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**Harvard**

Trinh, D., Jänicke, R., Auffray, N., Diebels, S. och Forest, S. (2012) *Evaluation of generalized continuum substitution models for heterogeneous materials*.

** BibTeX **

@article{

Trinh2012,

author={Trinh, Duy Khanh and Jänicke, Ralf and Auffray, Nicolas and Diebels, Stefan and Forest, Samuel},

title={Evaluation of generalized continuum substitution models for heterogeneous materials},

journal={International Journal for Multiscale Computational Engineering},

issn={1543-1649},

volume={10},

issue={6},

pages={527-549},

abstract={Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.},

year={2012},

keywords={higher order homogenization, composite materials, Cosserat, second gradient, micromorphic theory, polynomial boundary conditions, representative volume element, finite element},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 253355

A1 Trinh, Duy Khanh

A1 Jänicke, Ralf

A1 Auffray, Nicolas

A1 Diebels, Stefan

A1 Forest, Samuel

T1 Evaluation of generalized continuum substitution models for heterogeneous materials

YR 2012

JF International Journal for Multiscale Computational Engineering

SN 1543-1649

VO 10

IS 6

SP 527

OP 549

AB Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.

LA eng

DO 10.1615/IntJMultCompEng.2012003105

LK https://doi.org/10.1615/IntJMultCompEng.2012003105

OL 30