vorgelegt von Diplom-Physiker

This thesis describes the behavior of cracks and pores under the influence of elastic and curvature effects. In a continuum theory approach, these structure deformations are treated as free moving boundaries. Our investigation start with well established sharp interface equations for which no fully dynamical solutions exist so far. The equations include only linear dynamical elasticity, surface energy and non-equilibrium transport theory. By proper use of the phase-field concept, we are now able to tackle the fully time-dependent free moving boundary problem to describe crack propagation in a fully self-consistent way. We concentrate on two material transport processes, namely surface diffusion and phase transition dynamics. We show analytically that the intuitive and widely used approach for constructing a phase-field model for surface diffusion fails, since it does not reduce to the desired sharp interface equations, providing an uncontrolled approximation to the dynamics. We then develop two completely new models that ensure the correct asymptotic behavior and support our analytical findings by numerical simulations, which are are computationally very demanding due to the high order equations that have to be solved