Effective properties of composite materials with periodic microstructure: a computational approach

doi:10.1016/S0045-7825(98)00227-8

Computer Methods in Applied Mechanics and Engineering

Volume 172, Issues 1–4, 16 April 1999, Pages 109-143

https://doi.org/10.1016/S0045-7825(98)00227-8 Get rights and content

Abstract

This study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents. The theoretical background of the method is recalled first. Two different families of numerical methods are considered to solve the problem. The first is based on the Finite Element Method. The concept of ‘macroscopic degrees of freedom’ is presented. The implementation of periodicity conditions is discussed. A general framework permitting either a strain or stress control is proposed.

The second numerical method is based on Fast Fourier Transforms. It considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain. The solution of this problem is based on the explicit form of the periodic Green's function of the reference medium. The relative merits of the two methods are compared and several examples are discussed. Both methods give very comparable results on test examples and their domains of applications appear to be complementary.

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Effective properties of composite materials with periodic microstructure: a computational approach

Abstract

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Int. J. Engrg. Sci.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Int. J. Solids Struct.

J. Mech. Phys. Solids

Int. J. Solids Struct.

Comput. Methods Appl. Mech. Engrg.

Int. J. Solids Struct.

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Comput. Mater. Sci.

J. Mech. Phys. Solids

Acta Metall. Mater.

Acta Metall. Mater.

Acta Metall. Mater.

J. Mech. Phys. Solids

The structure of overall constitutive relations for a class of nonlinear composites

IMA J. Appl. Math.

The effective mechanical properties of nonlinear isotropic composites

J. Mech. Phys. Solids

Transverse normal loading of a unidirectional composite

J. Comput. Mat.

Void growth in an elastic plastic medium

J. Appl. Mech.

Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape

Acta Metall. Mater.

A FFT-based numerical method for computing the mechanical properties of composites from images of their microstructure

A numerical method for computing the overall response of nonlinear composites with complex microstructure

Comput. Methods Appl. Mech. Engrg.