Mechanics of Composite Materials

Richard M. Christensen

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486442396
• eBook ISBN: 9780486136660
• Topic: Physical Sciences
• Subtopic: Mechanics

A comprehensive account of the basic theory of the mechanical behavior of heterogeneous media, this volume assembles, interprets, and interrelates contributions to the field of composite materials from theoretical research, laboratory developments, and product applications.
The text focuses on the continuum mechanics aspects of behavior; specifically, it invokes idealized geometric models of the heterogeneous system to obtain theoretical predictions of macroscopic properties in terms of the properties of individual constituent materials. The wide range of subjects encompasses macroscopic stiffness properties, failure characterization, and wave propagation. Much of the book presumes a familiarity with the theory of linear elasticity; but it also takes into consideration behavior characterized by viscoelasticity and inviscid plasticity theories and problems involving nonlinear kinematics. Because of the close relationship between mechanical and thermal effects, the text also examines macroscopic, thermal properties of heterogeneous media.
Although the primary emphasis centers on the development of theory, this volume also pays critical attention to the practical assessment of results and applications. Comparisons between different approaches and with reliable experimental data appear at main junctures. Suitable as a graduate-level text, Mechanics of Composite Materials is also a valuable reference for professionals.

CHAPTER I

SOME ELEMENTS OF MECHANICS

We are concerned here with many different aspects of the mechanical behavior of heterogeneous media. A subject of this type can be approached from several different directions, and at various levels. For example, we could gather the very extensive data obtained from testing, collate it, interpret it, and, ultimately, manipulate it into a form with master curves in terms of nondimensional variables. Or we could go one step further and seek empirical analytical expressions that seem to model the data. We do not, however, take these approaches. Even though such approaches can be useful and convenient, the results are limited to the conditions under which data were obtained. The method has no power to predict behavior outside the range of laboratory experience. We seek a more fundamental approach, one that will give us a predictive capability.

In pursuing a general approach to the mechanics of heterogeneous media, we place a premium on this goal of predictive power. But a goal of this type is not obtained quickly or cheaply. The price to be paid is that of the expenditure of the time and effort to develop a rigorous theory(ies) of behavior. Carefully derived theories of behavior have as their basis certain assumptions or hypotheses that give the boundaries of applicability of the results. Within these boundaries the theory has a full and complete capability to model actual behavior.

Our objective then is to develop the theoretical framework for the behavior of heterogeneous media. It would be possible to approach the problem at a level of utmost generality, with completely nonlinear kinematics and the most general possible constitutive assumptions. Although this approach can be completely rigorous, it is too general for our interests in specific applications. We therefore pursue a middle level approach, one in which we do not hesitate to make assumptions and hypothesis that are in accordance with physical reality. However, after making these assumptions, we seek a rigorous mathematical structuring of the theory(ies) and its application. In fact, much of our work is based on mechanical behavior described by the linear theory of elasticity, which itself is a highly developed and rigorous theory.

Of the various aspects of the mechanics of deformable media (continuum mechanics), probably linear elasticity has had the most far-reaching impact. The tremendous success of linear elasticity theory can be attributed to several factors. First and foremost, it provides a realistic model of behavior for a wide class of materials. Second, the topic is highly developed and sophisticated; there is a vast library of methods and results to draw on. Third, in many practical problems the results take simple, but general forms that are amenable to design evaluation and application. For these reasons we develop the subject of the behavior of heterogeneous media primarily from the point of view of linear elasticity theory. We do not, however, wish to convey the impression that linear elasticity answers all the problems; it most certainly does not. The two most common generalizations of elasticity theory are those of viscoelastic behavior and elastic-plastic behavior. We are also concerned with these types of inelastic behavior for heterogeneous media. Furthermore, we also study some aspects of problems with completely nonlinear kinematics of deform...

Table of contents

• Title Page
• Copyright Page
• PREFACE TO THE DOVER EDITION
• PREFACE
• Table of Contents
• ERRATA
• CHAPTER I - SOME ELEMENTS OF MECHANICS
• CHAPTER II - EFFECTIVE MODULI: SPHERICAL INCLUSIONS
• CHAPTER III - EFFECTIVE MODULI: CYLINDRICAL AND LAMELLAR SYSTEMS
• CHAPTER IV - BOUNDS ON EFFECTIVE MODULI AND FURTHER RESULTS
• CHAPTER V - LAMINATES
• CHAPTER VI - ANALYSIS, STRENGTH, AND DESIGN
• CHAPTER VII - WAVE PROPAGATION
• CHAPTER VIII - INELASTIC AND NONLINEAR EFFECTS
• CHAPTER IX - EFFECTIVE THERMAL PROPERTIES
• AUTHOR INDEX
• SUBJECT INDEX