13 juil
13/07/2018 13:00

Sciences & Société

Soutenance de thèse : Arthur Glacet

Study of quasi-periodic beam latttices: Vibration, Fracture, Homogeneization

Doctorant : Arthur Glacet

Laboratoire INSA : LaMCoS
Ecole doctorale : ED162 MEGA

Quasi periodic (QP) structure have shown peculiar properties in the atomic domain, especially in vibration. It could be interesting to be able to transpose those properties in macroscopic meta-materials. Quasi periodic 2D beam lattices are studied in this thesis due to the simplicity of the Euler Bernoulli finite element (FE) model usually used to model beam lattice. These beam lattices can easily be produced by additive manufacturing or by laser cutting. beam slenderness ,i.e the ratio of height over length, is a important parameter for mechanical response therefore it will be the main point of interest in this thesis. Using finite element method the influence of the beam slenderness over the vibration behavior of the QP beam lattices will be studied. The KPM numerical method is successfully adapted form molecular dynamic in order to study vibrational modes of FE beam lattice without having to fully diagonalize the dynamic matrix. The QP lattices show similar properties as their atomic counterpart e.g mode localization over sub-stuctures.
The  fracture  behavior  is  also  studied  as  the  special  symmetries  allowed  by  quasi periodicity could result in beam lattices without weak planes for crack propagation. It have been shown to be true from static FE simulation with a brittle strain energy breaking criterion. The vibration properties of quasi periodic structures could also have an impact on the dynamic crack propagation thus a dynamic crack propagation model is developed. Several simulation are run in order to study the impact of the slenderness over the energy dissipated by fracture of QP lattices.
A coarse graining method (CG) is developed to create a continuous cosserat medium at different scale from the FE beam model. This CG method allow to identify, density, strain, stress and elasticity modulus of an equivalent continuous cosserat.

Informations complémentaires

  • Amphithéâtre Emilie du Châtelet - Bibliothèque Marie Curie - INSA Lyon

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