An extended finite element method with polygonal enrichment shape functions for crack propagation and stiff interface problems

The extended/generalized finite element method has proven significant efficiency for handling crack propagation and internal boundaries. In certain conditions, however, one of the major drawbacks relates to the representation of unrealistic traction oscillations, particularly in stiff interfaces. To the authors' best knowledge, the few remedies found in the literature depend on the type of underlying finite element, which in some aspects limits general applications. Since one of the major sources of oscillations is created by couplings within standard shape functions for certain crack arrangements, it is herein proposed a novel approach based on enrichment Laplace shape functions directly adapted to the underlying geometry of split subdomains. By doing so, all sources of oscillations are effectively removed, while enriched degrees of freedom are defined exclusively on one side of the domain. The performance is studied using both element and structural examples with highly stiff cracks. More importantly, further assessment in more complex crack propagation problems, including mixed-mode fracture of concrete beams and a peel test, shows excellent agreement with experimental/numerical data in terms of load-displacement curves and traction profiles. Results are shown to be objective with respect to the mesh for stiffness values virtually representing infinitely stiff interfaces.

Automated summary

The generalized finite element method has shown efficiency in handling crack propagation and internal boundaries. A novel approach based on enrichment Laplace shape functions effectively eliminates sources of oscillations, with excellent agreement with experimental/numerical data in structural examples with highly stiff cracks.