# Dimensional reduction for heterogeneous, slit or cracked bodies

Abstract : This thesis is concerned with the justification of membrane models as zero-thickness limits of three dimensional nonlinear "elastic behavior" (the quotes refer to the absence of the usual requirement that the energy should blow up as the Jacobian of the transformation tends to zero). The dimensional reduction is viewed as a $\Gamma$-convergence problem for the elastic energy. We first consider macroscopic heterogeneities, also taking into account the case where the external loads induce a density of bending moment that produces a Cosserat vector. Then, we study periodic microscopic heterogeneities, which introduces two competing features : dimensional reduction and reiterated homogenization. Thin films with complex degenerate microstructure due to the presence of voids on the mid-surface are investigated when the thickness is much smaller than the period of distribution of the perforations. Finally, brittle thin films and their quasistatic crack evolution are presented for a Griffith type surface energy density.
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https://tel.archives-ouvertes.fr/tel-00010233
Submitted on : Wednesday, March 6, 2013 - 9:56:36 AM
Last modification on : Saturday, February 15, 2020 - 2:04:01 AM
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### Identifiers

• HAL Id : tel-00010233, version 2

### Citation

Jean-François Babadjian. Dimensional reduction for heterogeneous, slit or cracked bodies. Mathematics [math]. Université Paris-Nord - Paris XIII, 2005. English. ⟨tel-00010233v2⟩

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