This book discusses principles, techniques, experimental results, and applications in the modeling and calculation of fracture behavior in brittle materials. Divided into five sections, chapters include: Introduction and Background; Techniques for Modeling Fracture, Traditional and Advanced Molecular Dynamics Modeling of Fracture, Molecular Dynamics Modeling of Fracture Using an Embedded Atom Approach; Ab-initio Calculations of Fracture; The Use of Density Functional Theory to Model Fracture; Atomistic Simulation of Fracture in Nanocrystals; Simplistic Predictive Methods for Fracture Toughness; Environmental Effects in Fracture; Molecular Modeling of Environmentally Enhanced Crack Growth; Atomistics of Environmentally Enhanced Fracture; Thermodynamic Approaches to Fracture; Crack Tip Instabilities; Low-speed Fracture Instabilities in a Brittle Crystal Crack Tip; Instabilities : Modeling and Experiment; Comparison of Crack Tip Fracture Modeling with Experiment; Geometric Effects at the Crack Tip; Influence of Molecular Rearrangements on Fracture; The Fourth Mode of Fracture in Fractal Fracture Mechanics; The Effect of Fracture Surface Morphology on Fracture Mechanics Simulations; Fractal Geometry Uniting Quantum Mechanics and Fracture Mechanics; The Future in Modeling & Experimentation; A New Approach to Fracture Modeling in Brittle Materials