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Talk

Quantitative homogenization of non-linear elastic periodic composites for small loads

  • Mathias Schäffner (TU Dresden)
A3 01 (Sophus-Lie room)

Abstract

In this talk, I consider periodic homogenization of non-convex integral functionals that are motivated by non-linear elasticity. In this situation long wavelength buckling can occur which mathematically implies that the homogenized integrand is given by an asymptotic multi-cell formula. From this formula it is difficult to deduce qualitative or quantitative properties of the effective energy. Under suitable assumptions, in particular that the integrand has a single, non-degenerate, energy well at the set of rotations, we show that the multi-cell formula reduces to a much simpler single-cell formula in a neighbourhood of the rotations. This allows for a more refined, corrector based, analysis. In particular, for small data, we obtain a quantitative two-scale expansion and uniform Lipschitz estimates for energy minimizer. This is joint work with Stefan Neukamm (Dresden).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher
  • May 21, 2024 tba with Immanuel Zachhuber