Third-order bound of nonlinear composites and porous media under hydrostatic deformation

•3rd-Order bound derived for nonlinear composites under hydrostatic deformation.•Hashin’s sphere assemblage not an optimal microstate in nonlinear cases.•Distinctive behaviors of a dry porous medium from a saturated one. In this study the third-order variational bound is explicitly derived for nonli...

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Bibliographic Details
Published inMechanics of materials Vol. 68; pp. 137 - 146
Main Authors Xu, X. Frank, Jie, Yuxin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2014
Subjects
Composites
Nonlinear homogenization
Porous media
Variational bounds
Porous media
Composites
Variational bounds
Nonlinear homogenization
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ISSN0167-6636
1872-7743
DOI10.1016/j.mechmat.2013.08.006

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Summary:•3rd-Order bound derived for nonlinear composites under hydrostatic deformation.•Hashin’s sphere assemblage not an optimal microstate in nonlinear cases.•Distinctive behaviors of a dry porous medium from a saturated one. In this study the third-order variational bound is explicitly derived for nonlinear composites subject to hydrostatic deformation. By formulating the stochastic extreme principle for nonlinear boundary value problems, the third-order upper bound of the potential is derived for nonlinear two-phase composites, which is further explicitly specialized to porous media. Examples of application are provided by applying the derived bound to various cases of composites and porous media characterized with power law nonlinearity.
ISSN:0167-6636
1872-7743
DOI:10.1016/j.mechmat.2013.08.006