Calculus of Variations and Geometric Measure Theory

G. Gargiulo - E. Zappale

The Energy Density of Non Simple Grade Two Materials Thin Films via a Young Measure Approach

created on 18 Feb 2009


Published Paper

Inserted: 18 feb 2009

Journal: Boll. UMI B
Volume: 10-B
Number: 8
Pages: 158-194
Year: 2007


Dimension reduction is used to derive the energy of non simple materials grade two thin films. Relaxation and $\Gamma$ convergence lead to a limit defined on a suitable space of bi-dimensional Young measures. The underlying Â’deformationÂ’ in the limit model takes into account the Cosserat theory.

Keywords: Dimensional Reduction, Young Measures, Second order problem, A-quasiconvexity, relaxation