On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I—Theory

This work presents an analytical framework for determining the overall constitutive response of elastomers that are reinforced by rigid or compliant fibers, and are subjected to finite deformations. The framework accounts for the evolution of the underlying microstructure, including particle rotation, which results from the finite changes in geometry that are induced by the applied loading. In turn, the evolution of the microstructure can have a significant geometric softening (or hardening) effect on the overall response, leading to the possible development of macroscopic instabilities through loss of strong ellipticity of the homogenized incremental moduli. The theory is based on a recently developed ‘‘second-order’’ homogenization method, which makes use of information on both the first and second moments of the fields in a suitably chosen ‘‘linear comparison composite,’’ and generates fairly explicit estimates—linearizing properly—for the large-deformation effective response of the reinforced elastomers. More specific applications of the results developed in this paper will be presented in Part II. r 2005 Elsevier Ltd. All rights reserved.