Overall Response of Composite Materials Undergoing Large Deformations

摘要

This research deals with the theoretical prediction of the effective behavior ofnonlinear composite materials undergoing large deformations. In particular, applications are envisaged to the high temperature creeping behavior of metal/metal, metal/ceramic composites, and also of porous materials. Both isotropic and anisotropic configurations are considered including the technologically important case of fiber-reinforced composites, and the fundamentally important case of polycrystalline aggregates. The approach is based on new variational principles developed recently by the author (under AFOSR sponsorship), which allow the estimation of the overall behavior of a given nonlinear composite in terms of the effective properties of a suitably optimized linear comparison composite (with the same microstructure). The key advantage of the method is that it allows direct application of the extensive literature on linear composite materials, in the form of estimates and rigorous bounds, to obtain corresponding results for nonlinear composites. Additionally, the procedure is remarkably simple to implement, and the final results are usually expressed in terms of finite-optimization problems, which can be readily solved with modest computational effort. Recent progress include the application of the method to the determination of extremal yield surfaces for anisotropic rigid/plastic systems, and to the computation of estimates for the effective yield stress of polycrystalline aggregates.