Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||35|
|Published online||01 March 2021|
A hierarchy of multilayered plate models
* Corresponding author: firstname.lastname@example.org
Accepted: 6 October 2020
We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of Γ-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary significantly in the small film direction and which also may have a (small) pre-stress. By computing the Γ-limits in the energy regimes in which the scaling of the pre-stress is non-trivial, we arrive at linearised Kirchhoff, von Kármán, and fully linear plate theories, respectively, which contain an additional spontaneous curvature tensor. The effective (homogenised) elastic constants of the plates will turn out to be given in terms of the moments of the pointwise elastic constants of the materials.
Mathematics Subject Classification: 74K20 / 49J45 / 74G65
Key words: Multilayers / dimension reduction / effective plate theories / Gamma-convergence
© EDP Sciences, SMAI 2021
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