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Loss of Strong Ellipticity Through Homogenization in 2D Linear Elasticity: A Phase Diagram

Abstract : Since the seminal contribution of Geymonat, Müller, and Triantafyllidis, it is known that strong ellipticity is not necessarily conserved through periodic homogenization in linear elasticity. This phenomenon is related to microscopic buckling of composite materials. Consider a mixture of two isotropic phases which leads to loss of strong ellipticity when arranged in a laminate manner, as considered by Gutiérrez and by Briane and Francfort. In this contribution we prove that the laminate structure is essentially the only microstructure which leads to such a loss of strong ellipticity. We perform a more general analysis in the stationary, ergodic setting.
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https://hal.inria.fr/hal-01876877
Contributor : Antoine Gloria <>
Submitted on : Wednesday, September 19, 2018 - 12:42:33 AM
Last modification on : Thursday, December 10, 2020 - 10:55:48 AM
Long-term archiving on: : Thursday, December 20, 2018 - 12:45:30 PM

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Antoine Gloria, Matthias Ruf. Loss of Strong Ellipticity Through Homogenization in 2D Linear Elasticity: A Phase Diagram. Archive for Rational Mechanics and Analysis, Springer Verlag, 2018, ⟨10.1007/s00205-018-1290-9⟩. ⟨hal-01876877⟩

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