Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions - Archive ouverte HAL Access content directly
Journal Articles Journal of the Mechanics and Physics of Solids Year : 2007

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

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François Willot
Yves-Patrick Pellegrini
Pedro Ponte Castañeda
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#### Abstract

Exact 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.

### Dates and versions

cea-00412543 , version 1 (02-09-2009)

### Identifiers

• HAL Id : cea-00412543 , version 1
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### Cite

François Willot, Yves-Patrick Pellegrini, Pedro Ponte Castañeda. Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions. Journal of the Mechanics and Physics of Solids, 2007, 56, pp.1245-1268. ⟨10.1016/j.jmps.2007.10.002⟩. ⟨cea-00412543⟩

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