Enriched crack-tip element for logarithmic stress singularities of Mode I and Mode II cracks in spring interfaces

Finite element simulations of cracks in Winkler-type spring interfaces encounter numerical difficulties due to logarithmic stress singularities at the crack tip. These singularities lead to poor convergence of standard FEM and typically require strong mesh refinement, resulting in high computational costs. This work proposes a novel enriched 2D finite element for fracture analysis in mixed Mode I+II, focusing on cracks in interfaces modeled by continuous spring distributions. The new element is triangular with 5 nodes obtained by collapsing a 6-node rectangular element. It incorporates the radial behaviour of the asymptotic elastic solutions with logarithmic stress singularities, improving the accuracy of Energy Release Rate (ERR) calculations compared to standard finite elements. The proposed approach achieves higher accuracy in interface crack growth simulations while substantially reducing computational costs, and demonstrating that this accuracy is maintained when the enriched element is placed along the whole interface, enabling unzipping-type crack propagation without re-meshing. Specifically, for small and moderate values of Lenci’s dimensionless parameter ( δ =1,10 and 100), the error in the displacement value at the crack tip is reduced by a factor of between 2 and 5 when enriched crack-tip elements are used instead of standard elements in Mode I, for both mesh patterns with 2 and 4 crack-tip elements. In Mode II, this error is consistently reduced only for the mesh pattern with 4 crack-tip elements, by a factor of between 2 and 7. Obtained results demonstrate the potential of the proposed enriched element to enhance the efficiency and accuracy of fracture analyses in adhesive joints, making it a promising tool for addressing challenges in interface crack modeling by FEM.