|A mathematical justification of the Reissner-Mindlin plate model |
Conference: Second European-Latin-American Conference of Theoretical and Applied Mechanics (La Havane, CU, 2019-02-11)
Ref HAL: hal-02070735_v1
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Due to its ability to account for shear effects, the Reissner–Mindlin plate model is often preferred in the engineering literature over the Kirchhoff–Love plate model. So, as already done for the Kirchhoff–Love plate model, it is challenging to proceed with a rigorous mathematical derivation of the Reissner–Mindlin plate model by studying the asymptotic behavior of a thin 3-dimensional elastic body when its thickness goes to zero. This was done in a simplified framework by using a second gradient or Cosserat continuum for the body, jointly with constitutive symmetry assumptions ; here – being aware of results on the bonding of thin plates – we prefer to consider a strongly heterogeneous classical linearly elastic body made of a periodic distribution of thin anisotropic plates abutted together. The mathematical study via variational convergence shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.