Mathematical Methods and Models in Composites

This book provides an in-depth treatment of the modern and rigorous mathematical methods and models applied to composites modeling on micro-, meso- and macroscale. The diversity of such methods and models used in the analysis and characterization of composites, their behavior, and different phenomena and processes associated with them has been steadily growing.The present book is a representative selection of the most relevant, innovative, and useful mathematical methods and models which establish the fundaments for a meaningful and accurate theoretical and computer modeling of these materials in the future. This unique volume is written by well-known experts in different areas of applied mathematics, physics, and composite engineering. It is mainly oriented on fiber reinforced composites, with ever increasing applications such as in the aerospace industry, though some of the results presented can be applied to other kinds of composites, such as particulate composites.The topics of contributed chapters range from scaling and homogenization procedures in composites, integral and statistic characteristic of composites, thin plate and wave solutions in anisotropic materials, laminated structures, instability, fracture and damage analysis of composites to highly efficient methods for simulation of composites manufacturing. The results presented are useful in the design, fabrication, testing, and industrial applications of composite components and structures.This book is an essential source of reference for a great variety of mathematical methods and models available in composite modeling today for graduate and doctoral students, as well as researchers in mathematics, physics, and composite engineering. Explanations and references in the book are detailed and comprehensive enough to provide necessary background into the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts in composites who wish to have an overview of both the mathematical methods and models used in the area of composites and of the open problems in this area requiring further research.