential
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# Defining damage evolution data as a tabular function of mode mix
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As discussed earlier, the data defining the evolution of damage at the cohesive interface can be tabular functions of the mode mix. The manner in which this dependence must be defined in Abaqus is outlined below for mode-mix definitions based on energy and traction, respectively. In the following discussion it is assumed that the evolution is defined in terms of energy. Similar observations can also be made for evolution definitions based on effective separation.
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# Mode mix based on energy
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For an energy-based definition of mode mix, in the most general case of a three-dimensional state of separation with anisotropic shear behavior the fracture energy, $G ^ { C }$ , must be defined as a function of $( m _ { 2 } + m _ { 3 } )$ and $\left[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) \right]$ . The quantity $( m _ { 2 } + m _ { 3 } ) = G _ { S } / G _ { T }$ is a measure of the fraction of the total separation that is shear, while $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ] = G _ { t } / G _ { S }$ is a measure of the fraction of the total shear separation that is in the second shear direction. Figure 37.1.10–6 shows a schematic of the fracture energy versus mode-mix behavior. The limiting cases of pure normal and pure shear separations in the first and second shear directions are denoted in Figure 37.1.10–6 by $G _ { n } ^ { C } , G _ { s } ^ { \bar { C } }$ , and $G _ { t } ^ { C }$ , respectively. The lines labeled “Modes n-s,” “Modes $\mathrm { n - t } , \mathrm { ? }$ and “Modes $\mathbf { S } { - } \mathbf { t } ^ { \gamma }$ show the transition in behavior between the pure normal and the pure shear in the first direction, pure normal and pure shear in the second direction, and pure shears in the first and second directions, respectively. In general, $G ^ { C }$ must be specified as a function of $( m _ { 2 } + m _ { 3 } )$ at various fixed values of $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ]$ . In the discussion that follows we refer to a data set of $G ^ { C }$ versus $( m _ { 2 } + m _ { 3 } )$ corresponding to a fixed $\left[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) \right]$ as a “data block.” The following guidelines are useful in defining the fracture energy as a function of the mode mix:
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<details>
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<summary>flowchart</summary>
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```mermaid
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graph TD
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A["G_s^c"] -->|Modes n-s| B["G_n^c"]
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A -->|Modes s-t| C["G_t^c"]
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B -->|Modes n-t| D["G_n^c"]
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C -->|Modes n-t| D
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E["O"] -->|1.0| F["A"]
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F -->|m_2 + m_3 = (G_S / G_T)| A
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G["B"] -->|m_3 / (m_2 + m_3) = (G_t / G_S)| D
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H["C"] -->|1.0| F
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H -->|1.0| B
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```
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</details>
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Figure 37.1.10–6 Fracture energy as a function of mode mix.
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• For a two-dimensional problem $G ^ { C }$ needs to be defined as a function of $m _ { 2 } \ ( m _ { 3 } = 0$ in this case) only. The data column corresponding to $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ]$ must be left blank. Hence, essentially only one “data block” is needed.
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• For a three-dimensional problem with isotropic shear response, the shear behavior is defined by the sum $( m _ { 2 } + m _ { 3 } )$ and not by the individual values of $m _ { 2 }$ and $m _ { 3 }$ . Therefore, in this case a single “data block” (the “data block” for $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ] = 0 )$ also suffices to define the fracture energy as a function of the mode mix.
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• In the most general case of three-dimensional problems with anisotropic shear behavior, several “data blocks” would be needed. As discussed earlier, each “data block” would contain $G ^ { C }$ versus $( m _ { 2 } + m _ { 3 } )$ at a fixed value of $\left[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) \right]$ . In each “data block” $\left( m _ { 2 } + m _ { 3 } \right)$ can vary between 0 and 1.0. The case $( m _ { 2 } + m _ { 3 } ) = 0$ (the first data point in any “data block”), which corresponds to a purely normal mode, can never be achieved when $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ] \neq 0 \ ( \mathrm { i } . \mathrm { e } .$ , the only valid point on line OB in Figure 37.1.10–6 is the point O, which corresponds to a purely normal separation). However, in the tabular definition of the fracture energy as a function of mode mix, this point simply serves to set a limit that ensures a continuous change in fracture energy as a purely normal state is approached from various combinations of normal and shear separations. Hence, the fracture energy of the first data point in each “data block” must always be set equal to the fracture energy in a purely normal separation $( G _ { n } ^ { C } )$ .
