2Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of the modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. The diversity of such methods and models used in the analysis and characterization of composites, their behavior, and different phenomena and processes associated to them has grown steadily. This second edition expands upon the success of the first edition and has been substantially revised and updated.Written by known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites, with ever increasing applications (e.g., the aerospace industry), though it covers also other kind of composites. The topics of contributed chapters range from scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, shells, thin-walled composite structures, fiber-reinforced nonlinearly elastic solids, instabilities, buckling and postbuckling, fiber kinking and splitting, fracture and damage analysis of composites to highly efficient methods for simulation of composites manufacturing like resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students and researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed to provide the necessary background to further investigate the fascinating subject of composites modelling and explore relevant research literature. It is also suitable for non-experts 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 that require further research.