A general feature of tectonic faults is the juxtaposition of materials with dissimilar elastic properties\nin a variety of contexts and scales. Normal and reverse faults offset vertical stratifications,\nlarge strike-slip faults displace different crustal blocks, oceanic and continental crusts at subduction\ninterfaces, and oceanic transforms juxtapose rocks of different ages. Bimaterial interfaces\nassociated with rock damage are present with various degrees of sharpness in typical fault zone\nstructures, and failure along a bimaterial interface can be effective even on microscopic scale of\ngrain boundaries.\nA first order representation of a geological fault for seismic events is a frictional interface\nembedded in an elastic body. This study focusses on dynamic effects in the presence of material\ndiscontinuities altering dynamics of failure and dynamic rupture propagation on frictional interfaces.\nWhen the medium surrounding a fault is heterogeneous, the symmetry of stress is broken\nup and perturbations of normal stress introduces additional instability potentially generating\nadditional propagation modes of rupture.\nThis study presents three specific numerical investigations of the aforementioned rupture\nphenomena associated with material contrasts at the fault. A first numerical study (a) investigates\n2-D in-plane ruptures in a model consisting of two different half-spaces separated by\na low-velocity layer and possible simultaneous slip along multiple faults. This study shows\nthat bimaterial frictional interfaces are attractive trajectories of rupture propagation, and ruptures\ntend to migrate to material interfaces and becoming self-sustained slip pulses for wide\nranges of conditions. In a second numerical study (b), the propagation of a purely material\ncontrast driven rupture mode, that is associated with the so-calledWeertman or Adams-instable\npulse, is shown to exist also in the general 3-D case, where there is a mixing of in-plane and\nanti-plane modes, the bimaterial mechanism acting in the in-plane direction only. Finally, in\na further numerical investigation (c) it is demonstrated, that the rupture dynamics and ground\nmotion can be significantly influenced by bimaterial mechanisms of rupture propagation for\nranges of parameters. The model studied here comprises heterogeneous initial shear stress on a\nslip-weakening frictional interfaces separating two dissimilar elastic bodies, a free surface. The\ndiscussion focusses on the diversity of existing rupture propagation modes and ground motion.\nThe investigated models and obtained results are motivated and discussed in the context of\ncomplementary numerical investigations, theoretical studies of stability analysis, seismological\nvii\nobservations of earthquakes and aftershock sequences, geological observations of fault zone\nstructures, tomographic studies, and geodetic observations.