The Fiber-Reinforced Composite
Exact elastodynamic solutions within the context of classical elasticity theory are not available for fiber-reinforced composites. It is, however, to be expected that qualitatively a difference analogous to the one observed in laminated solids, should exi
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LECTURES - No. 167
J.D. ACHENBACH NORTIIWESTERN UNIVERSITY EVANSTON, ILLINOIS
A THEORY OF ELASTICITY WITH MICROSTRUCTURE FOR DIRECTIONALLY REINFORCED COMPOSITES
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright.
All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustration broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1975 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien-New York in 1975
ISBN 978-3-211-81234-1 DOI 10.1007/978-3-7091-4313-1
ISBN 978-3-7091-4313-1 (eBook)
PREFACE The material presented in this volume is part of a set of notes for a series of lectures, which was given under the title "Mechanical Behavior of Directionally Reinforced Composites under Dynamic Loadin:_g Conditions," at the International Institute of Mechanical Sciences, Udine, Italy, in July 1973. Since the printed volume is mainly devoted to mathematical modeling of the mechanical behavior of directionally reinforced composites, in particularly by means of theories of elasticity with microstructure, the present title of the volume is more appropriate. For a laminated medium, a homogeneous continuum model whose mechanical behallior is described by a theory of elasticity with microstructure, was proposed in 1966, jointly by the author and G. Herrmann. Since then, the basic ideas have been extended to theories for fiber-reinforced composites, and to viscoelastic material behavior, as well as to theories to describe thermal effects, and effects of large deformations and nonlinear mechanical behavior. For laminated media and fiber-reinforced composites the development of the theory is presented in Part II. To place these new theories, and their areas of application, in a proper perspective, the well-established effective modulus theory is discussed in some detail in Part I. The research work in the area of the mechanical behavior of composite materials reported here, was carried out under the sponsorship of the Office of Naval Research under Contract ONR 064-483 with Northwestern University. This support is gratefully acknowledged. Evanston, October 1973 J.D. Achenbach
CONTENTS
Preface
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Page 1
PART I: THE EFFECTIVE MODULUS THEORY • • • • • • • • •
5
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Fiber-Reinforced Composites • • . • • • • • • • • • • 2 Mathematical Modeling • • • • • • • • • • • • • • • • • • • 3 Dynamic Effects • • • • • • • • • • • • • • • • • • • • • • • • • Classical Linearized Elasticity • • • • • • • • • • • • • 1 Notation and Mathematical Preliminaries • • • 2 Kinematics and Dynamics • • • • • • • • • • • • • • • • • 3 The Homogeneous, Isotropic, Linearly Elastic Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 4 Exact Solutions for Homogeneous Bodies of Arbitrary Shape . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3: The E
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