Calculus of Variations and Geometric Measure Theory
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A. Gloria - M. Ruf

Loss of strong ellipticity through homogenization in 2D linear elasticity: A phase diagram

created by ruf on 16 May 2018

[BibTeX]

preprint

Inserted: 16 may 2018
Last Updated: 16 may 2018

Year: 2018

ArXiv: 1805.05150 PDF

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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