Construction of first and second order grade anisotropic continuum media for 3D porous and textile composite structures

This paper aims at developing homogeneous, anisotropic strain-gradient continuum models as substitutes of 3D heterogeneous porous or composite materials and structures. We construct effective first and second order grade continuum models equivalent to such inhomogeneous structures. This in turn lead...

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Bibliographic Details
Published in:Composite structures 2016-05, Vol.141, p.292-327
Main Authors: Goda, Ibrahim, Ganghoffer, Jean-François
Format: Article
Language:English
Subjects:
Anisotropic strain-gradient continua
Anisotropy
Boundary conditions
Composite materials
Composites with inclusions
Construction
Continuums
Effective mechanical properties
Engineering Sciences
Equivalence
Random porous materials
Second order homogenization schemes
Strain energy methods
Three dimensional
Woven composites
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Summary:This paper aims at developing homogeneous, anisotropic strain-gradient continuum models as substitutes of 3D heterogeneous porous or composite materials and structures. We construct effective first and second order grade continuum models equivalent to such inhomogeneous structures. This in turn leads to the construction of a strain-gradient continuum with effective mechanical properties at the first and second order, accounting for the impact of the underlying microstructure on the overall effective mechanical response of the effective continuum. The effective properties are obtained based on the response of the representative volume element or unit cell of the initial structure under prescribed boundary conditions. Mixed boundary conditions comprising both traction and displacement boundary conditions are applied on the structure boundaries to identify the equivalent 3D strain gradient elasticity. The first and second order mechanical constants of the effective strain-gradient continuum are deduced by an equivalent strain energy method. We perform this study computationally using a finite element approach. The present methodology is exemplified in certain applications, considering sequentially three-dimensional random porous polymer scaffolds, composite reinforced by inclusions, and woven composites, including layered composites and 3D through-thickness orthogonal interlocks.
ISSN:0263-8223
1879-1085
DOI:10.1016/j.compstruct.2016.01.061