Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.

Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as 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, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.

Contents:

• Micromechanical Modeling of Advanced Composites and Smart Composite Structures Using the Asymptotic Homogenization Method (Alexander L Kalamkarov)


• Scaling Functions in Spatially Random Composites (Martin Ostoja-Starzewski and Shivakumar I Ranganathan)


• Stroh-Like Formalism for General Thin Laminated Plates and Its Applications (Chyanbin Hwu)


• Classical Refined, Zig-Zag, Layer-Wise Models and Best Theory Diagrams for Laminated Structures (Erasmo Carrera, Maria Cinefra, and Marco Petrolo)


• A Modeling Framework for the Analysis of Instabilities and Delamination in Composite Shells (José Reinoso, Marco Paggi, and Antonio Blázquez)


• Bifurcation of Elastic Multilayers (Davide Bigoni, Massimiliano Gei, and Sara Roccabianca)


• Instabilities Associated with Loss of Ellipticity in Fibre-Reinforced Nonlinearly Elastic Solids (José Merodio and Ray W Ogden)


• Propagation of Rayleigh Waves in Anisotropic Media and an Inverse Problem in the Characterization of Initial Stress (Kazumi Tanuma and Chi-Sing Man)


• Advanced Mathematical Models and Efficient Numerical Simulation in Composite Processes (Emmanuelle Abisset-Chavanne, Anais Barasinski, and Francisco Chinesta)


• Modeling Fracture and Complex Crack Networks in Laminated Composites (Carlos G Dávila, Cheryl A Rose, Endel V Iarve, and Frank A Leone)


• Delamination and Adhesive Contacts, Their Mathematical Modeling and Numerical Treatment (Tomáš Roubíček, Martin Kružík, Jan Zeman, Christos G Panagiotopoulos, Roman Vodička, and Vladislav Mantič)


• Interaction of Cracks with Interfaces (Dominique Leguillon and Eric Martin)


• Computational Procedure for Singularity Analysis of Anisotropic Elastic Multimaterial Corners — Applications to Composites and Their Joints (Vladislav Mantič, Alberto Barroso, and Federico París)

Readership: An essential reference for researchers and graduate and doctoral students in mathematics, physics and composite engineering interested in structural behaviour and damage mechanisms.

Key Features:

• The book will be a useful reference in the development of new theoretical and computer models for the design, manufacturing, testing and applications of composite components and structures


• Contributing authors are worldwide prominent experts in the very different areas of applied mathematics, physics and engineering related to composites


• Especially suitable for young researchers showing a great variety of different approaches available today to model composites manufacturing, structural behavior, and damage mechanisms