Mechanics of Composites

University of Cambridge, P. 58Basic notions
Introductory remarks
Definition of effective properties
Representative volume element
Other properties
Theory of Laminates
An example
A more general discussion of simple laminates
Hierarchical laminates
Energy Relations
The principle of virtual work
The classical energy principles
Implications for effective properties
Elementary bounds for overall properties
Some General Relations for Composites
Concentration tensors
A dilute suspension
Isotropic matrix
Approximation for a general composite
Self-consistent approximation
Thermoelastic Response of a Composite
General relations
The Levin relations
The isotropic spherical inclusion
General Formulation for Heterogeneous Media
A fundamental integral equation
Green’s function for an infinite body
Inclusion problems
Implications for a dilute suspension
Isotropic matrix
The Hashin–Shtrikman Variational Principle and its Implications
Derivation of the Hashin–Shtrikman principle
Random media
Bounds
The classical Hashin–Shtrikman bounds
More general two-point statistics
A general formula for a laminate
A remark on optimality
A remark on the self-consistent approximation
Nonlinear Response of Composites
Elementary bounds
Hashin–Shtrikman formalism
Other approximations