We present a novel method to simulate the dynamic evolution of spontaneous ruptures governed by rate-and state-dependent friction laws and the interaction with seismic waves in a prestressed elastically deforming body. We propose a multi-rate iterative coupling scheme based on the variational form of the elastic-gravitational equations, and discretize employing a discontinuous Galerkin method, with nonlinear interior boundary conditions being weakly imposed across the fault surface as numerical fluxes. We introduce necessary interface jump penalty terms as well as an artificial viscous regularization, with the conditions for penalty and viscosity coefficients given based on an energy estimate and a convergence analysis. In the multi-rate scheme, an implicit-explicit Euler scheme in time is invoked, and the time step for the evolution of friction is chosen significantly finer than that for wave propagation and scattering. This is facilitated by the iterative scheme through the underlying decoupling where the linear, elastic wave equation plays the role of a Schur-complement to the friction model. A nonlinearly constrained optimization problem localized to each element on the rupture surface is then formulated and solved using the Gauss-Newton method. We test our algorithm on several benchmark examples and illustrate the generality of our method for realistic rupture simulations.