Seminars

Computation of crack patterns is a challenging task in fracture mechanics. Phase field approaches have recently proven their excellent ability to reproduce complex situations including initiation of cracks and determination of unknown crack paths. In certain cases, e.g. for indentation fracture, additional constitutive assumptions have to be included in the phase field model to obtain physically reasonable solutions. These assumptions induce a tension-compression asymmetric material response and prevent damage in compressed regions or the onset of damage before a critical state is reached to account for brittle material response. To some extent, this can only be achieved at the cost of giving up the underlying variational concept. The lecture starts with an introduction to phase field approaches, including a brief overview of present formulations. Subsequently, the choice of constitutive assumptions and their impact on the phase field model for brittle fracture is analyzed and different formulations of non-variationally derived, but physically motivated phase field evolution laws, based on energetic concepts, strain or stress states, are introduced. Furthermore, the phase field approach is utilized to simulate fracture initiation at the defect-free surface of a brittle solid subjected to indentation loading, which has experimentally been investigated already by Hertz more than a century ago. However, its theoretical prediction is still a challenging task due to the lack of reliable criteria for crack formation in classical fracture mechanics. For comparison, the issue of indentation fracture initiation is solved semi-analytically and numerically by the concept of finite fracture mechanics, which requires the simultaneous fulfillment of a stress based and an energetic criterion.