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As an example of the anisotropic shear case, consider that you want to input three “data blocks” corresponding to fixed values of $[ m _ { 3 } / ( m _ { 2 } + m _ { 3 } ) ] = 0 . , 0 . 2$ , and 1.0, respectively. For each of the three “data blocks,” the first data point must be $( G _ { n } ^ { C } , 0 )$ for the reasons discussed above. The rest of the data points in each “data block” define the variation of the fracture energy with increasing proportions of shear separation.
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# Mode mix based on traction
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The fracture energy needs to be specified in tabular form of $G ^ { C }$ versus $\phi _ { 1 }$ and $\phi _ { 2 }$ . Thus, $G ^ { C }$ needs to be specified as a function of $\phi _ { 1 }$ at various fixed values of $\phi _ { 2 }$ . A “data block” in this case corresponds to a set of data for $G ^ { C }$ versus $\phi _ { 1 } ,$ at a fixed value of $\phi _ { 2 }$ . In each “data block” $\phi _ { 1 }$ may vary from 0 (purely normal separation) to 1 (purely shear separation). An important restriction is that each data block must specify the same value of the fracture energy for $\phi _ { 1 } = 0$ . This restriction ensures that the energy required for fracture as the traction vector approaches the normal direction does not depend on the orientation of the projection of the traction vector on the shear plane (see Figure 37.1.10–2).
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# Viscous regularization in Abaqus/Standard
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Models exhibiting various forms of softening behavior and stiffness degradation often lead to severe convergence difficulties in Abaqus/Standard. Viscous regularization of the constitutive equations defining surface-based cohesive behavior can be used to overcome some of these convergence difficulties. This technique is also applicable to cohesive elements, fastener damage, and the concrete material model in Abaqus/Standard. Viscous regularization damping causes the tangent stiffness matrix that defines the contact stresses to be positive for sufficiently small time increments.
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The approximate amount of energy associated with viscous regularization over the whole model is included in the output variable ALLCD.
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Input File Usage: \*DAMAGE STABILIZATION
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Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Damage: Stabilization tabbed page: Viscosity coefficient
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# Postfailure behavior
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Two types of postfailure behavior can be specified to define the cohesive behavior at a node on the slave surface after the maximum degradation value, $D _ { m a x } = 1 . 0$ , has been reached at the node.
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By default, once fully degraded, normal contact behavior is enforced at the node and no further cohesive constraints are enforced. If the slave node re-enters contact, penetrations will give rise to compressive contact stresses, and frictional stresses will be applied in the shear directions according to the prescribed friction model, if any. Separations can occur without giving rise to any cohesive stresses.
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In some situations it may be desirable to enforce cohesive behavior again if a slave node re-enters contact, even after maximum degradation has been reached. For cohesive behavior allowing repeated contacts, the overall damage variable will be re-initialized to zero when a failed slave node re-enters contact. Subsequently, normal separations may give rise to tensile cohesive stresses, and shear separations may give rise to tangential cohesive stresses in accordance with the type of cohesive
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behavior defined. Further loading can again cause the cohesive stresses to undergo progressive damage, degrade, and fail.
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<table><tr><td rowspan="2">Input File Usage:</td><td>Use the following option to enforce cohesive behavior subsequent to maximum degradation:</td></tr><tr><td>*COHESIVE BEHAVIOR, REPEATED CONTACTS</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Interaction module: contact property editor: Mechanical→Cohesive Behavior: Allow cohesive behavior during repeated post-failure contacts</td></tr></table>
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# Virtual Crack Closure Technique in Abaqus/Explicit
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In Abaqus/Explicit, the surface-based cohesive behavior framework can be used to model brittle crack propagation problems based on linear elastic fracture mechanics principles. The Virtual Crack Closure Technique (VCCT) fracture criterion can be used to model crack propagation in initially partially bonded surfaces. A detailed discussion of this topic can be found in “Crack propagation analysis,” Section 11.4.3.
