Boundary element method for 3D fracture mechanics analysis in quasicrystal solids under thermal loading

This study presents a boundary element approach for analyzing 3D cracks in thermoelastic quasicrystals. The approach uses compact notations, combining phonon and phason fields into extended vectors and tensors, simplifying the equilibrium equations. Boundary integral equations are derived for heat conduction and thermoelasticity, avoiding the need for volume discretization. Special methods are employed to evaluate integrals and determine stress intensity factors at the crack front.