Effective properties of disordered materials
Abstract
The paper gives a comprehensive report on the theory of gradually disordered materials whose properties are characterized by a random linear operator L. By gradual disorder, or order of grade n, is meant that the disorder reflects itself in the correlation functions up to order n of the randomly distributed parameters. The effective operator L(eff) is introduced along with a consistency condition requiring that the sources and the physical fields produced by them be uncorrelated. The Green's operator formed with L(eff) is the ensemble mean of the Green's operator of L. A variational principle is derived which allows one to obtain upper bounds on the effective material parameters. The concept of gradually disordered materials with cell structure is developed for n 2 and n 3.
 Publication:

Solid Mechanics Archives
 Pub Date:
 October 1976
 Bibcode:
 1976SMArc...1..183K
 Keywords:

 Crystal Structure;
 Linear Systems;
 Random Processes;
 Solid State Physics;
 Distributed Parameter Systems;
 Elastic Properties;
 Green'S Functions;
 Isotropic Media;
 Limits (Mathematics);
 Modulus Of Elasticity;
 Operators (Mathematics);
 Polycrystals;
 Stress Tensors;
 Variational Principles;
 SolidState Physics