Subsonic propagation of cracks between dissimilar quasicrystals

We analyse the subsonic propagation of a crack along the interface between two different quasicrystals in a two-dimensional (2D) ambient setting and small strain regime. In the absence of a phason self-action, we provide a closed-form solution of the related Riemann-Hilbert problem. Then, we use such a result as a benchmark for a numerical analysis of the influence of a phason self-action on the crack propagation, which is the focus of our work. In addition to the special attention to quasicrystals, our work extends the classical analyses of interface cracks in linear elasticity to more general elastic bodies with 'active' microstructure described by vector phase fields.