Evaluation of mixed-mode stress intensity factors by the mesh-free Galerkin method: Static and dynamic

TLDR: In this article, an element-free mesh-free Galerkin method using radial basis interpolation functions was developed to evaluate static and dynamic mixed-mode stress intensity factors, and the so-called enriched radial basis functions were introduced to capture accurately the singularity of stress at crack tip.

Abstract: Based on the variational principle of the potential energy, the element-free Galerkin method is developed using radial basis interpolation functions to evaluate static and dynamic mixed-mode stress intensity factors. For dynamic problems, the Laplace transform technique is used to transform the time domain problem to the frequency domain. The so-called enriched radial basis functions are introduced to capture accurately the singularity of stress at crack tip. In this approach, connectivity of the mesh in the domain or integrations with fundamental or particular solutions are not required. The accuracy and convergence of the mesh-free Galerkin method with enriched radial basis functions for the two-dimensional static and dynamic fracture mechanics are demonstrated through several benchmark examples. Comparisons have been made with benchmarks and solutions obtained by the boundary element method.