Modeling discontinuities as an enriched feature using the extended finite element method

Modeling discontinuities, such as cracks, as an enriched feature:

  • is commonly referred to as the extended finite element method (XFEM);

  • is an extension of the conventional finite element method based on the concept of partition of unity;

  • allows the presence of discontinuities in an element by enriching degrees of freedom with special displacement functions;

  • enables the modeling of discontinuities in the fluid pressure field as well as fluid flow within the cracked element surfaces as in hydraulically driven fracture;

  • does not require the mesh to match the geometry of the discontinuities;

  • is a very attractive and effective way to simulate initiation and propagation of a discrete crack along an arbitrary, solution-dependent path without the requirement of remeshing in the bulk materials;

  • can be simultaneously used with the surface-based cohesive behavior approach (see Contact cohesive behavior) or the Virtual Crack Closure Technique (see Crack propagation analysis), which are best suited for modeling interfacial delamination;

  • can be performed using the static procedure (see Static stress analysis), the implicit dynamic procedure (see Implicit dynamic analysis using direct integration), the low-cycle fatigue analysis using the direct cyclic approach (see Low-cycle fatigue analysis using the direct cyclic approach), the geostatic stress field procedure (see Geostatic stress state), or coupled pore fluid diffusion/stress analysis (see Coupled pore fluid diffusion and stress analysis);

  • can also be used to perform contour integral evaluations for an arbitrary stationary surface crack without the need to define the conforming mesh around the crack tip;

  • allows contact interaction of cracked element surfaces based on a small-sliding formulation or on a finite-sliding formulation within the general contact framework;

  • allows the application of distributed pressure loads to the cracked element surfaces;

  • allows the output of some surface variables on the cracked element surfaces;

  • allows both material and geometrical nonlinearity; and

  • is available only for first-order stress/displacement solid continuum elements, first-order displacement/pore pressure solid continuum elements, and second-order stress/displacement tetrahedron elements.

The following topics are discussed:

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In Other Guides
Using the extended finite element method to model fracture mechanics