The development of advanced numerical techniques such as eXtended/ Generalized Finite Elements Methods (XFEM/GFEM) has provided means for accurate prediction of material failure. However, the present theories mostly rely on a global formulation, where the system of equations is subject to progressive dimension increase with crack evolution. In this regard, an independent multilayered enrichment is proposed for the XFEM/GFEM family of methods where a few elements in close proximity are assigned to an enrichment layer independent of the remaining ones. The enhanced degrees of freedom can be condensed out at the layer level, which leads to system dimensions, sparsity, and bandness identical to those of the underlying finite elements. Nodal and elemental enrichment methods are shown to be particular limit cases of present approach. The robustness of the proposed approach is first demonstrated in element-level examples. The use of only few adjacent elements in a group enrichment is shown to suffice for acceptable results while the order of the condition number of the final stiffness matrix resembles the underlying uncracked finite element counterpart. Finally, using several structural examples, the accuracy and robustness of the method is shown in terms of force-displacement response, stress fields, and traction continuity in nonlinear 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.
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