An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom

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.

Automated summary

The advanced numerical techniques of XFEM/GFEM provide accurate prediction of material failure by independently enriching a few elements in a multilayered approach, allowing for condensed degrees of freedom at the layer level to maintain system dimensions, sparsity, and bandness. This approach enhances accuracy and computational efficiency without compromising on system performance.