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Quantitative homogenization of nonlinearly elastic periodic composites

Date: Tuesday, March 27, 2018 16:00 - 18:00
Speaker: Stefan Neukamm (TU Dresden)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Formal Sciences Seminar
Host: Julian Fischer
Lab building west seminar room


One of the main problems in homogenization of nonlinearly elastic composites is that long wavelength buckling prevents the possibility of homogenization by averaging over a single period cell. A careful convexification argument (that invokes a perturbation of the stored energy function by a Null Lagrangian) combined with regularity theory for monotone systems shows that long wavelength buckling cannot occur for small loads. Based on this observation we obtain a quantitative two-scale expansion for energy minimizers and we can discuss the linearization of periodic composites at strained equilibrium states. The talk is based on a joint work with M. Schffner.
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