Elastomeric Composites

Elastomeric composites are used pervasively in commercial and industrial applications, and in recent years have shown great promise for utilization in new technologies. This raises the practical and theoretical need to understand in detail the interplay between the microscopic properties of these material systems and their physical macroscopic properties, and how the latter may be enhanced with changes in the former. The main aim of this work is the development of a nonlinear homogenization framework for determining the macroscopic response and stability of large classes of elastomeric composites directly in terms of the constitutive behaviors of the constituents and of the underlying microstructure. The key technical idea behind the proposed approach is the construction of novel variational principles based on "linear comparison media". This work includes applications of the proposed theory to various classes of reinforced and porous elastomers with random and periodic microstructures. A comprehensive analysis of the effective behavior, the microstructure evolution, and the development of instabilities is provided for all these applications.