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The VCCT fracture criterion cannot be combined with a damage-based surface behavior of the traction-separation response. However, you can use a surface-based VCCT fracture criterion in conjunction with cohesive elements. VCCT could model brittle failure/crack propagation while the cohesive elements could model other aspects of the bonded interface such as stitches.
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Input File Usage: Use the following options to enforce cohesive behavior subsequent to maximum degradation:
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<table><tr><td>*COHESIVE BEHAVIOR</td></tr><tr><td>*FRACTURE CRITERION, TYPE= VCCT</td></tr></table>
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# Cohesive surfaces versus cohesive elements
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As described above, the formulation used for surface-based cohesive behavior is very similar to that for cohesive elements with traction-separation response. However, certain differences exist.
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Interface thickness effects are never considered for cohesive surfaces; in cohesive elements with traction-separation response, thickness effects can be incorporated by either specifying a nonzero thickness for the interface or by requiring the initial constitutive thickness to be determined from the nodal coordinates of the cohesive elements. Since thickness effects are not considered for cohesive surfaces, material properties used to describe the constitutive response for traction-separation cohesive elements with thickness effects may not be directly reusable for cohesive surfaces.
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For cohesive surfaces the cohesive constraint is enforced at each slave node; in cohesive elements the cohesive constraints are calculated at the material points (for the locations of material points in cohesive elements, see “Two-dimensional cohesive element library,” Section 32.5.9, and “Three-dimensional cohesive element library,” Section 32.5.10). Hence for cohesive surfaces, refining the slave surface as compared to the master surface will likely lead to improved constraint satisfaction and more accurate results.
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# Output
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In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), the following variables have special meaning for cohesive surfaces with traction-separation behavior:
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<table><tr><td>CSDMG</td><td>Overall value of the scalar damage variable, D.</td></tr><tr><td>CSMAXSCRT</td><td>This variable indicates whether the maximum contact stress damage initiation criterion has been satisfied at a contact point. It is evaluated as max{ $\frac{\langle t_n \rangle}{t_n^o}$ , $\frac{t_s}{t_s^o}$ , $\frac{t_t}{t_t^o}$ }.</td></tr><tr><td>CSMAXUCRT</td><td>This variable indicates whether the maximum separation damage initiation criterion has been satisfied at a contact point. It is evaluated as max{ $\frac{\langle \delta_n \rangle}{\delta_n^o}$ , $\frac{\delta_s}{\delta_s^o}$ , $\frac{\delta_t}{\delta_t^o}$ }.</td></tr><tr><td>CSQUADSCRT</td><td>This variable indicates whether the quadratic contact stress damage initiation criterion has been satisfied at a contact point. It is evaluated as $(\frac{\langle t_n \rangle}{t_n^o})^2 + (\frac{t_s}{t_s^o})^2 + (\frac{t_t}{t_t^o})^2$ .</td></tr><tr><td>CSQUADUCRT</td><td>This variable indicates whether the quadratic separation damage initiation criterion has been satisfied at a contact point. It is evaluated as $(\frac{\langle \delta_n \rangle}{\delta_n^o})^2 + (\frac{\delta_s}{\delta_s^o})^2 + (\frac{\delta_t}{\delta_t^o})^2$ .</td></tr></table>
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For the variables above that indicate whether a certain damage initiation criterion has been satisfied or not, a value that is less than 1.0 indicates that the criterion has not been satisfied, while a value of 1.0 indicates that the criterion has been satisfied. If damage evolution is specified for this criterion, the maximum value of this variable does not exceed 1.0.
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# Additional references
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• Benzeggagh, M. L., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” Composites Science and Technology, vol. 56, pp. 439–449, 1996.
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• Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002.
