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This book is concerned with describing, analyzing, and discussing topical problems in the mechanics
of advanced composite materials and structural elements whose mechanical properties are controlled
by high-strength and/or high-stiffness continuous fibers embedded in a polymeric, metal, or ceramic
matrix. Although the idea of combining two or more components to produce materials with controlled properties has been known and used from time immemorial, modern composites have been developed only over the last five or six decades and now have widespread applications in many different fields of engineering, but are of particular importance in aerospace structures for which high strength-to-weight and stiffness-to-weight ratios are required.


Due to these widespread existing and potential applications, composite technology has been
developed very intensively over recent decades, and there exist publications that cover anisotropic
elasticity, mechanics of composite materials, design, analysis, fabrication, and application of composite structures. A particular feature of this book, which distinguishes it from the existing publications, is that it addresses a wide range of advanced problems in the mechanics of composite materials, such as the  physical statistical aspects of fiber strength, stress diffusion in composites with damaged fibers, nonlinear elasticity, plasticity and creep of composite materials, hybrid and two-matrix composites, spatial fibrous structures, tensor strength criteria, progressive failure, and environmental and manufacturing effects, as well as the traditional basic composite material mechanics.


In addition to classical lamination theory and its application to beams and plates, this book covers the problems of consistency of non-classical theories, buckling and postbuckling behavior of symmetrically and nonsymmetrically laminated plates, and applied theories of composite cylindrical shells. Since the advantages of composite materials are best demonstrated by the optimal fibrous structures, we have particularly addressed the issues of optimality criteria and the analysis of the most significant optimal composite structures: filament-wound pressure vessels, rotating disks, and lattice cylindrical shells.


The authors of this book are experienced designers of composite structures who over the last 40 years have been involved in practically all the main Russian projects in composite technology. This experience has led us to carefully select the problems addressed in our book, which can be referred to as material problems challenging design engineers. Our discussions are illustrated with composite parts and structures designed and built within the frameworks of these projects.


In connection with this, the authors appreciate the permission of the Russian Composite Center – Central Institute of Special Machinery (CRISM) – to use in our book several pictures of structures developed and fabricated at CRISM as part of the joint research and design projects. The primary aim of the book is the combined coverage of mechanics, technology, and analysis of composite materials and structural elements at an advanced level.


Such an approach enables an engineer to take into account the essential mechanical properties of the material itself and the special features of practical implementation, including manufacturing technology, experimental results, and design characteristics.  The book consists of twelve chapters and can be divided into two main parts: the first part including Chapters 3–7, is devoted to composite materials, whereas the second part, Chapters 8–12, covers the analysis and design of typical composite structural elements. Chapter 1 is an introduction in which typical reinforcing and matrix materials, as well as the typical manufacturing processes used in composite technology, are described.


Chapter 2 is an introduction to the fundamentals of mechanics of solids, i.e., stress, strain, and
constitutive theories, governing equations, and principles that are used in the subsequent chapters for the analysis of composite materials and structures.


Chapter 3 is devoted to the basic structural element of a composite material: a unidirectional
composite ply. In addition to the conventional description of micromechanical models and experimental results, the physical nature of fiber strength, its statistical characteristics, and the interaction of damaged fibers through the matrix are discussed, and we show that fibrous composites comprise a special class of man-made materials utilizing the natural potentials of material strength and structure.


Chapter 4 contains a description of typical composite layers made of unidirectional, fabric, and
spatially reinforced composite materials. Conventional linear elastic models are supplemented in this
chapter with nonlinear elastic and elastic-plastic analyses demonstrating specific types of the behavior of composites with metal and thermoplastic matrices.


Chapter 5 is concerned with the mechanics of laminates and includes a conventional description of
the laminate stiffness matrix, coupling effects in typical laminates, and procedures for stress calculations for in-plane and interlaminar stresses.


Chapter 6 presents a practical approach to the evaluation of laminate strength. Three main types of
failure criteria, i.e., structural criteria indicating the modes of failure, approximation polynomial
criteria treated as formal approximations of experimental data, and tensor-polynomial criteria are
discussed and compared with available experimental results for unidirectional and fabric composites.
A combined elastoplastic damage model and a strain-driven implicit integration procedure for fiber
reinforced composite materials and structures that involves a consideration of their mechanical
response prior to the initiation of damage, prediction of damage initiation, and modeling of postfailure behavior are discussed.