# The Theory of Composites

@inproceedings{Milton2002TheTO, title={The Theory of Composites}, author={Graeme W. Milton}, year={2002} }

Einstein, have contributed to the theory of composite materials. Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than 100 years, an explosion of ideas in the last four decades (and particularly in the last two decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the…

## 1,917 Citations

On the effective behavior, microstructure evolution, and macroscopic stability of elastomeric composites

- Materials Science
- 2006

Elastomeric composites are currently used in numerous commercial applications and have shown great promise for utilization in new technologies. This raises the practical—as well as theoretical—need…

Theory of Elasticity at the Nanoscale

- Materials Science
- 2009

Abstract We have shown in a series of recent papers that the classical theory of elasticity can be extended to the nanoscale by supplementing the equations of elasticity for the bulk material with…

Variational linear comparison bounds for nonlinear composites with anisotropic phases. I. General results

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2006

This work is concerned with the development of bounds for nonlinear composites with anisotropic phases by means of an appropriate generalization of the ‘linear comparison’ variational method,…

Problems In Nonlinear Homogenization: Bounds, Estimates, Macroscopic Instabilities, And Post-Bifurcation Response

- Mathematics
- 2019

PROBLEMS IN NONLINEAR HOMOGENIZATION: BOUNDS, ESTIMATES, MACROSCOPIC INSTABILITIES, AND POST-BIFURCATION RESPONSE Joshua Robert Furer Pedro Ponte Castañeda Due to the ever-growing interest in…

Micromechanics-Based Homogenization of the Effective Physical Properties of Composites With an Anisotropic Matrix and Interfacial Imperfections

- Materials ScienceFront. Mater.
- 2019

Micromechanics-based homogenization has been employed extensively to predict the effective properties of technologically important composites. In this review article, we address its application to…

Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach

- Materials ScienceMathematics and Mechanics of Solids
- 2019

The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. During…

Geometric Variational Principles for Computational Homogenization

- MathematicsJournal of Elasticity
- 2018

The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the…

Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory

- Mathematics
- 2002

Abstract This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the…

Asymptotic Analysis of Thin Interface in Composite Materials with Coated Boundary

- Materials Science
- 2011

It should be noted, that interaction between the neighbouring fibres can cause a significant variation of physical fields in the composite on the microlevel. Increase in the rigidity of fibers and…

Asymptotic Homogenization of Composite Materials and Structures

- Materials Science
- 2009

The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their…

## References

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Publisher Summary This chapter focuses on variational and related methods for the overall properties of composites. A wide range of phenomena that are observable macroscopically are governed by…

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A new method is presented for evaluating the performance of 1–3 polymer/piezoelectric ceramic composites for hydrophone applications. The Poisson’s ratio effect, i.e., the enhancement of the…