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# 37.2 Thermal contact properties
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• “Thermal contact properties,” Section 37.2.1
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# 37.2.1 THERMAL CONTACT PROPERTIES
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Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
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# References
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• “Contact interaction analysis: overview,” Section 36.1.1
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• “User-defined interfacial constitutive behavior,” Section 37.1.6
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• “GAPCON,” Section 1.1.10 of the Abaqus User Subroutines Reference Guide
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• \*GAP
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• \*GAP CONDUCTANCE
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• \*GAP HEAT GENERATION
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• \*GAP RADIATION
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• \*INTERFACE
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• \*SURFACE INTERACTION
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• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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# Overview
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Thermal interaction at the surface of a body:
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• can be included in heat transfer problems (“Uncoupled heat transfer analysis,” Section 6.5.2; “Fully coupled thermal-stress analysis,” Section 6.5.3; “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4; and “Coupled thermal-electrical analysis,” Section 6.7.3);
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• can involve conductive heat transfer between surfaces;
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• can involve radiative heat transfer between surfaces when the surfaces are separated by a narrow gap;
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• in Abaqus/Standard can involve convective heat flow across the boundary layer between a solid surface and a moving fluid;
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• can involve heat generated by frictional work in fully coupled thermomechanical or fully coupled thermal-electrical-structural simulations; and
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• in Abaqus/Standard can involve heat generated by an electrical current (Joule heating) in fully coupled thermal-electrical and fully coupled thermal-electrical-structural analyses.
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General radiative heat transfer between surfaces is not discussed in this section. For information on modeling these types of problems in Abaqus/Standard, see “Cavity radiation,” Section 41.1.1. The thermal contact property models described here are for bodies in close proximity or in contact. For these problems gap radiation may be more efficient and robust than cavity radiation.
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# Including thermal properties in a contact property definition
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All of the thermal properties discussed in this section—gap conductance, gap radiation, and gap heat generation—can be included in a contact property definition for both surface-based contact and element-based contact. All three types of thermal properties can be included in the same contact property definition.
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The thermal contact property model between two surfaces can also be completely defined through user subroutine UINTER, VUINTER, or VUINTERACTION (see “User-defined interfacial constitutive behavior,” Section 37.1.6).
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Input File Usage: Use the following options for surface-based contact:
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\*SURFACE INTERACTION, NAME=name
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\*GAP CONDUCTANCE
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\*GAP RADIATION
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\*GAP HEAT GENERATION
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Use the following options for element-based contact in Abaqus/Standard:
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\*INTERFACE or \*GAP, ELSET=name
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\*GAP CONDUCTANCE
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\*GAP RADIATION
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\*GAP HEAT GENERATION
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Use the following option for user-defined, surface-based contact:
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\*SURFACE INTERACTION, USER
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Abaqus/CAE Usage: Interaction module: contact property editor: Thermal→Thermal Conductance, Heat Generation, and/or Radiation
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Element-based contact and user-defined surface-based contact are not supported in Abaqus/CAE.
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# Thermal contact considerations in Abaqus/Explicit
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Gap conductance and gap radiation are enforced in Abaqus/Explicit with an explicit algorithm analogous to the penalty method for mechanical contact interaction. Therefore, gap conductance and gap radiation can influence the stability condition; although in a fully coupled temperature-displacement analysis the mechanical portion of the system usually governs the overall stability condition (see “Fully coupled thermal-stress analysis,” Section 6.5.3). Extremely large values of gap conductance or gap radiation can result in a decrease in the stable time increment, which will be accounted for by the automatic time incrementation algorithm in Abaqus/Explicit.
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Gap heat generation is applied within whichever algorithm (kinematic or penalty) is used to enforce the mechanical contact constraints. Gap heat generation has no effect on the stable time increment.
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Thermal contact fluxes may be inaccurate during increments in which mesh adaptivity occurs if the mechanical contact constraints are enforced kinematically, because mesh adjustments occur in Abaqus/Explicit between the determination of the mechanical contact state for kinematic contact and
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