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