Piezoelectric materials, as an important class of crystalline materials, are fundamental components of smart systems with coupled electric and mechanical fields. Quasicrystals, in contrast to the piezoelectrics, represent a relatively new class of materials which, in a sense, fills the gap between crystalline and amorphous materials and can be described in the framework of continuum mechanics by two types of fields, phonon and phason fields. Meanwhile, it is already known that quasicrystals can also have piezoelectric properties and consequently three coupled field types are present in these materials. From the technical point of view, quasicrystals and piezoelectrics are interesting due to advantageous properties, which allow diverse potential applications and give rise to intensive research. The focus of this thesis is on the influence of coupling effects of the different fields and the electrical loading on the fracture mechanical behavior. The major objective is crack paths, based on which the plausibility of materialspecific models, simulation methods and crack deflection criteria are evaluated. For this purpose, a comprehensive framework in terms of continuum mechanics is developed, including phonon, phason, and electric fields in piezoelectric QCs. The fracture mechanics quantities are generalized for the materials and based on the closed-form solutions they are implemented into numerical methods. To simulate the crack growth by using a re-meshing algorithm, which relies on an adaptive meshing strategy in conjunction with finite element software, the classical and new proposed crack deflection criteria are implemented. The influence of the coupling coefficients and the configuration of specimens as well as the electrical loading on crack paths is investigated based on the simulation results. In addition, three-point bending tests are performed on ferroelectric specimens under different loading combinations. The experimental results and the recording of the crack growth process with a high-speed camera show remarkable details.