# Textbook "Composite Materials"

## Preface

The growth of the use of composite materials in structures has required the development of tools needed for modeling their mechanical behavior and for the analysis of laminate and sandwich structures. The objective of this book is to establish a synthesis of the analysis of the mechanical behavior and the theory of laminate and sandwich plates and to apply them to the problems of bending, buckling and vibrations.

To develop the concepts of the mechanical analysis of composite materials and structures one needs the basic theory of the
mechanics of deformable media. We have chosen to make a synthesis of the necessary basics in the second part, *Basic Concepts of the Mechanical Behavior of
Materials*, where the classical tools are developed: stresses (Chapter 5); strains (Chapter 6); the elastic behavior of materials (Chapter 7); mechanics of deformable solids
(Chapter 8).

The third part, *Mechanical Behavior of Composite Materials*, develops the
analysis of the local mechanical behavior of composites. Chapter 9 treats the elastic behavior of a unidirectional composite material: the law of behavior, estimation of moduli, and comparison of
results with experiments. Composites with a cloth reinforcement are orthotropic materials whose elastic behavior is studied in Chapter 10. Laminated composite materials are formed of successive
layers whose principal directions are changed from one layer to another. Chapter 11 analyzes the elastic behavior of a layer off its principal directions. Part of the chapter is devoted to the state
called plane stress, a state whose importance will appear in the theory of laminates. Lastly, Chapter 12 presents the basic mechanisms of fracture observed in composite materials, and develops the
criteria for fracture that a designer will have available for evaluating the mechanical resistance of a laminate.

The fourth part, *Modeling the Mechanical Behavior of Laminates and Sandwich plates*, develops the basics of the theory of laminate and
sandwich plates. The general assumptions of the theories are introduced first in Chapter 13. The classical theory of laminates is developed next in Chapter 14. The study of the effect of the stacking
of layers (Chapter 15 allows us to analyze the processes of coupling between in-plane stretching, bending, and twisting. The classical laminate theory also allows us to estimate the elastic behavior
of layers reinforced with cloths or mats. Chapter 16 develops the fundamental equations of the classical laminate theory as well as the energy formulation. The boundary conditions are also analyzed.
Accounting for transverse shear effects is next developed in Chapter 17. Lastly, Chapter 18 analyzes the theory of sandwich plates.

The fifth part,
*Analysis* * of the Mechanical Behavior of Composite Material Structures*, treats
problems of bending, buckling, and vibrations of structures made of composite materials. Chapters 19 and 20 consider the problems of one-dimensions bending. The first type of problems concerns
cylindrical bending (Chapter 19), and the second type is that of the bending of beams (Chapter 20). Chapter 21 next studies the bending of orthotropic laminated plates for which there is neither
bending-twisting/stretching coupling nor twisting/bending coupling. Chapter 22 considers the bending of symmetric laminates, cross-ply laminates, and angle-ply laminates, and shows the difficulty of
finding analytical solutions. Chapter 23 treats the study of the buckling of beams and laminates or sandwich plates, including the governing equations and analytical solutions. The analysis of the
free vibrations of beams and plates is next developed in Chapter 24. Hygrothermal effects on the behavior of laminate plates are analyzed in Chapter 25. Lastly the book is ended by a chapter devoted
to the predesigning of laminate and sandwich structures, providing a synthesis of the concepts developed all along the text.

The intention of this book is to provide *a fundamental and unified
approach* to the mechanical behavior of composite materials and structures. The different parts have been carefully developed to have continuity of the concepts and theories. It is
hoped that this book will provide the necessary elements for advancing the reader's understanding of the mechanical behavior of composite materials and structures.

Vallouise,France, April 1998