김경종
312 lines
16 KiB
Markdown
312 lines
16 KiB
Markdown
<!-- source-page: 901 -->
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\*ENRICHMENT ACTIVATION, NAME=name, ACTIVATE=AUTO OFF
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# Abaqus/CAE Usage:
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To modify the status of the crack propagation capability in a step, you must first create an XFEM crack growth interaction:
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Interaction module: Create Interaction: select initial step: XFEM Crack Growth: select crack: Interaction manager: select interaction in step: Edit: toggle on/off Allow crack growth in this step
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# Contour integral
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When you evaluate the contour integrals using the conventional finite element method (“Contour integral evaluation,” Section 11.4.2), you must define the crack front explicitly and specify the virtual crack extension direction in addition to matching the mesh to the cracked geometry. Detailed focused meshes are generally required and obtaining accurate contour integral results for a crack in a three-dimensional curved surface can be cumbersome. The extended finite element in conjunction with the level set method alleviates these shortcomings. The adequate singular asymptotic fields and the discontinuity are ensured by the special enrichment functions in conjunction with additional degrees of freedom. In addition, the crack front and the virtual crack extension direction are determined automatically by the level set signed distance functions.
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# Input File Usage:
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Use the following option to obtain contour integral for a named enriched feature with the extended finite element method:
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\*CONTOUR INTEGRAL, XFEM, CRACK NAME=name
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# Abaqus/CAE Usage:
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Step module: history output request editor: Domain: Crack: crack name
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# Specifying the enrichment radius
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Although XFEM has alleviated the shortcomings associated with refining the mesh in the neighborhood of the crack front due to the added asymptotic fields, you must generate a sufficient number of elements around the crack front to obtain path-independent contours. The group of elements within a small radius from the crack front are enriched and become involved in the contour integral calculations. The default enrichment radius is three times the typical element characteristic length in the enriched area. You must include the elements inside the enrichment radius in the element set used to define the enriched region.
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# Input File Usage:
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Use the following option to specify an enrichment radius:
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\*ENRICHMENT, ENRICHMENT RADIUS
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# Abaqus/CAE Usage:
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Interaction module: crack editor: Enrichment radius: Analysis default or Specify
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# Procedures
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Modeling discontinuities as an enriched feature can be performed using any of the following:
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• static analysis (see “Static stress analysis,” Section 6.2.2);
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• implicit dynamic analysis (see “Implicit dynamic analysis using direct integration,” Section 6.3.2); or
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• low-cycle fatigue analysis using the direct cyclic approach (“Low-cycle fatigue analysis using the direct cyclic approach,” Section 6.2.7).
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• geostatic stress field analysis (see “Geostatic stress state,” Section 6.8.2); or
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• coupled pore fluid diffusion/stress analysis (see “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1).
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# Initial conditions
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Initial conditions to identify initial boundaries or interfaces of an enriched feature can be specified (see “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1).
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# Boundary conditions
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Boundary conditions can be applied to any of the displacement or pore pressure degrees of freedom (see “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.3.1).
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# Loads
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The following types of loading can be prescribed in a model with an enriched feature:
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• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–3) or the pore pressure degree of freedom (8); see “Concentrated loads,” Section 34.4.2.
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• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 34.4.3. The distributed load types available with particular elements are described in Part VI, “Elements.”
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# Predefined fields
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The following predefined fields can be specified in a model with an enriched feature, as described in “Predefined fields,” Section 34.6.1:
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• Nodal temperatures (although temperature is not a degree of freedom in stress/displacement elements). The specified temperature affects temperature-dependent critical stress and strain failure criteria.
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• The values of user-defined field variables. The specified value affects field-variable-dependent material properties.
