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Nonlinear Composite Materials: Effective Constitutive Behavior and Microstructure Evolution

  • P. Ponte Castañeda
Part of the International Centre for Mechanical Sciences book series (CISM, volume 377)

Abstract

This article is a review of some recent developments in the field of nonlinear composite materials. More precisely, it is an attempt to summarize and relate certain methods that have been developed over the past 10 years for estimating the effective, homogenized or overall constitutive behavior of composite materials with nonlinear constituents. In addition to their ability to handle constitutive nonlinearity, these homogenization methods have also been extended in a consistent fashion to account for geometric nonlinearity. In other words, they are able to incorporate the effect of changes in the microstructure, due to the presence of finite deformations, on the effective constitutive behavior of the composites. These homogenization procedures — like some of the earlier, now classical procedures — make use of a “linear comparison composite,” for which the effective behavior can be assumed to be readily available from the extensive literature in the field of linear composite materials. In particular, the use of a linear comparison composite provides a way of bringing in higher- order statistics (beyond volume fractions) into the description of the effective behavior of composites with random microstructures, whether they be “particulate” or “granular” in character. However, the choice of the linear comparison composite in these modern homogenization procedures is dictated by appropriate approximations in the context of rigorous variational principles for the effective energy of the composite. This simple fact goes a long way toward explaining the significant improvements achieved by the new methods over the more classical procedures, where the choice of the comparison composite was not derived from a variational principle.

Keywords

Variational Principle Microstructure Evolution Secant Modulus Ellipsoidal Inclusion Effective Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • P. Ponte Castañeda
    • 1
  1. 1.University of PennsylvaniaPhiladelphiaUSA

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