Mathematical Methods and Models in Composites

This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in...
More Description

This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites.

The topics covered include: scaling and homogenization procedures in composite structures, thin plate and wave solutions in anisotropic materials, laminated structures, instabilities, fracture and damage analysis of composites, and 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.

The book is written by well-known experts in different areas of applied mathematics, physics, and composite engineering and is an essential source of reference for graduate and doctoral students, as well as researchers. It is also suitable for non-experts in composites who wish to have an overview of both the mathematical methods and models used in this area and the related open problems requiring further research.Contents: Asymptotic Homogenization Method and Micromechanical Models for Composite Materials and Thin-Walled Composite Structures "(Alexander L Kalamkarov)"Scaling and Homogenization 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 and Layer-Wise Models for Laminated Structures "(Erasmo Carrera and Maria Cinefra)"Bifurcation of Elastic Multilayers "(Davide Bigoni, Massimiliano Gei and Sara Roccabianca)"Propagation of Rayleigh Waves in Anisotropic Media and an Inverse Problem in the Characterization of Initial Stress "(Kazumi Tanuma and Chi-Sing Man)"Advanced Model Order Reduction for Simulating Composite-Forming Processes "(Francisco Chinesta, Adrien Leygue and Arnaud Poitou)"Modeling Fracture and Complex Crack Networks in Laminated Composites "(Carlos G Dávila, Cheryl A Rose and Endel V Iarve)"Delamination and Adhesive Contact Models and Their Mathematical Analysis and Numerical Treatment "(Tomáš Roubíček, Martin Kružík and Jan Zeman)"Crack Nucleation at Stress Concentration Points in Composite Materials — Application to Crack Deflection by an Interface "(Dominique Leguillon and Eric Martin)"Singular Elastic Solutions in Anisotropic Multimaterial Corners. Applications to Composites "(Vladislav Mantič, Alberto Barroso and Federico París)"
Readership: Graduate students and researchers in composite engineering.