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# Material options
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Any of the mechanical constitutive models in Abaqus/Standard, including user-defined materials (defined using user subroutine “UMAT,” Section 1.1.44 of the Abaqus User Subroutines Reference Guide) can be used to model the mechanical behavior of the enriched element in a crack propagation analysis. See Part V, “Materials.” The inelastic definition at a material point must be used in conjunction with the linear elastic material model (“Linear elastic behavior,” Section 22.2.1) or the hypoelastic material model (“Hypoelastic behavior,” Section 22.4.1). Only isotropic elastic materials are supported when evaluating the contour integral for a stationary crack.
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<!-- source-page: 903 -->
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# Elements
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Only first-order solid continuum stress/displacement elements, first-order displacement/pore pressure solid continuum elements, and second-order stress/displacement tetrahedron elements can be associated with an enriched feature. For propagating cracks these include bilinear plane strain and plane stress elements, bilinear axisymmetric elements, linear brick elements, linear tetrahedron elements, and secondorder tetrahedron elements. For stationary cracks, these include linear brick elements, linear tetrahedron elements, and second-order tetrahedron elements.
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For an incompatible mode element, Abaqus/Standard discards the contribution due to the incompatible deformation mode immediately after the element is fractured under a tensile loading. Therefore, the stress level at the cracked element may not return completely to its originally unloaded state even when this cracked element is unloaded completely and the contact of the cracked element surfaces is reestablished.
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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), the following nodal, whole element, and surface variables have special meaning for a model with an enriched feature.
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Nodal variables:
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<table><tr><td>PHILSM</td><td>Signed distance function to describe the crack surface.</td></tr><tr><td>PSILSM</td><td>Signed distance function to describe the initial crack front.</td></tr></table>
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Whole element variables:
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<table><tr><td>STATUSXFEM</td><td>Status of the enriched element. (The status of an enriched element is 1.0 if the element is completely cracked and 0.0 if the element contains no crack. If the element is partially cracked, the value of STATUSXFEM lies between 1.0 and 0.0.)</td></tr></table>
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<table><tr><td>ENRRTXFEM</td><td>All components of strain energy release rate when linear elastic fracture mechanics with the extended finite element method is used.</td></tr></table>
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<table><tr><td>LOADSXFEM</td><td>Distributed pressure loads applied to the crack surface.</td></tr></table>
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The following whole element output variables are available only when fluid flow is enabled within the cracked enriched element surfaces:
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<table><tr><td>GFVRXFEM</td><td>Gap fluid volume rate of the enriched element.</td></tr><tr><td>CRDCUTXFEM</td><td>Crack midpoint coordinates at the element edges of the enriched element.</td></tr></table>
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<!-- source-page: 904 -->
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PFOPENXFEM Fracture opening of the enriched element.
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PFOPENXFEMCOMP Fracture opening at the element edges of the enriched element.
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PORPRES Fluid pressure of the enriched element.
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PORPRESCOMP Fluid pressure at the element edges of the enriched element.
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LEAKVRTXFEM Leak-off flow rate at the top of the enriched element.
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LEAKVRBXFEM Leak-off flow rate at the bottom of the enriched element.
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ALEAKVRTXFEM Accumulated leak-off flow volume at the top of the enriched element.
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ALEAKVRBXFEM Accumulated leak-off flow volume at the bottom of the enriched element.
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Surface variables (available only for propagating cracks modeled with first-order solid continuum elements):
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CRKDISP Crack opening and relative tangential motions on cracked surfaces in enriched elements.
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CSDMG Damage variable on cracked surfaces in enriched elements.
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CRKSTRESS Remaining residual pressure and tangential shear stresses on cracked surfaces in enriched elements.
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The following surface output variables are available only when fluid flow is enabled within the cracked enriched element surfaces:
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GFVR Fluid volume rate within the cracked surfaces in the enriched element.
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PORPRES Pore pressure within the cracked surfaces in the enriched element.
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PORPRESURF Pore pressure on the cracked surfaces in the enriched element.
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LEAKVR Leak-off flow rate on the cracked surfaces in the enriched element.
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ALEAKVR Accumulated leak-off flow volume on the cracked surfaces in the enriched element.
