Analysis of crack propagation path of multiphase structure with multiple cracks and inclusions by using a fast multipole BEM

Purpose A fast multipole boundary element method (BEM) with a novel variable-order asymptotic element (VAE) is used to investigate the effects of inclusions and elastic properties on the crack propagation paths. Design/methodology/approach The fast multipole BEM provides high computational efficiency, and by using VAE at the crack tip, stress singularities can be accurately captured and the crack propagation path can be finely described. Findings Soft inclusions attract propagating cracks, whereas hard ones repel or deflect them, thereby hindering growth. The shape of the inclusion has obvious influence on the crack propagation paths even if they have the same area; it needs to be considered with caution when using the circular inclusion to replace the polygonal inclusion to simplify analysis. Originality/value The findings offer valuable insights for the design of composite materials with controlled crack resistance and for understanding microstructure–fracture relationships, contributing to more reliable failure prevention strategies in engineering applications.