Abaqus/Standard can evaluate contour integrals with the conventional finite element method or with the extended finite element method (XFEM).

The conventional method requires a mesh that conforms to the crack geometry, typically with a very detailed, focused mesh at the crack tip. You must define the crack front explicitly and specify the virtual crack extension direction in addition to matching the mesh to the cracked geometry.

The XFEM-based method does not require the mesh to explicitly match the geometry of the crack. The built-in enrichment functions provide the singular asymptotic fields and jump discontinuities needed to compute the contour integrals. With respect to the element shape, the primary difference between the conventional method and XFEM is that XFEM does not require the construction of collapsed elements around the crack front. Regularly shaped elements can be used, and as a result the specification of an initial crack is greatly simplified. In addition, the crack front and the virtual crack extension direction are determined automatically by the level set signed distance functions.

However, it is imperative to understand that both the conventional and XFEM approaches require a fine mesh in the vicinity of the crack front in order to ensure accurate contour integral calculations. In addition, the use of a mesh that conforms to the crack geometry is recommended because it efficiently allocates degrees of freedom to the area of interest.  This improves both the accuracy and the runtime of the solution.

For XFEM you must generate a sufficient number of elements around the crack front to obtain path-independent contours, particularly in regions of high crack-front curvature. 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 six times the typical element characteristic length of those elements along the crack front in the enriched area. You must include the elements inside the enrichment radius in the element set used to define the enriched region.

In this document, we will discuss contour integral evaluation using Abaqus XFEM. With Abaqus 2017, there are now two evaluation methods within the XFEM framework: line integral and domain integral. Prior to Abaqus 2017, domain integral was the only method available for XFEM. Three different examples have been analyzed to compare the XFEM results with those obtained from the conventional method. We will demonstrate the advantage of using the line integral method over the domain integral method and the importance of mesh refinement to the contour integral results. Finally, a set of best practice guidelines is established.