Abstract.We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing statistically inhomogeneous random set of heterogeneities and loaded by inhomogeneous remote loading. The new general integral equation is obtained by a centering procedure without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. The method makes it possible to abandon the basic concepts of classical micromechanics such as effective field hypothesis, and the hypothesis of ``ellipsoidal symmetry". The results of this abandonment leads to detection of some fundamentally new effects that is impossible in the framework of a classical background of micromechanics.

Received: December 23, 2009

AMS Subject Classification: 65R20, 74B05, 74Q15, 74G15, 74G70

Key Words and Phrases: microstructures, elastic material

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 2