Homogenization of thin models in elasticity: periodic and non-periodic

par Igor Velcic (University of Zagreb, Croatia)

mardi 22 mars 2016, 15:15 → 16:15 Europe/Paris

4e étage, salle 435 (UMPA, ENS Lyon - Site Monod)

We will give an overview on the thin models in elasticity derived by means of $Gamma$-convergence using simultaneous homogenization and dimensional reduction. In the case of periodic homogenization we obtain different models depending on the quotient of the periodicity of the changes in the material and the thickness of the body. Some peculiarities arise in the case of bending plate and von Karman shell as a consequence of geometric constraint (penalization) in the limiting procedure. In some simpler cases (von Karman plate, bending rod) we are able to characterize the limiting models without periodicity assumption. We are also able to analyze the equations (stationary points) in the case of von Karman rod and plate, but only under non-physical assumption on the linear growth of the differential of the stored energy density function. In the talk we will give special emphasis on the derivation of the bending rod model by simultaneous homogenization and dimensional reduction without periodicity assumption, using $Gamma$-convergence.