Mechanics of Composite Materials

A Unified Micromechanical Approach


  • J. Aboudi, Tel-Aviv University, Israel

In the last decade the author has been engaged in developing a micromechanical composite model based on the study of interacting periodic cells. In this two-phase model, the inclusion is assumed to occupy a single cell whereas the matrix material occupies several surrounding cells. A prominent feature of the micromechanical method of cells is the transition from a medium, with a periodic microstructure to an equivalent homogeneous continuum which effectively represents the composite material. Of great importance is the significant advantage of the cells model in its capability to analyze elastic as well as nonelastic constituents (e.g. viscoelastic, elastoplastic and nonlinear elastic), thus forming a unified approach in the prediction of the overall behaviour of composite material. This book deals almost exclusively with this unified theory and its various applications.
View full description


Book information

  • Published: July 1991
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-88452-7


... should prove to be a useful addition to the library of all those engaged in the prediction of the behavior of composite materials from a knowledge of their constituents and geometry.
Applied Mechanics Reviews

Table of Contents

1. Fundamentals of the Mechanics of Composites. Representative volume element. Volumetric averaging. Homogeneous boundary conditions. Average strain theorem. Average stress theorem. Effective elastic moduli. Relations between averages-direct approach. Relations between averages - energy approach. 2. Basic Models in the Mechanics of Composites. The Voigt approximation. The Reuss approximation. Hill's theorem. The dilute approximation. The composite spheres model. The self-consistent scheme. The generalized self-consistent scheme. The differential scheme. The mori-tanaka theory. Exhelby equivalent inclusion method. 3. The Micromechanical Method of Cells. The method of cells for fiber reinforced materials. Coefficients of thermal expansion. Hill's relations. Thermal conductivities. Specific heats. The method of cells for short-fiber composites. Randomly reinforced materials. Periodically billlminated materials. 4. Strength and Fatigue Failure. Micromechanics prediction of composite failure. 5. Viscoelastic Behaviour of Composites. Linearly viscoelastic composites. Thermoviscoelastic behaviour of composites. Nonlinear viscoelastic behaviour of composites. 6. Nonlinear Behaviour of Resin Matrix Composites. Macromechanical analysis. Micromechanical analysis. 7. Initial Yield Surfaces of Metal Matrix Composites. The initiation of yielding in isotropic materials. Initial yielding of metal matrix composites. Investigation of the convexity of initial yield surfaces. 8. Inelastic Behaviour of Metal Matrix Composites. Constitutive equations of plasticity. Unified theories of viscoplasticity. Bodner-partom viscoplastic equations. Inelastic behaviour of laminated media. Inelastic behaviour of fibrous composites. Matrix mean-field and local-field. Subsequent yield surfaces prediction of metal matrix composites. Metal matrix composite laminates. Short-fiber metal-matrix composites. 9. Imperfect Bonding in Composites. General considerations. The flexible interface imperfect bonding model. Periodically billaminated materials. Fiber-reinforced materials. Short-fiber and particulate composites. The Coulomb frictional law for the modeling of interfacial damage in composites. Index.