Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions

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dc.creatorWillot, Francois
dc.creatorPellegrini, Yves-Patrick
dc.creatorCastaneda, Pedro Ponte
dc.date2007-10-12
dc.date.accessioned2026-07-07T09:32:49Z
dc.date.available2026-07-07T09:32:49Z
dc.descriptionExact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and their histograms are provided, with particular emphasis on the singularities of the latter. The behavior of the system near the void close packing fraction is also investigated. The results of this work shed light on corresponding results for strongly nonlinear porous media, which have been obtained recently by means of the ``second-order'' homogenization method, and where the dilute estimates also exhibit fractional powers of the porosity.
dc.description22 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/0710.2456
dc.identifierhttp://arxiv.org/abs/0710.2456
dc.identifierJ. Mech. Phys. Solids, Vol 56/4 pp 1245-1268 (2008)
dc.identifierdoi:10.1016/j.jmps.2007.10.002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158917
dc.subjectMaterials Science
dc.titleLocalization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions
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