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# Use of unsymmetric matrix storage and solution
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When the pore pressure degrees of freedom are activated in the enriched elements, matrices are unsymmetric; therefore, unsymmetric matrix storage and solution may be needed to improve convergence (see “Matrix storage and solution scheme in Abaqus/Standard” in “Defining an analysis,” Section 6.1.2).
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# Visualization
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A crack can be visualized through the iso-surface for the signed distance function PHILSM.
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If a crack cuts through a very tiny corner of an enriched element, the displacements along the crack front in the enriched element may be distorted in rare cases in the Visualization module of Abaqus/CAE
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<!-- source-page: 905 -->
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(Abaqus/Viewer) when displaying the contours. The distortion, however, is not present when viewing only the deformed shape.
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When an element is cut through by a crack, the cracked element splits into two parts, each part formed by a real domain and a phantom domain, as illustrated in Figure 10.7.1–2. Contour plot integration point values for cracked elements consider contributions from only the real domains in both parts of the cracked elements. However, when you probe cracked elements, only the contribution from the part of the elements containing the real domain $\Omega _ { 0 } ^ { - }$ and the phantom domain $\Omega _ { p } ^ { + }$ is reported.
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When evaluating the contour integrals in a stationary crack, additional integration stations are introduced internally in the elements enriched with singular asymptotic crack-tip fields. However, visualization of the element output variables in those additional integration points is not supported in the Visualization module of Abaqus/CAE (Abaqus/Viewer).
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# Limitations
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The following limitations exist with an enriched feature:
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• An enriched element cannot be intersected by more than one crack.
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• A crack is not allowed to turn more than $9 0 ^ { \circ }$ in one increment during an analysis.
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• Only asymptotic crack-tip fields in an isotropic elastic material are considered for a stationary crack.
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• Adaptive remeshing is not supported.
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• Composite solid elements are not supported.
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• Import analysis is not supported.
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# Input file template
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The following is an example of modeling crack propagation with the XFEM-based cohesive segments method:
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```txt
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*HEADING
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...
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*NODE, NSET=ALL
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...
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*ELEMENT, TYPE=C3D8, ELSET=REGULAR
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*ELEMENT, TYPE=C3D8, ELSET=ENRICHED
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...
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*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR
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*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED
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*ENRICHMENT, TYPE=PROPAGATION CRACK, ELSET=ENRICHED, NAME=ENRICHMENT, INTERACTION=INTERACTION
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*SURFACE, TYPE=XFEM, NAME=SURF_NAME
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Data lines to specify the names of enriched features
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*MATERIAL, NAME=STEEL1
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...
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```
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<!-- source-page: 906 -->
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```python
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*MATERIAL, NAME=STEEL2
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* DAMAGE INITIATION, CRITERION=MAXPS, TOLERANCE=0.05
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* DAMAGE EVOLUTION, TYPE=ENERGY
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Data lines to specify the failure mechanism
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...
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*SURFACE INTERACTION, NAME=INTERACTION
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*SURFACE BEHAVIOR
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Data lines to specify the contact of cracked element surfaces
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...
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*STEP
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*STATIC
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...
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*END STEP
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*STEP
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*STATIC
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...
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*ENRICHMENT ACTIVATION, TYPE=PROPAGATION CRACK,
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NAME=ENRICHMENT, ACTIVATE=OFF
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...
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*END STEP
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```
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The following is an example of modeling crack propagation with the XFEM-based LEFM approach:
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```txt
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*HEADING
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...
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*NODE, NSET=ALL
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...
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*ELEMENT, TYPE=C3D8, ELSET=REGULAR
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*ELEMENT, TYPE=C3D8, ELSET=ENRICHED
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...
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*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR
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*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED
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*ENRICHMENT, TYPE=PROPAGATION CRACK, ELSET=ENRICHED, NAME=ENRICHMENT, INTERACTION=INTERACTION
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*MATERIAL, NAME=STEEL1
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...
