A fundamental challenge in predicting the reliability and lifetime of brittle coating systems and advanced composites is modeling the response of initial cracks and flaws, which are inevitably present within bulk sections and along interfaces. As these multi-material systems continue to increase in complexity due to ever rising structural design requirements, the number of possible failure modes tends to simultaneously increase. Consequently, there is a concurrent need for advanced simulation approaches capable of predicting arbitrary fracture paths and complex interaction between competing failure mechanisms.

Unfortunately, explicit simulation of cracking in brittle materials has historically proven to be quite challenging. The physical fracture process zone lengths in an ordinary brittle material are on the nanometer length scale and would there require sub-nanometer spatial resolution for numerical accuracy. This presents a major modeling obstacle, as typical modern engineered systems are designed at much larger length scales (e.g., microns, millimeters, etc). The multi-scale nature of this problem is an ongoing challenge, even considering the raw processing power of the most advanced supercomputers.

In this dissertation, a computational approach for capturing arbitrary crack trajectories within a material is presented based on the Distributed cohesive zone method (DCZM). At the heart of the DZCM approach is the use of cohesive zones that idealize the fracture processes at the tip of cracks. It will be illustrated that the method recovers all of the salient features of continuum elasticity and linear elastic fracture mechanics (LEFM) without necessarily requiring explicit resolution at the atomic scale. Scaling of the computation and parallel implementation of the DCZM algorithm will be outlined in detail.

Lastly, several applications of the method will presented. It will be demonstrated that DCZM can be extended to accurately capture arbitrary crack kinking angles as predicted by He and Hutchinson, without the explicit inclusion of a pre-defined putative kinked segment. This is a particularly novel result that has not yet been illustrated with any mesh based approach, and paves the way for accurate simulation of complex material systems where non-planar cracks are routinely observed. Specifically, the method will be applied to analyze fracture in heterogeneous bio-inspired brick-and-mortar composites, and the design of femtosecond laser experiments. When combined carefully with experimental measurements, the method can be used to back out effective fracture toughness values in these complex systems, parameters that largely dictate the reliability of the structure as a whole. This is a major fundamental research contribution, as measurement and prediction of fracture toughness in complex material systems has proven quite difficult. Future modeling avenues will be presented in each section, in terms of both algorithm development and applications in structural materials.