This book brings together a diverse compilation of inter-disciplinary chapters on fundamental aspects of carbon fiber composite materials and multi-functional composite structures: including synthesis, characterization, and evaluation from the nano-structure to structure meters in length. The content and focus of contributions under the umbrella of structural integrity of composite materials embraces topics at the forefront of composite materials science and technology, the disciplines of mechanics, and development of a new predictive design methodology of the safe operation of engineering structures from cradle to grave. Multi-authored papers on multi-scale modelling of problems in material design and predicting the safe performance of engineering structure illustrate the inter-disciplinary nature of the subject. The book examines topics such as Stochastic micro-mechanics theory and application for advanced composite systems Construction of the evaluation process for structural integrity of material and structure Nano- and meso-mechanics modelling of structure evolution during the accumulation of damage Statistical meso-mechanics of composite materials Hierarchical analysis including age-aware, high-fidelity simulation and virtual mechanical testing of composite structures right up to the point of failure. The volume is ideal for scientists, engineers, and students interested in carbon fiber composite materials, and other composite material systems.