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Journal Articles Archive for Rational Mechanics and Analysis Year : 2019

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

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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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Dates and versions

hal-01876877 , version 1 (19-09-2018)

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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, 2019, 231, pp.845-886. ⟨10.1007/s00205-018-1290-9⟩. ⟨hal-01876877⟩
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