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*MATERIAL, NAME=STEEL2
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*DAMAGE INITIATION, CRITERION=MAXPS, TOLERANCE=0.05
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Data lines to specify the crack nucleation mechanism
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...
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*SURFACE INTERACTION, NAME=INTERACTION
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```
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<!-- source-page: 907 -->
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```txt
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* SURFACE BEHAVIOR
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* FRACTURE CRITERION, TYPE=VCCT, TOLERANCE=0.05, VISCOSITY=0.00001
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Data lines to specify the crack propagation criterion
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...
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* END STEP
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```
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The following is an example of calculating contour integrals in stationary cracks with the extended finite element method:
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```txt
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*HEADING
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...
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*NODE, NSET=ALL
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...
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*ELEMENT, TYPE=C3D8, ELSET=REGULAR
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*ELEMENT, TYPE=C3D8, ELSET=ENRICHED
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...
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*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR
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*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED
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*ENRICHMENT, TYPE=STATIONARY CRACK, ELSET=ENRICHED, NAME=ENRICHMENT, ENRICHMENT RADIUS
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*MATERIAL, NAME=STEEL1
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...
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*MATERIAL, NAME=STEEL2
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...
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*STEP
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*STATIC
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...
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*CONTOUR INTEGRAL, CRACK NAME=ENRICHMENT, XFEM
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*END STEP
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```
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# Additional references
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• Belytschko, T., and T. Black, “Elastic Crack Growth in Finite Elements with Minimal Remeshing,” International Journal for Numerical Methods in Engineering, vol. 45, pp. 601–620, 1999.
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• Benzeggagh, M., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” Composite Science and Technology, vol. 56, p. 439, 1996.
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• Elguedj, T., A. Gravouil, and A. Combescure, “Appropriate Extended Functions for X-FEM Simulation of Plastic Fracture Mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 501–515, 2006.
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<!-- source-page: 908 -->
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• Melenk, J., and I. Babuska, “The Partition of Unity Finite Element Method: Basic Theory and Applications,” Computer Methods in Applied Mechanics and Engineering, vol. 39, pp. 289–314, 1996.
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• Reeder, J., S. Kyongchan, P. B. Chunchu, and D. R.. Ambur, “Postbuckling and Growth of Delaminations in Composite Plates Subjected to Axial Compression” 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, vol. 1746, p. 10, 2002.
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• Remmers, J. J. C., R. de Borst, and A. Needleman, “The Simulation of Dynamic Crack Propagation using the Cohesive Segments Method,” Journal of the Mechanics and Physics of Solids, vol. 56, pp. 70–92, 2008.
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• Song, J. H., P. M. A. Areias, and T. Belytschko, “A Method for Dynamic Crack and Shear Band Propagation with Phantom Nodes,” International Journal for Numerical Methods in Engineering, vol. 67, pp. 868–893, 2006.
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• Sukumar, N., Z. Y. Huang, J.-H. Prevost, and Z. Suo, “Partition of Unity Enrichment for Bimaterial Interface Cracks,” International Journal for Numerical Methods in Engineering, vol. 59, pp. 1075–1102, 2004.
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• Sukumar, N., and J.-H. Prevost, “Modeling Quasi-Static Crack Growth with the Extended Finite Element Method Part I: Computer Implementation,” International Journal for Solids and Structures, vol. 40, pp. 7513–7537, 2003.
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• Wu, E. M., and R. C. Reuter Jr., “Crack Extension in Fiberglass Reinforced Plastics,” T and M Report, University of Illinois, vol. 275, 1965.
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<!-- source-page: 909 -->
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# 11. Special-Purpose Techniques
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Inertia relief 11.1
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Mesh modification or replacement 11.2
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Geometric imperfections 11.3
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Fracture mechanics 11.4
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Surface-based fluid modeling 11.5
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Mass scaling 11.6
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Selective subcycling 11.7
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Steady-state detection 11.8
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<!-- source-page: 910 -->
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